Energy Technology Data Exchange (ETDEWEB)
Brics, Martins; Kapoor, Varun; Bauer, Dieter [Institut fuer Physik, Universitaet Rostock, 18051 Rostock (Germany)
2013-07-01
Time-dependent density functional theory (TDDFT) with known and practicable exchange-correlation potentials does not capture highly correlated electron dynamics such as single-photon double ionization, autoionization, or nonsequential ionization. Time-dependent reduced density matrix functional theory (TDRDMFT) may remedy these problems. The key ingredients in TDRDMFT are the natural orbitals (NOs), i.e., the eigenfunctions of the one-body reduced density matrix (1-RDM), and the occupation numbers (OCs), i.e., the respective eigenvalues. The two-body reduced density matrix (2-RDM) is then expanded in NOs, and equations of motion for the NOs can be derived. If the expansion coefficients of the 2-RDM were known exactly, the problem at hand would be solved. In practice, approximations have to be made. We study the prospects of TDRDMFT following a top-down approach. We solve the exact two-electron time-dependent Schroedinger equation for a model Helium atom in intense laser fields in order to study highly correlated phenomena such as the population of autoionizing states or single-photon double ionization. From the exact wave function we calculate the exact NOs, OCs, the exact expansion coefficients of the 2-RDM, and the exact potentials in the equations of motion. In that way we can identify how many NOs and which level of approximations are necessary to capture such phenomena.
Mazziotti, David A
2016-10-07
A central challenge of physics is the computation of strongly correlated quantum systems. The past ten years have witnessed the development and application of the variational calculation of the two-electron reduced density matrix (2-RDM) without the wave function. In this Letter we present an orders-of-magnitude improvement in the accuracy of 2-RDM calculations without an increase in their computational cost. The advance is based on a low-rank, dual formulation of an important constraint on the 2-RDM, the T2 condition. Calculations are presented for metallic chains and a cadmium-selenide dimer. The low-scaling T2 condition will have significant applications in atomic and molecular, condensed-matter, and nuclear physics.
Mazziotti, David A.
2016-10-01
A central challenge of physics is the computation of strongly correlated quantum systems. The past ten years have witnessed the development and application of the variational calculation of the two-electron reduced density matrix (2-RDM) without the wave function. In this Letter we present an orders-of-magnitude improvement in the accuracy of 2-RDM calculations without an increase in their computational cost. The advance is based on a low-rank, dual formulation of an important constraint on the 2-RDM, the T 2 condition. Calculations are presented for metallic chains and a cadmium-selenide dimer. The low-scaling T 2 condition will have significant applications in atomic and molecular, condensed-matter, and nuclear physics.
Schwerdtfeger, Christine A; Mazziotti, David A
2011-11-03
Parametrization of the 2-electron reduced density matrix (2-RDM) rather than the many-electron wave function yields a new family of electronic-structure methods that are faster and more accurate than traditional coupled electron-pair methods including coupled cluster with single and double excitations. Deriving the parametrization from N-representability conditions generates a 2-RDM that captures significant correlation from triple and higher-order excitations at the cost of double excitations. We apply the parametric 2-RDM method to confirm recent experiments determining the relative thermodynamic populations of the cis-cis and cis-trans isomers of carbonic acid. In 2010 Bernard et al. showed by infrared spectroscopy that the populations of cis-cis and cis-trans isomers have a 10:1 ratio at 210 K. By use of the parametric 2-RDM method, we predict a 8:1 ratio at 210 K. Comparable ab initio methods overestimate the stability of the cis-cis isomer with 24:1 and 21:1 ratios. These 2-RDM-based methods promise to have significant applications throughout chemistry.
Energy Technology Data Exchange (ETDEWEB)
Sand, Andrew M.; Mazziotti, David A., E-mail: damazz@uchicago.edu [Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 (United States)
2015-10-07
Determination of the two-electron reduced density matrix (2-RDM) from the solution of the anti-Hermitian contracted Schrödinger equation (ACSE) yields accurate energies and properties for both ground and excited states. Here, we develop a more efficient method to solving the ACSE that uses second-order information to select a more optimal step towards the solution. Calculations on the ground and excited states of water, hydrogen fluoride, and conjugated π systems show that the improved ACSE algorithm is 10-20 times faster than the previous ACSE algorithm. The ACSE can treat both single- and multi-reference electron correlation with the initial 2-RDM from a complete-active-space self-consistent-field (CASSCF) calculation. Using the improved algorithm, we explore the relationship between truncation of the active space in the CASSCF calculation and the accuracy of the energy and 2-RDM from the ACSE calculation. The accuracy of the ACSE, we find, is less sensitive to the size of the active space than the accuracy of other wavefunction methods, which is useful when large active space calculations are computationally infeasible.
Sand, Andrew M; Mazziotti, David A
2015-10-01
Determination of the two-electron reduced density matrix (2-RDM) from the solution of the anti-Hermitian contracted Schrödinger equation (ACSE) yields accurate energies and properties for both ground and excited states. Here, we develop a more efficient method to solving the ACSE that uses second-order information to select a more optimal step towards the solution. Calculations on the ground and excited states of water, hydrogen fluoride, and conjugated π systems show that the improved ACSE algorithm is 10-20 times faster than the previous ACSE algorithm. The ACSE can treat both single- and multi-reference electron correlation with the initial 2-RDM from a complete-active-space self-consistent-field (CASSCF) calculation. Using the improved algorithm, we explore the relationship between truncation of the active space in the CASSCF calculation and the accuracy of the energy and 2-RDM from the ACSE calculation. The accuracy of the ACSE, we find, is less sensitive to the size of the active space than the accuracy of other wavefunction methods, which is useful when large active space calculations are computationally infeasible.
Pair 2-electron reduced density matrix theory using localized orbitals
Head-Marsden, Kade; Mazziotti, David A.
2017-08-01
Full configuration interaction (FCI) restricted to a pairing space yields size-extensive correlation energies but its cost scales exponentially with molecular size. Restricting the variational two-electron reduced-density-matrix (2-RDM) method to represent the same pairing space yields an accurate lower bound to the pair FCI energy at a mean-field-like computational scaling of O (r3) where r is the number of orbitals. In this paper, we show that localized molecular orbitals can be employed to generate an efficient, approximately size-extensive pair 2-RDM method. The use of localized orbitals eliminates the substantial cost of optimizing iteratively the orbitals defining the pairing space without compromising accuracy. In contrast to the localized orbitals, the use of canonical Hartree-Fock molecular orbitals is shown to be both inaccurate and non-size-extensive. The pair 2-RDM has the flexibility to describe the spectra of one-electron RDM occupation numbers from all quantum states that are invariant to time-reversal symmetry. Applications are made to hydrogen chains and their dissociation, n-acene from naphthalene through octacene, and cadmium telluride 2-, 3-, and 4-unit polymers. For the hydrogen chains, the pair 2-RDM method recovers the majority of the energy obtained from similar calculations that iteratively optimize the orbitals. The localized-orbital pair 2-RDM method with its mean-field-like computational scaling and its ability to describe multi-reference correlation has important applications to a range of strongly correlated phenomena in chemistry and physics.
Application of variational reduced-density-matrix theory to organic molecules.
Gidofalvi, Gergely; Mazziotti, David A
2005-03-01
Variational calculation of the two-electron reduced-density matrix (2-RDM), using a new first-order algorithm [D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)], is applied to medium-sized organic molecules. The calculations reveal systematic trends in the accuracy of the energy with well-known chemical concepts such as hybridization, electronegativity, and atomic size. Furthermore, correlation energies from hydrocarbon chains indicate that the calculation of the 2-RDM subject to two-positivity conditions is size extensive, that is, the energy grows linearly with the number of electrons. Because organic molecules have a well-defined set of functional groups, we employ the trends in energy accuracy of the functional groups to design a correction to the 2-RDM energy for an arbitrary organic molecule. We apply the 2-RDM calculations with the functional-group correction to a large set of organic molecules with different functional groups. Energies with millihartree accuracy are obtained both at equilibrium and nonequilibrium geometries.
Gidofalvi, Gergely; Mazziotti, David A
2005-05-15
The acceleration of the variational two-electron reduced-density-matrix (2-RDM) method, using a new first-order algorithm [D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)], has shown its usefulness in the accurate description of potential energy surfaces in nontrivial basis sets. Here we apply the first-order 2-RDM method to the potential energy surfaces of the nitrogen and carbon dimers in polarized valence double-zeta basis sets for which benchmark full-configuration-interaction calculations exist. In a wave function formalism accurately stretching the triple bond of the nitrogen dimer requires at least six-particle excitations from the Hartree-Fock reference. Furthermore, cleaving the double bond of C2 should produce a "non-Morse"-like potential curve because the ground state near equilibrium (X 1sigma(g)+) has an avoided crossing with the second excited state (B' 1sigma(g)+) and a level crossing with the first excited state (B 1delta(g)). Because the 2-RDM method variationally optimizes the energy over correlated 2-RDMs on the two-electron space without parametrization of the many-electron wave function, it captures multireference correlations that are difficult to describe with approximate wave functions. The 2-RDM method yields for N2 a potential energy surface with features and spectroscopic constants that are more accurate than those from single-reference methods and similar in accuracy to multireference techniques, and it describes the non-Morse-like behavior of C2 which is not captured by single-reference methods.
Gidofalvi, Gergely; Mazziotti, David A
2006-04-27
The variational optimization of the energy with respect to the two-electron reduced-density matrix (2-RDM), constrained by N-representability conditions, can determine the shape of molecular potential energy surfaces with useful accuracy. In this paper, we apply the 2-RDM method with a first-order optimization algorithm [Mazziotti, D. A. Phys. Rev. Lett. 2004, 93, 213001] to investigating the potential energy surfaces of carbon monoxide in the presence and absence of an electric field. Two beneficial characteristics of the 2-RDM method for computing potential energy surfaces include the following: (i) its ability to capture multireference effects without specifying any reference wave function or density matrix and (ii) its guarantee of a global energy minimum in the variational optimization. The 2-RDM method produces electronic ground-state energies with similar accuracy at equilibrium and nonequilibrium geometries in both the presence and the absence of the electric field. Computed dipole moments are similar in accuracy to the values from the computationally expensive configuration interaction with single, double, triple, and quadruple excitations. These surfaces have important applications in quantum molecular control theory.
Accurate high-harmonic spectra from time-dependent two-particle reduced density matrix theory
Lackner, Fabian; Sato, Takeshi; Ishikawa, Kenichi L; Burgdörfer, Joachim
2016-01-01
The accurate description of the non-linear response of many-electron systems to strong-laser fields remains a major challenge. Methods that bypass the unfavorable exponential scaling with particle number are required to address larger systems. In this paper we present a fully three-dimensional implementation of the time-dependent two-particle reduced density matrix (TD-2RDM) method for many-electron atoms. We benchmark this approach by a comparison with multi-configurational time-dependent Hartree-Fock (MCTDHF) results for the harmonic spectra of beryllium and neon. We show that the TD-2RDM is very well-suited to describe the non-linear atomic response and to reveal the influence of electron-correlation effects.
Schwerdtfeger, Christine A; Mazziotti, David A
2009-06-14
Quantum phase transitions in N-particle systems can be identified and characterized by the movement of the two-particle reduced density matrix (2-RDM) along the boundary of its N-representable convex set as a function of the Hamiltonian parameter controlling the phase transition [G. Gidofalvi and D. A. Mazziotti, Phys. Rev. A 74, 012501 (2006)]. For the one-dimensional transverse Ising model quantum phase transitions as well as their finite-lattice analogs are computed and characterized by the 2-RDM movement with respect to the transverse magnetic field strength g. The definition of a 2-RDM "speed" quantifies the movement of the 2-RDM per unit of g, which reaches its maximum at the critical point of the phase transition. For the infinite lattice the convex set of 2-RDMs and the 2-RDM speed are computed from the exact solution of the 2-RDM in the thermodynamic limit of infinite N [P. Pfeuty, Ann. Phys. 57, 79 (1970)]. For the finite lattices we compute the 2-RDM convex set and its speed by the variational 2-RDM method [D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)] in which approximate ground-state 2-RDMs are calculated without N-particle wave functions by using constraints, known as N-representability conditions, to restrict the 2-RDMs to represent quantum system of N fermions. Advantages of the method include: (i) rigorous lower bounds on the ground-state energies, (ii) polynomial scaling of the calculation with N, and (iii) independence of the N-representability conditions from a reference wave function, which enables the modeling of multiple quantum phases. Comparing the 2-RDM convex sets for the finite- and infinite-site lattices reveals that the variational 2-RDM method accurately captures the shape of the convex set and the signature of the phase transition in the 2-RDM movement. From the 2-RDM all one- and two-particle expectation values (or order parameters) of the quantum Ising model can also be computed including the pair correlation function, which
Shenvi, Neil; van Aggelen, Helen; Yang, Yang; Yang, Weitao; Schwerdtfeger, Christine; Mazziotti, David
2013-08-07
Tensor hypercontraction is a method that allows the representation of a high-rank tensor as a product of lower-rank tensors. In this paper, we show how tensor hypercontraction can be applied to both the electron repulsion integral tensor and the two-particle excitation amplitudes used in the parametric 2-electron reduced density matrix (p2RDM) algorithm. Because only O(r) auxiliary functions are needed in both of these approximations, our overall algorithm can be shown to scale as O(r(4)), where r is the number of single-particle basis functions. We apply our algorithm to several small molecules, hydrogen chains, and alkanes to demonstrate its low formal scaling and practical utility. Provided we use enough auxiliary functions, we obtain accuracy similar to that of the standard p2RDM algorithm, somewhere between that of CCSD and CCSD(T).
Conditions for describing triplet states in reduced density matrix functional theory
Theophilou, Iris; Helbig, Nicole
2016-01-01
We consider necessary conditions for the one body-reduced density matrix (1RDM) to correspond to a triplet wave-function of a two electron system. The conditions concern the occupation numbers and are different for the high spin projections, $S_z=\\pm 1$, and the $S_z=0$ projection. We employ these conditions in reduced density matrix functional theory calculations for the triplet excitations of two electron systems. In addition, we propose that these conditions can be used in the calculation of triplet states of systems with more than two electrons by restricting the active space and assess this procedure in calculations for a few atomic and molecular systems. We show that the quality of the optimal 1RDMs improves by applying the conditions in all the cases we studied.
Reduced density-matrix functionals from many-particle theory
Schade, Robert; Kamil, Ebad; Blöchl, Peter
2017-07-01
In materials with strong electron correlation the proper treatment of local atomic physics described by orbital occupations is crucial. Reduced density-matrix functional theory is a natural extension of density functional theory for systems that are dominated by orbital physics. We review the current state of reduced density-matrix functional theory (RDMFT). For atomic structure relaxations or ab-initio molecular dynamics the combination of density functional theory (DFT) and dynamical mean-field theory (DMFT) possesses a number of disadvantages, like the cumbersome evaluation of forces. We therefore describe a method, DFT+RDMFT, that combines many-particle effects based on reduced density-matrix functional theory with a density functional-like framework. A recent development is the construction of density-matrix functionals directly from many-particle theory such as methods from quantum chemistry or many-particle Green's functions. We present the underlying exact theorems and describe current progress towards quantitative functionals.
Possibility of Quantum Teleportation and the Reduced Density Matrix
Institute of Scientific and Technical Information of China (English)
朱红波; 曾谨言
2001-01-01
It is shown that only the maximally entangled two-particle (spin 1/2) states whose one-particle reduced density matrix is p (i) = (1/2)I2 can realize the teleportation of an arbitrary one-particle spin state. Based on this,to teleport an arbitrary k-particle spin state, one must prepare an N-particle entangled state whose k-particle (k ＜ N) reduced density matrix has the structure 2-kI2k (I2k being the 2k × 2k identity matrix). The N-particle Greenberger-Horne-Zeilinger states cannot realize the teleportation of an arbitrary k-particle (N＞k≥2) state,except for special states with only two components.
Gidofalvi, Gergely; Mazziotti, David A
2007-01-14
Molecular ground-state energies and two-electron reduced density matrices (2-RDMs) have recently been computed without the many-electron wave function by constraining the 2-RDM to satisfy a complete set of three-positivity conditions for N representability [D. A. Mazziotti, Phys. Rev. A 74, 032501 (2006)]. Energies at both equilibrium and nonequilibrium geometries are obtained within 0.3% of the correlation energy. In this paper the authors extend this work to examine the accuracy of molecular properties, including multipole moments and components of the ground-state energy, relative to full configuration interaction (FCI). Comparisons are also made with 2-RDM methods with two-positivity conditions and two-positivity plus the generalized T1T2 conditions as well as several approximate wave function methods. Using the 2-RDM method with three-positivity conditions, the authors obtain dipole, quadrupole, and octupole moments for BeH2, BH, H2O, CO, and NH3 at equilibrium geometries that are within 0.04% of their FCI values. In addition, for the potential energy surface of N2, the 2-RDM method with three-positivity yields not only accurate total ground-state energies but also accurate expectation values of the kinetic energy operator, the electron-nuclei potential, and electron-electron repulsion.
Reduced density matrix and order parameters of a topological insulator
Yu, Wing Chi; Li, Yan Chao; Sacramento, P. D.; Lin, Hai-Qing
2016-12-01
It has been recently proposed that the reduced density matrix may be used to derive the order parameter of a condensed matter system. Here we propose order parameters for the phases of a topological insulator, specifically a spinless Su-Schrieffer-Heeger (SSH) model, and consider the effect of short-range interactions. All the derived order parameters and their possible corresponding quantum phases are verified by the entanglement entropy and electronic configuration analysis results. The order parameter appropriate to the topological regions is further proved by calculating the Berry phase under twisted boundary conditions. It is found that the topological nontrivial phase is robust to the introduction of repulsive intersite interactions and can appear in the topological trivial parameter region when appropriate interactions are added.
Transition matrices and orbitals from reduced density matrix theory
Energy Technology Data Exchange (ETDEWEB)
Etienne, Thibaud [Université de Lorraine – Nancy, Théorie-Modélisation-Simulation, SRSMC, Boulevard des Aiguillettes 54506, Vandoeuvre-lès-Nancy (France); CNRS, Théorie-Modélisation-Simulation, SRSMC, Boulevard des Aiguillettes 54506, Vandoeuvre-lès-Nancy (France); Unité de Chimie Physique Théorique et Structurale, Université de Namur, Rue de Bruxelles 61, 5000 Namur (Belgium)
2015-06-28
In this contribution, we report two different methodologies for characterizing the electronic structure reorganization occurring when a chromophore undergoes an electronic transition. For the first method, we start by setting the theoretical background necessary to the reinterpretation through simple tensor analysis of (i) the transition density matrix and (ii) the natural transition orbitals in the scope of reduced density matrix theory. This novel interpretation is made more clear thanks to a short compendium of the one-particle reduced density matrix theory in a Fock space. The formalism is further applied to two different classes of excited states calculation methods, both requiring a single-determinant reference, that express an excited state as a hole-particle mono-excited configurations expansion, to which particle-hole correlation is coupled (time-dependent Hartree-Fock/time-dependent density functional theory) or not (configuration interaction single/Tamm-Dancoff approximation). For the second methodology presented in this paper, we introduce a novel and complementary concept related to electronic transitions with the canonical transition density matrix and the canonical transition orbitals. Their expression actually reflects the electronic cloud polarisation in the orbital space with a decomposition based on the actual contribution of one-particle excitations from occupied canonical orbitals to virtual ones. This approach validates our novel interpretation of the transition density matrix elements in terms of the Euclidean norm of elementary transition vectors in a linear tensor space. A proper use of these new concepts leads to the conclusion that despite the different principles underlying their construction, they provide two equivalent excited states topological analyses. This connexion is evidenced through simple illustrations of (in)organic dyes electronic transitions analysis.
Transition matrices and orbitals from reduced density matrix theory
Etienne, Thibaud
2015-06-01
In this contribution, we report two different methodologies for characterizing the electronic structure reorganization occurring when a chromophore undergoes an electronic transition. For the first method, we start by setting the theoretical background necessary to the reinterpretation through simple tensor analysis of (i) the transition density matrix and (ii) the natural transition orbitals in the scope of reduced density matrix theory. This novel interpretation is made more clear thanks to a short compendium of the one-particle reduced density matrix theory in a Fock space. The formalism is further applied to two different classes of excited states calculation methods, both requiring a single-determinant reference, that express an excited state as a hole-particle mono-excited configurations expansion, to which particle-hole correlation is coupled (time-dependent Hartree-Fock/time-dependent density functional theory) or not (configuration interaction single/Tamm-Dancoff approximation). For the second methodology presented in this paper, we introduce a novel and complementary concept related to electronic transitions with the canonical transition density matrix and the canonical transition orbitals. Their expression actually reflects the electronic cloud polarisation in the orbital space with a decomposition based on the actual contribution of one-particle excitations from occupied canonical orbitals to virtual ones. This approach validates our novel interpretation of the transition density matrix elements in terms of the Euclidean norm of elementary transition vectors in a linear tensor space. A proper use of these new concepts leads to the conclusion that despite the different principles underlying their construction, they provide two equivalent excited states topological analyses. This connexion is evidenced through simple illustrations of (in)organic dyes electronic transitions analysis.
Transition matrices and orbitals from reduced density matrix theory.
Etienne, Thibaud
2015-06-28
In this contribution, we report two different methodologies for characterizing the electronic structure reorganization occurring when a chromophore undergoes an electronic transition. For the first method, we start by setting the theoretical background necessary to the reinterpretation through simple tensor analysis of (i) the transition density matrix and (ii) the natural transition orbitals in the scope of reduced density matrix theory. This novel interpretation is made more clear thanks to a short compendium of the one-particle reduced density matrix theory in a Fock space. The formalism is further applied to two different classes of excited states calculation methods, both requiring a single-determinant reference, that express an excited state as a hole-particle mono-excited configurations expansion, to which particle-hole correlation is coupled (time-dependent Hartree-Fock/time-dependent density functional theory) or not (configuration interaction single/Tamm-Dancoff approximation). For the second methodology presented in this paper, we introduce a novel and complementary concept related to electronic transitions with the canonical transition density matrix and the canonical transition orbitals. Their expression actually reflects the electronic cloud polarisation in the orbital space with a decomposition based on the actual contribution of one-particle excitations from occupied canonical orbitals to virtual ones. This approach validates our novel interpretation of the transition density matrix elements in terms of the Euclidean norm of elementary transition vectors in a linear tensor space. A proper use of these new concepts leads to the conclusion that despite the different principles underlying their construction, they provide two equivalent excited states topological analyses. This connexion is evidenced through simple illustrations of (in)organic dyes electronic transitions analysis.
Reduced density matrix functional theory at finite temperature
Energy Technology Data Exchange (ETDEWEB)
Baldsiefen, Tim
2012-10-15
Density functional theory (DFT) is highly successful in many fields of research. There are, however, areas in which its performance is rather limited. An important example is the description of thermodynamical variables of a quantum system in thermodynamical equilibrium. Although the finite-temperature version of DFT (FT-DFT) rests on a firm theoretical basis and is only one year younger than its brother, groundstate DFT, it has been successfully applied to only a few problems. Because FT-DFT, like DFT, is in principle exact, these shortcomings can be attributed to the difficulties of deriving valuable functionals for FT-DFT. In this thesis, we are going to present an alternative theoretical description of quantum systems in thermal equilibrium. It is based on the 1-reduced density matrix (1RDM) of the system, rather than on its density and will rather cumbersomly be called finite-temperature reduced density matrix functional theory (FT-RDMFT). Its zero-temperature counterpart (RDMFT) proved to be successful in several fields, formerly difficult to address via DFT. These fields include, for example, the calculation of dissociation energies or the calculation of the fundamental gap, also for Mott insulators. This success is mainly due to the fact that the 1RDM carries more directly accessible ''manybody'' information than the density alone, leading for example to an exact description of the kinetic energy functional. This sparks the hope that a description of thermodynamical systems employing the 1RDM via FT-RDMFT can yield an improvement over FT-DFT. Giving a short review of RDMFT and pointing out difficulties when describing spin-polarized systems initiates our work. We then lay the theoretical framework for FT-RDMFT by proving the required Hohenberg-Kohn-like theorems, investigating and determining the domain of FT-RDMFT functionals and by deriving several properties of the exact functional. Subsequently, we present a perturbative method to
Pernal, Katarzyna; Giesbertz, Klaas J H
2016-01-01
Recent advances in reduced density matrix functional theory (RDMFT) and linear response time-dependent reduced density matrix functional theory (TD-RDMFT) are reviewed. In particular, we present various approaches to develop approximate density matrix functionals which have been employed in RDMFT. We discuss the properties and performance of most available density matrix functionals. Progress in the development of functionals has been paralleled by formulation of novel RDMFT-based methods for predicting properties of molecular systems and solids. We give an overview of these methods. The time-dependent extension, TD-RDMFT, is a relatively new theory still awaiting practical and generally useful functionals which would work within the adiabatic approximation. In this chapter we concentrate on the formulation of TD-RDMFT response equations and various adiabatic approximations. None of the adiabatic approximations is fully satisfactory, so we also discuss a phase-dependent extension to TD-RDMFT employing the concept of phase-including-natural-spinorbitals (PINOs). We focus on applications of the linear response formulations to two-electron systems, for which the (almost) exact functional is known.
Reduced density matrix hybrid approach: application to electronic energy transfer.
Berkelbach, Timothy C; Markland, Thomas E; Reichman, David R
2012-02-28
Electronic energy transfer in the condensed phase, such as that occurring in photosynthetic complexes, frequently occurs in regimes where the energy scales of the system and environment are similar. This situation provides a challenge to theoretical investigation since most approaches are accurate only when a certain energetic parameter is small compared to others in the problem. Here we show that in these difficult regimes, the Ehrenfest approach provides a good starting point for a dynamical description of the energy transfer process due to its ability to accurately treat coupling to slow environmental modes. To further improve on the accuracy of the Ehrenfest approach, we use our reduced density matrix hybrid framework to treat the faster environmental modes quantum mechanically, at the level of a perturbative master equation. This combined approach is shown to provide an efficient and quantitative description of electronic energy transfer in a model dimer and the Fenna-Matthews-Olson complex and is used to investigate the effect of environmental preparation on the resulting dynamics.
Time-dependent renormalized Redfield theory II for off-diagonal transition in reduced density matrix
Kimura, Akihiro
2016-09-01
In our previous letter (Kimura, 2016), we constructed time-dependent renormalized Redfield theory (TRRT) only for diagonal transition in a reduced density matrix. In this letter, we formulate the general expression for off-diagonal transition in the reduced density matrix. We discuss the applicability of TRRT by numerically comparing the dependencies on the energy gap of the exciton relaxation rate by using the TRRT and the modified Redfield theory (MRT). In particular, we roughly show that TRRT improves MRT for the detailed balance about the excitation energy transfer reaction.
Performance of one-body reduced density-matrix functionals for the homogeneous electron gas
Lathiotakis, N. N.; Helbig, N.; Gross, E. K. U.
2007-05-01
The subject of this study is the exchange-correlation-energy functional of reduced density-matrix functional theory. Approximations of this functional are tested by applying them to the homogeneous electron gas. We find that two approximations recently proposed by Gritsenko , [J. Chem. Phys. 122, 204102 (2005)] yield considerably better correlation energies and momentum distributions than previously known functionals. We introduce modifications to these functionals, which, by construction, reproduce the exact correlation energy of the homogeneous electron gas.
2015-04-07
units (GPUs), which are automatically detected and utilized by our software (if the software is configured with a “ cuda ” option). Figure 5 provides...library (for the diagonalization) and the cublasDgemm call of the NVIDIA CUDA Basic Linear Algebra Subroutine (cuBLAS) library (for the transformation
Energy Technology Data Exchange (ETDEWEB)
Kapoor, Varun; Brics, Martins; Bauer, Dieter [Institut fuer Physik, Universitaet Rostock, 18051 Rostock (Germany)
2013-07-01
Autoionizing states are inaccessible to time-dependent density functional theory (TDDFT) using known, adiabatic Kohn-Sham (KS) potentials. We determine the exact KS potential for a numerically exactly solvable model Helium atom interacting with a laser field that is populating an autoionizing state. The exact single-particle density of the population in the autoionizing state corresponds to that of the energetically lowest quasi-stationary state in the exact KS potential. We describe how this exact potential controls the decay by a barrier whose height and width allows for the density to tunnel out and decay with the same rate as in the ab initio time-dependent Schroedinger calculation. However, devising a useful exchange-correlation potential that is capable of governing such a scenario in general and in more complex systems is hopeless. As an improvement over TDDFT, time-dependent reduced density matrix functional theory has been proposed. We are able to obtain for the above described autoionization process the exact time-dependent natural orbitals (i.e., the eigenfunctions of the exact, time-dependent one-body reduced density matrix) and study the potentials that appear in the equations of motion for the natural orbitals and the structure of the two-body density matrix expanded in them.
Turning reduced density matrix theory into a practical tool for studying the Mott transition
Pernal, Katarzyna
2015-11-01
Strongly correlated systems pose a challenge for theoretical methods based on an independent electron approximation. Such methods struggle to predict a nonzero gap in Mott insulators or to capture the correct physics of the insulator-to-metal phase transition in strongly correlated materials. In a recent paper by Shinohara et al (2015 New J. Phys. 17 093038) it is shown that strongly correlated materials and correct descriptions of their phase transitions are within the reach of reduced density matrix functional theory (RDMFT) approximations. For a doping-induced phase transition, not only is a satisfactory agreement with experimental spectra found for NiO but it is also shown that the physical picture of the observed Mott transition stays in line with more computationally demanding many-body theories. This is an important step toward providing an RDMFT-based computation tool for studying strongly correlated materials.
Reduced-density-matrix spectrum and block entropy of permutationally invariant many-body systems.
Salerno, Mario; Popkov, Vladislav
2010-07-01
Spectral properties of the reduced density matrix (RDM) of permutational invariant quantum many-body systems are investigated. The RDM block diagonalization which accounts for all symmetries of the Hamiltonian is achieved. The analytical expression of the RDM spectrum is provided for arbitrary parameters and rigorously proved in the thermodynamical limit. The existence of several sum rules and recurrence relations among RDM eigenvalues is also demonstrated and the distribution function of RDM eigenvalues (including degeneracies) characterized. In particular, we prove that the distribution function approaches a two-dimensional Gaussian in the limit of large subsystem sizes n>1. As a physical application we discuss the von Neumann entropy (VNE) of a block of size n for a system of hard-core bosons on a complete graph, as a function of n and of the temperature T. The occurrence of a crossover of VNE from purely logarithmic behavior at T=0 to a purely linear behavior in n for T≥Tc, is demonstrated.
A reduced density-matrix theory of absorption line shape of molecular aggregate.
Yang, Mino
2005-09-22
A theory for the absorption line shape of molecular aggregates in condensed phase is formulated based on a reduced density-matrix approach. Intermolecular couplings in the aggregates are assumed to be weak (Förster type of energy transfer mechanism). The spin-Boson model is employed to include the effect of electron-phonon coupling. Using the projection operator technique, we derive kinetic equations for the reduced electronic density matrix associated with the absorption spectrum. General expressions of time-dependent rate constants in the kinetic equations are derived by using the cumulant expansion technique. The resulting time-dependent kinetic equations are solved numerically. We illustrate the applicability of the present theory by calculating the line shape of a dimer (a pair of donor and acceptor of energy transfer). For a J-aggregate type of molecular pair (with excitonic redshift), a tail appears on the blue side of the absorption spectrum due to the existence of inhomogeneity in electronic state mixing which is originated from the electron-phonon coupling.
Han, Ping; Xu, Rui-Xue; Li, Baiqing; Xu, Jian; Cui, Ping; Mo, Yan; Yan, Yijing
2006-06-15
A nonperturbative electron transfer rate theory is developed on the basis of reduced density matrix dynamics, which can be evaluated readily for the Debye solvent model without further approximation. Not only does it recover for reaction rates the celebrated Marcus' inversion and Kramers' turnover behaviors, but the present theory also predicts reaction thermodynamics, such as equilibrium Gibbs free energy and entropy, some interesting solvent-dependent features that are calling for experimental verification. Moreover, a continued fraction Green's function formalism is also constructed, which can be used together with the Dyson equation technique for efficient evaluation of nonperturbative reduced density matrix dynamics.
Zhao, Zhengji
We study the reduced density matrix method, a variational approach for electronic structure calculations based on the two-body reduced density matrix. This method minimizes the ground state energy with respect to the two-body reduced density matrix subject to some conditions which it must satisfy, known as N-representability conditions. The resulting optimization problem is a semidefinite program, a convex optimization problem for which computational methods have greatly advanced during the past decade. Two significant advances are reported in this thesis. First, we formulate the reduced density matrix method using the dual formulation of semidefinite programming instead of the previously-used primal one; this results in substantial computational savings and makes it possible to study larger systems than was done previously. Second, in addition to the previously-used P, Q and G conditions we investigate a pair of positive semidefinite conditions that has a three-index form; we call them the T1 and T2 conditions. We find that the inclusion of the T1 and T2 conditions gives a significant improvement over results previously obtained using only the P, Q and G conditions; and provides in all cases we have studied (47 molecules) more accurate results than other more familiar methods: Hartree-Fork; 2nd order Moller-Plesset method (MP2), singly and doubly substituted configuration interaction (SDCI), quadratic configuration interaction including single and double substitutions (QCISD), Brueckner doubles (with triples) (BD(T)) and coupled cluster singles and doubles with perturbational treatment of triples (CCSD(T)).
Shenvi, Neil; Yang, Yang; Yang, Weitao; Schwerdtfeger, Christine; Mazziotti, David
2013-01-01
Tensor hypercontraction is a method that allows the representation of a high-rank tensor as a product of lower-rank tensors. In this paper, we show how tensor hypercontraction can be applied to both the electron repulsion integral (ERI) tensor and the two-particle excitation amplitudes used in the parametric reduced density matrix (pRDM) algorithm. Because only O(r) auxiliary functions are needed in both of these approximations, our overall algorithm can be shown to scale as O(r4), where r is the number of single-particle basis functions. We apply our algorithm to several small molecules, hydrogen chains, and alkanes to demonstrate its low formal scaling and practical utility. Provided we use enough auxiliary functions, we obtain accuracy similar to that of the traditional pRDM algorithm, somewhere between that of CCSD and CCSD(T).
Energy Technology Data Exchange (ETDEWEB)
SivaRanjan, Uppala; Ramachandran, Ramesh, E-mail: rramesh@iisermohali.ac.in [Department of Chemical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Sector 81, Manauli, P.O. Box-140306, Mohali, Punjab (India)
2014-02-07
A quantum-mechanical model integrating the concepts of reduced density matrix and effective Hamiltonians is proposed to explain the multi-spin effects observed in rotational resonance (R{sup 2}) nuclear magnetic resonance (NMR) experiments. Employing this approach, the spin system of interest is described in a reduced subspace inclusive of its coupling to the surroundings. Through suitable model systems, the utility of our theory is demonstrated and verified with simulations emerging from both analytic and numerical methods. The analytic results presented in this article provide an accurate description/interpretation of R{sup 2} experimental results and could serve as a test-bed for distinguishing coherent/incoherent effects in solid-state NMR.
SivaRanjan, Uppala; Ramachandran, Ramesh
2014-02-01
A quantum-mechanical model integrating the concepts of reduced density matrix and effective Hamiltonians is proposed to explain the multi-spin effects observed in rotational resonance (R2) nuclear magnetic resonance (NMR) experiments. Employing this approach, the spin system of interest is described in a reduced subspace inclusive of its coupling to the surroundings. Through suitable model systems, the utility of our theory is demonstrated and verified with simulations emerging from both analytic and numerical methods. The analytic results presented in this article provide an accurate description/interpretation of R2 experimental results and could serve as a test-bed for distinguishing coherent/incoherent effects in solid-state NMR.
SivaRanjan, Uppala; Ramachandran, Ramesh
2014-02-07
A quantum-mechanical model integrating the concepts of reduced density matrix and effective Hamiltonians is proposed to explain the multi-spin effects observed in rotational resonance (R(2)) nuclear magnetic resonance (NMR) experiments. Employing this approach, the spin system of interest is described in a reduced subspace inclusive of its coupling to the surroundings. Through suitable model systems, the utility of our theory is demonstrated and verified with simulations emerging from both analytic and numerical methods. The analytic results presented in this article provide an accurate description/interpretation of R(2) experimental results and could serve as a test-bed for distinguishing coherent/incoherent effects in solid-state NMR.
Giesbertz, K J H
2015-08-07
A theorem for the invertibility of arbitrary response functions is presented under the following conditions: the time dependence of the potentials should be Laplace transformable and the initial state should be a ground state, though it might be degenerate. This theorem provides a rigorous foundation for all density-functional-like theories in the time-dependent linear response regime. Especially for time-dependent one-body reduced density matrix (1RDM) functional theory, this is an important step forward, since a solid foundation has currently been lacking. The theorem is equally valid for static response functions in the non-degenerate case, so can be used to characterize the uniqueness of the potential in the ground state version of the corresponding density-functional-like theory. Such a classification of the uniqueness of the non-local potential in ground state 1RDM functional theory has been lacking for decades. With the aid of presented invertibility theorem presented here, a complete classification of the non-uniqueness of the non-local potential in 1RDM functional theory can be given for the first time.
Jacobs, Verne; Kutana, Alex
The frequency-dependent transition rates for single-photon and multi-photon processes in quantized many-electron systems are evaluated using a reduced-density-matrix approach. We provide a fundamental quantum-mechanical foundation for systematic spectral simulations. A perturbation expansion of the frequency-domain Liouville-space self-energy operator is introduced for detailed evaluations of the spectral-line shapes. In the diagonal-resolvent (isolated-line) and short-memory-time (Markov) approximations, the lowest-order contributions to the spectral-line widths and shifts associated with environmental electron-photon and electron-phonon interactions are systematically evaluated. Our description is directly applicable to electromagnetic processes in a wide variety of many-electron systems, without premature approximations. In particular, our approach can be applied to investigate quantum optical phenomena involving electrons in both bulk and nanoscale semiconductor materials entirely from first principles, using a single-electron basis set obtained from density functional theory as a starting point for a many-electron description. Work supported by the Office of Naval Research through the Basic Research Program at The Naval Research Laboratory. A portion of this work was performed under the ASEE post doc program at NRL.
Indian Academy of Sciences (India)
Paul W Ayers; Mel Levy
2005-09-01
Using the constrained search and Legendre-transform formalisms, one can derive ``generalized” density-functional theories, in which the fundamental variable is either the electron pair density or the second-order reduced density matrix. In both approaches, the -representability problem is solved by the functional, and the variational principle is with respect to all pair densities (density matrices) that are nonnegative and appropriately normalized. The Legendre-transform formulation provides a lower bound on the constrained-search functional. Noting that experience in density-functional and density-matrix theories suggests that it is easier to approximate functionals than it is to approximate the set of -representable densities sheds some light on the significance of this work.
Jacobs, Verne
2015-05-01
The frequency-dependent transition rates for multi-photon processes in quantized many-electron systems are evaluated using a reduced-density-matrix approach. A fundamental foundation, based on quantum electrodynamics, is provided for systematic spectral simulations for electromagnetic interactions in quantized many-electron systems, including atomic, molecular, and solid-state systems. A perturbation expansion of the frequency-domain Liouville-space self-energy operator is employed in detailed evaluations of the spectral-line shapes. The self-energy contributions associated with environmental electron-photon and electron-phonon interactions are systematically taken into account. Detailed evaluations have been carried out for the spectral-line widths and shifts in the diagonal-resolvent, lowest order (Born), and short-memory-time (Markov) approximations. Work supported by the Office of Naval Research through the Basic Research Program at The Naval Research Laboratory.
Energy Technology Data Exchange (ETDEWEB)
Kozlowski, K.K.
2010-12-15
Starting from the form factor expansion in finite volume, we derive the multidimensional generalization of the so-called Natte series for the zero-temperature, time and distance dependent reduced density matrix in the non-linear Schroedinger model. This representation allows one to read-off straightforwardly the long-time/large-distance asymptotic behavior of this correlator. Our method of analysis reduces the complexity of the computation of the asymptotic behavior of correlation functions in the so-called interacting integrable models, to the one appearing in free fermion equivalent models. We compute explicitly the first few terms appearing in the asymptotic expansion. Part of these terms stems from excitations lying away from the Fermi boundary, and hence go beyond what can be obtained by using the CFT/Luttinger liquid based predictions. (orig.)
Dorfner, F.; Heidrich-Meisner, F.
2016-06-01
We study properties of the single-site reduced density matrix in the Bose-Bose resonance model as a function of system parameters. This model describes a single-component Bose gas with a resonant coupling to a diatomic molecular state, here defined on a lattice. A main goal is to demonstrate that the eigenstates of the single-site reduced density matrix have structures that are characteristic for the various quantum phases of this system. Since the Hamiltonian conserves only the global particle number but not the number of bosons and molecules individually, these eigenstates, referred to as optimal modes, can be nontrivial linear combinations of bare eigenstates of the molecular and boson particle number. We numerically analyze the optimal modes and their weights, the latter giving the importance of the corresponding state, in the ground state of the Bose-Bose resonance model. We find that the single-site von Neumann entropy is sensitive to the location of the phase boundaries. We explain the structure of the optimal modes and their weight spectra using perturbation theory and via a comparison to results for the single-component Bose-Hubbard model. We further study the dynamical evolution of the optimal modes and of the single-site entanglement entropy in two quantum quenches that cross phase boundaries of the model and show that these quantities are thermal in the steady state. For our numerical calculations, we use the density-matrix renormalization group method for ground-state calculations and time evolution in a Krylov subspace for the quench dynamics as well as exact diagonalization.
Exact equations of motion for natural orbitals of strongly driven two-electron systems
Rapp, J; Bauer, D
2014-01-01
Natural orbital theory is a computationally useful approach to the few and many-body quantum problem. While natural orbitals are known and applied since many years in electronic structure applications, their potential for time-dependent problems is being investigated only since recently. Correlated two-particle systems are of particular importance because the structure of the two-body reduced density matrix expanded in natural orbitals is known exactly in this case. However, in the time-dependent case the natural orbitals carry time-dependent phases that allow for certain time-dependent gauge transformations of the first kind. Different phase conventions will, in general, lead to different equations of motion for the natural orbitals. A particular phase choice allows us to derive the exact equations of motion for the natural orbitals of any (laser-) driven two-electron system explicitly, i.e., without any dependence on quantities that, in practice, require further approximations. For illustration, we solve th...
Necessary N-representability Constraints from Time-reversal Symmetry for Periodic Systems
Rubin, Nicholas C
2016-01-01
The variational calculation of the two-electron reduced density matrix (2-RDM) is extended to periodic molecular systems. If the 2-RDM theory is extended to the periodic case without consideration of time-reversal symmetry, however, it can yields energies that are significantly lower than the correct energies. We derive and implement linear constraints that enforce time-reversal symmetry on the 2-RDM without destroying its computationally favorable block-diagonal structure from translational invariance. Time-reversal symmetry is distinct from space-group or spin (SU(2)) symmetries which can be expressed by unitary transformations. The time-reversal symmetry constraints are demonstrated through calculations of the metallic hydrogen chain and the one-dimensional lithium hydride crystal.
Two-Electron Transfer Pathways.
Lin, Jiaxing; Balamurugan, D; Zhang, Peng; Skourtis, Spiros S; Beratan, David N
2015-06-18
The frontiers of electron-transfer chemistry demand that we develop theoretical frameworks to describe the delivery of multiple electrons, atoms, and ions in molecular systems. When electrons move over long distances through high barriers, where the probability for thermal population of oxidized or reduced bridge-localized states is very small, the electrons will tunnel from the donor (D) to acceptor (A), facilitated by bridge-mediated superexchange interactions. If the stable donor and acceptor redox states on D and A differ by two electrons, it is possible that the electrons will propagate coherently from D to A. While structure-function relations for single-electron superexchange in molecules are well established, strategies to manipulate the coherent flow of multiple electrons are largely unknown. In contrast to one-electron superexchange, two-electron superexchange involves both one- and two-electron virtual intermediate states, the number of virtual intermediates increases very rapidly with system size, and multiple classes of pathways interfere with one another. In the study described here, we developed simple superexchange models for two-electron transfer. We explored how the bridge structure and energetics influence multielectron superexchange, and we compared two-electron superexchange interactions to single-electron superexchange. Multielectron superexchange introduces interference between singly and doubly oxidized (or reduced) bridge virtual states, so that even simple linear donor-bridge-acceptor systems have pathway topologies that resemble those seen for one-electron superexchange through bridges with multiple parallel pathways. The simple model systems studied here exhibit a richness that is amenable to experimental exploration by manipulating the multiple pathways, pathway crosstalk, and changes in the number of donor and acceptor species. The features that emerge from these studies may assist in developing new strategies to deliver multiple
Quantum entanglement for two electrons in the excited states of helium-like systems
Lin, Yen-Chang
2013-01-01
The quantum entanglement for the two electrons in the excited states of the helium-like atom/ions is investigated using the two-electron wave functions constructed by the B-spline basis. As a measure of the spatial (electron-electron orbital) entanglement, the von Neumann entropy and linear entropy of the reduced density matrix are calculated for the 1s2s 1,3S excited states for systems with some selected Z values from Z=2 to Z=100. Results for the helium atom are compared with other available calculations. We have also investigated the entropies for these excited states when the nucleus charge is reduced from Z=2 to Z=1. At such a critical charge, all the singly-excited states of this system become unbound, and the linear entropies and the von Neumann entropies for the excited states are approaching 1/2 and 1, respectively, the limits for the entropies when one electron is bound to the nucleus, and the other being free.
Brics, M
2013-01-01
Favorably scaling numerical time-dependent many-electron techniques such as time-dependent density functional theory (TDDFT) with adiabatic exchange-correlation potentials typically fail in capturing highly correlated electron dynamics. We propose a method based on natural orbitals, i.e., the eigenfunctions of the one-body reduced density matrix, that is almost as inexpensive numerically as adiabatic TDDFT, but which is capable of describing correlated phenomena such as doubly excited states, autoionization, Fano profiles in the photoelectron spectra, and strong-field ionization in general. Equations of motion (EOM) for natural orbitals and their occupation numbers have been derived earlier. We show that by using renormalized natural orbitals (RNO) both can be combined into one equation governed by a hermitian effective Hamiltonian. We specialize on the two-electron spin-singlet system, known as being a "worst case" testing ground for TDDFT, and employ the widely used, numerically exactly solvable, one-dimens...
Mazziotti, David A
2007-05-14
Two-electron reduced density matrices (2-RDMs) have recently been directly determined from the solution of the anti-Hermitian contracted Schrodinger equation (ACSE) to obtain 95%-100% of the ground-state correlation energy of atoms and molecules, which significantly improves upon the accuracy of the contracted Schrodinger equation (CSE) [D. A. Mazziotti, Phys. Rev. Lett. 97, 143002 (2006)]. Two subsets of the CSE, the ACSE and the contraction of the CSE onto the one-particle space, known as the 1,3-CSE, have two important properties: (i) dependence upon only the 3-RDM and (ii) inclusion of all second-order terms when the 3-RDM is reconstructed as only a first-order functional of the 2-RDM. The error in the 1,3-CSE has an important role as a stopping criterion in solving the ACSE for the 2-RDM. Using a computationally more efficient implementation of the ACSE, the author treats a variety of molecules, including H2O, NH3, HCN, and HO3-, in larger basis sets such as correlation-consistent polarized double- and triple-zeta. The ground-state energy of neon is also calculated in a polarized quadruple-zeta basis set with extrapolation to the complete basis-set limit, and the equilibrium bond length and harmonic frequency of N2 are computed with comparison to experimental values. The author observes that increasing the basis set enhances the ability of the ACSE to capture correlation effects in ground-state energies and properties. In the triple-zeta basis set, for example, the ACSE yields energies and properties that are closer in accuracy to coupled cluster with single, double, and triple excitations than to coupled cluster with single and double excitations. In all basis sets, the computed 2-RDMs very closely satisfy known N-representability conditions.
Gravitational force between two electrons in superconductors
de Matos, Clovis Jacinto
2007-01-01
The attractive gravitational force between two electrons in superconductors is deduced from the Eddington-Dirac large number relation, together with Beck and Mackey electromagnetic model of vacuum energy in superconductors. This force is estimated to be weaker than the gravitational attraction between two electrons in the vacuum.
Brics, M; Bauer, D
2016-01-01
Recently introduced time-dependent renormalized-natural-orbital theory (TDRNOT) is based on the equations of motion for the so-called natural orbitals, i.e., the eigenfunctions of the one-body reduced density matrix. Exact TDRNOT can be formulated for any time-dependent two-electron system in either spin configuration. In this paper, the method is tested against high-order harmonic generation (HHG) and Fano profiles in absorption spectra with the help of a numerically exactly solvable one-dimensional model He atom, starting from the spin-singlet ground state. Such benchmarks are challenging because Fano profiles originate from transitions involving autoionizing states, and HHG is a strong-field phenomenon well beyond linear response. TDRNOT with just one natural orbital per spin in the helium spin-singlet case is equivalent to time-dependent Hartree-Fock or time-dependent density functional theory (TDDFT) in exact exchange-only approximation. It is not unexpected that TDDFT fails in reproducing Fano profiles ...
Entangled Electrons Foil Synthesis of Elusive Low-Valent Vanadium Oxo Complex.
Schlimgen, Anthony W; Heaps, Charles W; Mazziotti, David A
2016-02-18
We examine the recently reported first synthesis of the elusive low-valent vanadium(III) in a vanadium oxo complex with a computation representing 10(21) quantum degrees of freedom. While this computation is intractable with a conventionally constructed wave function, it is performed here by a direct calculation of the system's two-electron reduced density matrix (2-RDM), where the 2-RDM is constrained by nontrivial conditions, known as N-representability conditions, that restrict the 2-RDM to represent an N electron quantum system. We show that the added (reducing) electron becomes entangled among the five pyridine ligands. While smaller calculations predict a metal-centered addition, large-scale 2-RDM calculations show that quantum entanglement redirects the electron transfer to the pyridine ligands, resulting in a ligand-centered addition. Beyond its implications for the synthesis of low-valent vanadium oxo complexes, the result suggests new possibilities for using quantum entanglement to predict and control electron transfer in chemical and biological materials.
Two-electron photoionization of endohedral atoms
Amusia, M Ya; Mandelzweig, V B
2006-01-01
Using $He@C_{60}$ as an example, we demonstrate that static potential of the fullerene core essentially alters the cross section of the two-electron ionization differential in one-electron energy $d\\sigma ^{++}(\\omega )/d\\epsilon $. We found that at high photon energy prominent oscillations appear in it due to reflection of the second, slow electron wave on the $% C_{60}$ shell, which "dies out" at relatively high $\\epsilon $ values, of about 2$\\div $3 two-electron ionization potentials. The results were presented for ratios $R_{C_{60}}(\\omega ,\\epsilon)\\equiv d\\sigma ^{++}(\\omega ,\\epsilon)/d\\sigma ^{a++}(\\omega,\\epsilon)$, where $d\\sigma ^{a++}(\\omega,\\epsilon)/d\\epsilon$ is the two-electron differential photoionization cross section. We have calculated the ratio $R_{i,ful}= \\sigma_{i} ^{++}(\\omega)/\\sigma_{i}^{a++}(\\omega)$, that accounts for reflection of both photoelectrons by the $C_{60}$ shell. We have calculated also the value of two-electron photoionization cross section $\\sigma ^{++}(\\omega)$ and fo...
Double ionization of two-electron systems
Energy Technology Data Exchange (ETDEWEB)
Ancarani, L U; Cappello, C Dal [Laboratoire de Physique Moleculaire et des Collisions, Universite Paul Verlaine - Metz, 57078 Metz (France); Gasaneo, G, E-mail: ancarani@univ-metz.f [Departamento de Fisica, Universidad Nacional del Sur and Consejo Nacional de Investigaciones CientIficas y Tecnicas, 8000 BahIa Blanca, Buenos Aires (Argentina)
2010-02-01
We address various issues related to the double ionization by electron impact of two-electron systems. The emphasis will be put on the theoretical description of high incident energy (e,3e) processes, for which the first Born approximation should be suitable. In the case of helium, absolute experimental data for fivefold differential cross sections are available in coplanar geometry. We will review and discuss the divergencies existing between the results obtained with different theoretical models, and those appearing when compared to the experiments in particular with respect to the absolute scale. We will then discuss some results obtained in a recently proposed out of plane geometry.
Some remarks on the two-electron atom
Apostol, M
1996-01-01
New, approximate, two-electron wavefunctions are introduced for the two-electron atoms (cations), which account remarkably well for the ground-state energies and the lowest-excxited states (where available). A new scheme of electronic configurations is also proposed for the multi-electron atoms.
A Tale of Two Electrons: Correlation at High Density
Loos, Pierre-François
2010-01-01
We review our recent progress in the determination of the high-density correlation energy $\\Ec$ in two-electron systems. Several two-electron systems are considered, such as the well known helium-like ions (helium), and the Hooke's law atom (hookium). We also present results regarding two electrons on the surface of a sphere (spherium), and two electrons trapped in a spherical box (ballium). We also show that, in the large-dimension limit, the high-density correlation energy of two opposite-spin electrons interacting {\\em via} a Coulomb potential is given by $\\Ec \\sim -1/(8D^2)$ for any radial external potential $V(r)$, where $D$ is the dimensionality of the space. This result explains the similarity of $\\Ec$ in the previous two-electron systems for $D=3$.
Natural occupation numbers in two-electron quantum rings
Energy Technology Data Exchange (ETDEWEB)
Tognetti, Vincent, E-mail: vincent.tognetti@univ-rouen.fr [Normandy Univ., COBRA UMR 6014 & FR 3038, Université de Rouen, INSA Rouen, CNRS, 1 rue Tesniére, 76821 Mont Saint Aignan, Cedex (France); Loos, Pierre-François [Research School of Chemistry, Australian National University, Canberra ACT 2601 (Australia)
2016-02-07
Natural orbitals (NOs) are central constituents for evaluating correlation energies through efficient approximations. Here, we report the closed-form expression of the NOs of two-electron quantum rings, which are prototypical finite-extension systems and new starting points for the development of exchange-correlation functionals in density functional theory. We also show that the natural occupation numbers for these two-electron paradigms are in general non-vanishing and follow the same power law decay as atomic and molecular two-electron systems.
Natural occupation numbers in two-electron quantum rings
Tognetti, Vincent; Loos, Pierre-François
2016-02-01
Natural orbitals (NOs) are central constituents for evaluating correlation energies through efficient approximations. Here, we report the closed-form expression of the NOs of two-electron quantum rings, which are prototypical finite-extension systems and new starting points for the development of exchange-correlation functionals in density functional theory. We also show that the natural occupation numbers for these two-electron paradigms are in general non-vanishing and follow the same power law decay as atomic and molecular two-electron systems.
Natural occupation numbers in two-electron quantum rings.
Tognetti, Vincent; Loos, Pierre-François
2016-02-07
Natural orbitals (NOs) are central constituents for evaluating correlation energies through efficient approximations. Here, we report the closed-form expression of the NOs of two-electron quantum rings, which are prototypical finite-extension systems and new starting points for the development of exchange-correlation functionals in density functional theory. We also show that the natural occupation numbers for these two-electron paradigms are in general non-vanishing and follow the same power law decay as atomic and molecular two-electron systems.
On the Beebe-Linderberg two-electron integral approximation
Røeggen, I.; Wisløff-Nilssen, E.
1986-12-01
The Beebe-Linderberg two-electron integral approximation, which is generated by a Cholesky decomposition of the two-electron integral matrix ([μν|λσ]), is slightly modified. On the basis of test calculations, two key questions concerning this approximation are discussed: The numerical rank of the two-electron integral matrix and the relationship between the integral threshold and electronic properties. The numerical results presented in this work suggest that the modified Beebe-Linderberg approximation might be considered as an alternative to effective core potential methods.
Majorana solutions to the two-electron problem
Esposito, S
2012-01-01
A review of the known different methods and results devised to study the two-electron atom problem, appeared in the early years of quantum mechanics, is given, with particular reference to the calculations of the ground state energy of helium. This is supplemented by several, unpublished results obtained around the same years by Ettore Majorana, which results did not convey in his published papers on the argument, and thus remained unknown until now. Particularly interesting, even for current research in atomic and nuclear physics, is a general variant of the variational method, developed by Majorana in order to take directly into account, already in the trial wavefunction, the action of the full Hamiltonian operator of a given quantum system. Moreover, notable calculations specialized to the study of the two-electron problem show the introduction of the remarkable concept of an effective nuclear charge different for the two electrons (thus generalizing previous known results), and an application of the pertu...
Two-electron quantum ring in short pulses
Institute of Scientific and Technical Information of China (English)
Poonam Silotia; Rakesh Kumar Meena; Vinod Prasad
2015-01-01
The response of two-electron quantum ring system to the short laser pulses of different shapes in the presence of external static electric field is studied. The variation of transition probabilities of the two-electron quatum ring from ground state to excited states with a number of parameters is shown and explained. The energy levels and wavefunctions of the system in the presence of static electric field are found by solving the time-independent Schr ¨odinger equation numerically by finite difference method. The shape of the pulse plays a dominant role on the dynamics.
Attosecond-correlated dynamics of two electrons in argon
Indian Academy of Sciences (India)
V Sharma; N Camus; B Fischer; M Kremer; A Rudenko; B Bergues; M Kuebel; N G Johnson; M F Kling; T Pfeifer; J Ullrich; R Moshammer
2014-01-01
In this work we explored strong field-induced decay of doubly excited transient Coulomb complex Ar** → Ar2++2. We measured the correlated two-electron emission as a function of carrier envelop phase (CEP) of 6 fs pulses in the non-sequential double ionization (NSDI) of argon. Classical model calculations suggest that the intermediate doubly excited Coulomb complex loses memory of its formation dynamics. We estimated the ionization time difference between the two electrons from NSDI of argon and it is 200 ± 100 as (N Camus et al, Phys. Rev. Lett. 108, 073003 (2012)).
Foley, Jonathan J.; Mazziotti, David A.
2010-10-01
An efficient method for geometry optimization based on solving the anti-Hermitian contracted Schrödinger equation (ACSE) is presented. We formulate a reduced version of the Hellmann-Feynman theorem (HFT) in terms of the two-electron reduced Hamiltonian operator and the two-electron reduced density matrix (2-RDM). The HFT offers a considerable reduction in computational cost over methods which rely on numerical derivatives. While previous geometry optimizations with numerical gradients required 2M evaluations of the ACSE where M is the number of nuclear degrees of freedom, the HFT requires only a single ACSE calculation of the 2-RDM per gradient. Synthesizing geometry optimization techniques with recent extensions of the ACSE theory to arbitrary electronic and spin states provides an important suite of tools for accurately determining equilibrium and transition-state structures of ground- and excited-state molecules in closed- and open-shell configurations. The ability of the ACSE to balance single- and multi-reference correlation is particularly advantageous in the determination of excited-state geometries where the electronic configurations differ greatly from the ground-state reference. Applications are made to closed-shell molecules N2, CO, H2O, the open-shell molecules B2 and CH, and the excited state molecules N2, B2, and BH. We also study the HCN ↔ HNC isomerization and the geometry optimization of hydroxyurea, a molecule which has a significant role in the treatment of sickle-cell anaemia.
Excitations and benchmark ensemble density functional theory for two electrons
Pribram-Jones, Aurora; Trail, John R; Burke, Kieron; Needs, Richard J; Ullrich, Carsten A
2014-01-01
A new method for extracting ensemble Kohn-Sham potentials from accurate excited state densities is applied to a variety of two electron systems, exploring the behavior of exact ensemble density functional theory. The issue of separating the Hartree energy and the choice of degenerate eigenstates is explored. A new approximation, spin eigenstate Hartree-exchange (SEHX), is derived. Exact conditions that are proven include the signs of the correlation energy components, the virial theorem for both exchange and correlation, and the asymptotic behavior of the potential for small weights of the excited states. Many energy components are given as a function of the weights for two electrons in a one-dimensional flat box, in a box with a large barrier to create charge transfer excitations, in a three-dimensional harmonic well (Hooke's atom), and for the He atom singlet-triplet ensemble, singlet-triplet-singlet ensemble, and triplet bi-ensemble.
Excitations and benchmark ensemble density functional theory for two electrons
Energy Technology Data Exchange (ETDEWEB)
Pribram-Jones, Aurora; Burke, Kieron [Department of Chemistry, University of California-Irvine, Irvine, California 92697 (United States); Yang, Zeng-hui; Ullrich, Carsten A. [Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211 (United States); Trail, John R.; Needs, Richard J. [Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE (United Kingdom)
2014-05-14
A new method for extracting ensemble Kohn-Sham potentials from accurate excited state densities is applied to a variety of two-electron systems, exploring the behavior of exact ensemble density functional theory. The issue of separating the Hartree energy and the choice of degenerate eigenstates is explored. A new approximation, spin eigenstate Hartree-exchange, is derived. Exact conditions that are proven include the signs of the correlation energy components and the asymptotic behavior of the potential for small weights of the excited states. Many energy components are given as a function of the weights for two electrons in a one-dimensional flat box, in a box with a large barrier to create charge transfer excitations, in a three-dimensional harmonic well (Hooke's atom), and for the He atom singlet-triplet ensemble, singlet-triplet-singlet ensemble, and triplet bi-ensemble.
CMS: Simulated Higgs to two jets and two electrons
1997-01-01
This track is an example of simulated data modelled for the CMS detector on the Large Hadron Collider (LHC) at CERN, which will begin taking data in 2008. Here a Higgs boson is produced which decays into two jets of hadrons and two electrons. The lines represent the possible paths of particles produced by the proton-proton collision in the detector while the energy these particles deposit is shown in blue.
Quantum Transport in Solids: Two-Electron Processes.
1995-06-01
The central objective of this research program has been to study theoretically the underlying principles of quantum transport in solids. The area of...research investigated has emphasized the understanding of two electron processes in quantum transport . The problems have been treated analytically to...the extent possible through the use of dynamical localized Wannier functions. These results have been and are being incorporated in a full quantum
Dissipative two-electron transfer: A numerical renormalization group study
Tornow, Sabine; Bulla, Ralf; Anders, Frithjof B.; Nitzan, Abraham
2008-07-01
We investigate nonequilibrium two-electron transfer in a model redox system represented by a two-site extended Hubbard model and embedded in a dissipative environment. The influence of the electron-electron interactions and the coupling to a dissipative bosonic bath on the electron transfer is studied in different temperature regimes. At high temperatures, Marcus transfer rates are evaluated, and at low temperatures, we calculate equilibrium and nonequilibrium population probabilities of the donor and acceptor with the nonperturbative numerical renormalization group approach. We obtain the nonequilibrium dynamics of the system prepared in an initial state of two electrons at the donor site and identify conditions under which the electron transfer involves one concerted two-electron step or two sequential single-electron steps. The rates of the sequential transfer depend nonmonotonically on the difference between the intersite and on-site Coulomb interaction, which become renormalized in the presence of the bosonic bath. If this difference is much larger than the hopping matrix element, the temperature as well as the reorganization energy, simultaneous transfer of both electrons between donor and acceptor can be observed.
Dynamics of two-electron excitations in helium
Energy Technology Data Exchange (ETDEWEB)
Caldwell, C.D.; Menzel, A.; Frigo, S.P. [Univ. of Central Florida, Orlando, FL (United States)] [and others
1997-04-01
Excitation of both electrons in helium offers a unique window for studying electron correlation at the most basic level in an atom in which these two electrons and the nucleus form a three-body system. The authors utilized the first light available at the U-8 undulator-SGM monochromator beamline to investigate the dynamic parameters, partial cross sections, differential cross sections, and photoelectron angular distribution parameters ({beta}), with a high resolving power for the photon beam and at the highly differential level afforded by the use of their electron spectrometer. In parallel, they carried out detailed calculations of the relevant properties by a theoretical approach that is based on the hyperspherical close-coupling method. Partial photoionization cross sections {sigma}{sub n}, and photoelectron angular distributions {beta}{sub n} were measured for all possible final ionic states He{sup +}(n) in the region of the double excitations N(K,T){sup A} up to the N=5 threshold. At a photon energy bandpass of 12 meV below the thresholds N=3, 4, and 5, this level of differentiation offers the most critical assessment of the dynamics of the two-electron excitations to date. The experimental data were seen to be very well described by the most advanced theoretical calculations.
Magnetic alteration of entanglement in two-electron quantum dots
Simonovic, N S
2015-01-01
Quantum entanglement is analyzed thoroughly in the case of the ground and lowest states of two-electron axially symmetric quantum dots under a perpendicular magnetic field. The individual-particle and the center-of-mass representations are used to study the entanglement variation at the transition from interacting to noninteracting particle regimes. The mechanism of symmetry breaking due to the interaction, that results in the states with symmetries related to the later representation only, being entangled even at the vanishing interaction, is discussed. The analytical expression for the entanglement measure based on the linear entropy is derived in the limit of noninteracting electrons. It reproduces remarkably well the numerical results for the lowest states with the magnetic quantum number M>2 in the interacting regime. It is found that the entanglement of the ground state is a discontinuous function of the field strength. A method to estimate the entanglement of the ground state, characterized by the quan...
Frustrated double ionization in two-electron triatomic molecules
Chen, A.; Price, H.; Staudte, A.; Emmanouilidou, A.
2016-10-01
Using a semiclassical model, we investigate frustrated double ionization (FDI) in D3+ , a two-electron triatomic molecule, when driven by an intense, linearly polarized, near-infrared (800 nm) laser field. We compute the kinetic energy release of the nuclei and find a good agreement between experiment and our model. We explore the two pathways of FDI and show that, with increasing field strength, over-the-barrier ionization overtakes tunnel ionization as the underlying mechanism of FDI. Moreover, we compute the angular distribution of the ion fragments for FDI and identify a feature that can potentially be observed experimentally and is a signature of only one of the two pathways of FDI.
Frustrated double ionization in two-electron triatomic molecules
Chen, A; Staudte, A; Emmanouilidou, A
2016-01-01
Using a semi-classical model, we investigate frustrated double ionization (FDI) in $\\mathrm{D_3^+}$, a two-electron triatomic molecule, when driven by an intense, linearly polarized, near-infrared (800 nm) laser field. We do so using a semi-classical model. We find a good agreement between experiment and our model. We explore the two pathways of FDI and show that, with increasing field strength, over-the-barrier ionization overtakes tunnel ionization as the underlying mechanism of FDI. Moreover, we compute the angular distribution of the ion fragments for FDI and identify a feature that can be observed experimentally and that is a signature of only one of the two pathways of FDI.
Complex dynamics in planar two-electron quantum dots
Energy Technology Data Exchange (ETDEWEB)
Schroeter, Sebastian Josef Arthur
2013-06-25
Quantum dots play an important role in a wide range of recent experimental and technological developments. In particular they are promising candidates for realisations of quantum bits and further applications in quantum information theory. The harmonically confined Hooke's atom model is experimentally verified and separates in centre-of-mass and relative coordinates. Findings that are contradictory to this separability call for an extension of the model, in particular changing the confinement potential. In order to study effects of an anharmonic confinement potential on spectral properties of planar two-electron quantum dots a sophisticated numerical approach is developed. Comparison between the Helium atom, Hooke's atom and an anharmonic potential model are undertaken in order to improve the description of quantum dots. Classical and quantum features of complexity and chaos are investigated and used to characterise the dynamics of the system to be mixed regular-chaotic. Influence of decoherence can be described by quantum fidelity, which measures the effect of a perturbation on the time evolution. The quantum fidelity of eigenstates of the system depends strongly on the properties of the perturbation. Several methods for solving the time-dependent Schrödinger equation are implemented and a high level of accuracy for long time evolutions is achieved. The concept of offset entanglement, the entanglement of harmonic models in the noninteracting limit, is introduced. This concept explains different questions raised in the literature for harmonic quantum dot models, recently. It shows that only in the groundstate the electrons are not entangled in the fermionic sense. The applicability, validity, and origin of Hund's first rule in general quantum dot models is further addressed. In fact Hund's first rule is only applicable, and in this case also valid, for one pair of singlet and triplet states in Hooke's atom. For more realistic models of two-electron
Van Aggelen, Helen; Bultinck, Patrick; Verstichel, Brecht; Van Neck, Dimitri; Ayers, Paul W
2009-07-21
The behaviour of diatomic molecules is examined using the variational second-order density matrix method under the P, Q and G conditions. It is found that the method describes the dissociation limit incorrectly, with fractional charges on the well-separated atoms. This can be traced back to the behaviour of the energy versus the number of electrons for the isolated atoms. It is shown that the energies for fractional charges are much too low.
Giesbertz, Klaas J H
2016-01-01
In [J. Chem. Phys. 143, 054102 (2015)] I have derived conditions to characterize the kernel of the retarded response function, under the assumption that the initial state is a ground state. In this article I demonstrate its generalization to mixed states (ensembles). To make the proof work, the weights in the ensemble need to be decreasing for increasing energies of the pure states from which the mixed state is constructed. The resulting conditions are not easy to verify, but under the additional assumptions that the ensemble weights are directly related to the energies and that the full spectrum of the Hamiltonian participates in the ensemble, it is shown that potentials only belong to the kernel of the retarded response function if they commute with the initial Hamiltonian. These additional assumptions are valid for thermodynamic ensembles, which makes this result also physically relevant. The conditions on the potentials for the thermodynamic ensembles are much stronger than in the pure state (zero tempera...
Controlling autoionization in strontium two-electron-excited states
Fields, Robert; Zhang, Xinyue; Dunning, F. Barry; Yoshida, Shuhei; Burgdörfer, Joachim
2016-05-01
One challenge in engineering long-lived two-electron-excited states, i.e., so-called planetary atoms, is autoionization. Autoionization, however, can be suppressed if the outermost electron is placed in a high- n, n ~ 300 - 600 , high- L state because such states have only a very small overlap with the inner electron, even when this is also excited to a state of relatively high n and hence of relatively long lifetime. Here the L-dependence of the autoionization rate for high- n strontium Rydberg atoms is examined during excitation of the core ion 5 s 2S1 / 2 - 5 p 2P3 / 2 transition. Measurements in which the angular momentum of the Rydberg electron is controlled using a pulsed electric field show that the autoionization rate decreases rapidly with increasing L and becomes very small for values larger than ~ 20 . The data are analyzed with the aid of calculations undertaken using complex scaling. Research supported by the NSF and Robert A. Welch Foundation.
van Meer, R; Gritsenko, O V; Baerends, E J
2014-01-14
Time dependent density matrix functional theory in its adiabatic linear response formulation delivers exact excitation energies ωα and oscillator strengths fα for two-electron systems if extended to the so-called phase including natural orbital (PINO) theory. The Löwdin-Shull expression for the energy of two-electron systems in terms of the natural orbitals and their phases affords in this case an exact phase-including natural orbital functional (PILS), which is non-primitive (contains other than just J and K integrals). In this paper, the extension of the PILS functional to N-electron systems is investigated. With the example of an elementary primitive NO functional (BBC1) it is shown that current density matrix functional theory ground state functionals, which were designed to produce decent approximations to the total energy, fail to deliver a qualitatively correct structure of the (inverse) response function, due to essential deficiencies in the reconstruction of the two-body reduced density matrix (2RDM). We now deduce essential features of an N-electron functional from a wavefunction Ansatz: The extension of the two-electron Löwdin-Shull wavefunction to the N-electron case informs about the phase information. In this paper, applications of this extended Löwdin-Shull (ELS) functional are considered for the simplest case, ELS(1): one (dissociating) two-electron bond in the field of occupied (including core) orbitals. ELS(1) produces high quality ωα(R) curves along the bond dissociation coordinate R for the molecules LiH, Li2, and BH with the two outer valence electrons correlated. All of these results indicate that response properties are much more sensitive to deficiencies in the reconstruction of the 2RDM than the ground state energy, since derivatives of the functional with respect to both the NOs and the occupation numbers need to be accurate.
Energy Technology Data Exchange (ETDEWEB)
Meer, R. van; Gritsenko, O. V. [Faculty of Exact Sciences, Theoretical Chemistry, VU University, Amsterdam (Netherlands); WCU Program, Dep. of Chemistry, Pohang Univ. of Science and Techn., Pohang (Korea, Republic of); Baerends, E. J. [Faculty of Exact Sciences, Theoretical Chemistry, VU University, Amsterdam (Netherlands); WCU Program, Dep. of Chemistry, Pohang Univ. of Science and Techn., Pohang (Korea, Republic of); Department of Chemistry, Faculty of Science, King Abdulaziz University, Jeddah 21589 (Saudi Arabia)
2014-01-14
Time dependent density matrix functional theory in its adiabatic linear response formulation delivers exact excitation energies ω{sub α} and oscillator strengths f{sub α} for two-electron systems if extended to the so-called phase including natural orbital (PINO) theory. The Löwdin-Shull expression for the energy of two-electron systems in terms of the natural orbitals and their phases affords in this case an exact phase-including natural orbital functional (PILS), which is non-primitive (contains other than just J and K integrals). In this paper, the extension of the PILS functional to N-electron systems is investigated. With the example of an elementary primitive NO functional (BBC1) it is shown that current density matrix functional theory ground state functionals, which were designed to produce decent approximations to the total energy, fail to deliver a qualitatively correct structure of the (inverse) response function, due to essential deficiencies in the reconstruction of the two-body reduced density matrix (2RDM). We now deduce essential features of an N-electron functional from a wavefunction Ansatz: The extension of the two-electron Löwdin-Shull wavefunction to the N-electron case informs about the phase information. In this paper, applications of this extended Löwdin-Shull (ELS) functional are considered for the simplest case, ELS(1): one (dissociating) two-electron bond in the field of occupied (including core) orbitals. ELS(1) produces high quality ω{sub α}(R) curves along the bond dissociation coordinate R for the molecules LiH, Li{sub 2}, and BH with the two outer valence electrons correlated. All of these results indicate that response properties are much more sensitive to deficiencies in the reconstruction of the 2RDM than the ground state energy, since derivatives of the functional with respect to both the NOs and the occupation numbers need to be accurate.
Real-time electron dynamics simulation of two-electron transfer reactions induced by nuclear motion
Suzuki, Yasumitsu; Yamashita, Koichi
2012-04-01
Real-time electron dynamics of two-electron transfer reactions induced by nuclear motion is calculated by three methods: the numerically exact propagation method, the time-dependent Hartree (TDH) method and the Ehrenfest method. We find that, as long as the nuclei move as localized wave packets, the TDH and Ehrenfest methods can reproduce the exact electron dynamics of a simple charge transfer reaction model containing two electrons qualitatively well, even when nonadiabatic transitions between adiabatic states occur. In particular, both methods can reproduce the cases where a complete two-electron transfer reaction occurs and those where it does not occur.
Energy Technology Data Exchange (ETDEWEB)
Hoy, Erik P.; Mazziotti, David A., E-mail: damazz@uchicago.edu [Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 (United States)
2015-08-14
Tensor factorization of the 2-electron integral matrix is a well-known technique for reducing the computational scaling of ab initio electronic structure methods toward that of Hartree-Fock and density functional theories. The simplest factorization that maintains the positive semidefinite character of the 2-electron integral matrix is the Cholesky factorization. In this paper, we introduce a family of positive semidefinite factorizations that generalize the Cholesky factorization. Using an implementation of the factorization within the parametric 2-RDM method [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)], we study several inorganic molecules, alkane chains, and potential energy curves and find that this generalized factorization retains the accuracy and size extensivity of the Cholesky factorization, even in the presence of multi-reference correlation. The generalized family of positive semidefinite factorizations has potential applications to low-scaling ab initio electronic structure methods that treat electron correlation with a computational cost approaching that of the Hartree-Fock method or density functional theory.
Hoy, Erik P; Mazziotti, David A
2015-08-14
Tensor factorization of the 2-electron integral matrix is a well-known technique for reducing the computational scaling of ab initio electronic structure methods toward that of Hartree-Fock and density functional theories. The simplest factorization that maintains the positive semidefinite character of the 2-electron integral matrix is the Cholesky factorization. In this paper, we introduce a family of positive semidefinite factorizations that generalize the Cholesky factorization. Using an implementation of the factorization within the parametric 2-RDM method [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)], we study several inorganic molecules, alkane chains, and potential energy curves and find that this generalized factorization retains the accuracy and size extensivity of the Cholesky factorization, even in the presence of multi-reference correlation. The generalized family of positive semidefinite factorizations has potential applications to low-scaling ab initio electronic structure methods that treat electron correlation with a computational cost approaching that of the Hartree-Fock method or density functional theory.
Two-electron reduction of ethylene carbonate: a quantum chemistry re-examination of mechanisms
Leung, Kevin
2013-01-01
Passivating solid-electrolyte interphase (SEI) films arising from electrolyte decomposition on low-voltage lithium ion battery anode surfaces are critical for battery operations. We review the recent theoretical literature on electrolyte decomposition and emphasize the modeling work on two-electron reduction of ethylene carbonate (EC, a key battery organic solvent). One of the two-electron pathways, which releases CO gas, is re-examined using simple quantum chemistry calculations. Excess electrons are shown to preferentially attack EC in the order (broken EC^-) > (intact EC^-) > EC. This confirms the viability of two electron processes and emphasizes that they need to be considered when interpreting SEI experiments. An estimate of the crossover between one- and two-electron regimes under a homogeneous reaction zone approximation is proposed.
Vacuum polarization screening corrections to the ground state energy of two-electron ions
Artemiev, A N; Yerokhin, V A
1997-01-01
Vacuum polarization screening corrections to the ground state energy of two-electron ions are calculated in the range $Z=20-100$. The calculations are carried out for a finite nucleus charge distribution.
ATLAS proton-proton event containing two electrons and two muons
ATLAS Collaboration
2011-01-01
An event with two identified muons and two identified electrons from a proton- proton collision in ATLAS. This event is consistent with coming from two Z particles decaying: one Z decays to two muons, the other to two electrons. Such events are produced by Standard Model processes without Higgs particles. They are also a possible signature for Higgs particle production, but many events must be analysed together in order to tell if there is a Higgs signal. The two muons are picked out as red tracks penetrating right through the detector. The two electrons are picked out as green tracks in the central, inner detector, matching narrow green clusters of energy in the barrel part of the calorimeters. The inset at the bottom right shows a map of the energy seen in the detector: the two big yellow spikes correspond to the two electrons.
Study of two-electron jumps in relaxation of Coulomb glasses
Energy Technology Data Exchange (ETDEWEB)
Bergli, J. [Department of Physics, University of Oslo, Blindern (Norway); Somoza, A.M.; Ortuno, M. [Departamento de Fisica - CIOyN, Universidad de Murcia (Spain)
2009-12-15
A long-standing debate in the theory of hopping insulators concerns the role of multi-electron transitions in the dynamics of the system. The natural assumption is that as temperature is lowered, two-electron transitions will play an increasingly important role since they provide a way of tunneling through additional energy barriers which would be energetically unfavorable as successive one-electron transitions. This was disputed in[1], but later it was seen in[2]. The reason for this discrepancy is not clear and deserves further attention. One point where the two approaches diverged was in the selection and weighting of the two-electron transitions relative to one-electron transitions. We present calculations of the transition rates to second order in the tunneling matrix element, which will be used in improved numerical studies. We compare results for only one-electron jumps with results including also two-electron jumps. (Abstract Copyright [2009], Wiley Periodicals, Inc.)
Benchmark values for molecular two-electron integrals arising from the Dirac equation
Baǧcı, A.; Hoggan, P. E.
2015-02-01
The two-center two-electron Coulomb and hybrid integrals arising in relativistic and nonrelativistic ab initio calculations on molecules are evaluated. Compact, arbitrarily accurate expressions are obtained. They are expressed through molecular auxiliary functions and evaluated with the numerical Global-adaptive method for arbitrary values of parameters in the noninteger Slater-type orbitals. Highly accurate benchmark values are presented for these integrals. The convergence properties of new molecular auxiliary functions are investigated. The comparison for two-center two-electron integrals is made with results obtained from single center expansions by translation of the wave function to a single center with integer principal quantum numbers and results obtained from the Cuba numerical integration algorithm, respectively. The procedures discussed in this work are capable of yielding highly accurate two-center two-electron integrals for all ranges of orbital parameters.
Benchmark values for molecular two-electron integrals arising from the Dirac equation.
Bağcı, A; Hoggan, P E
2015-02-01
The two-center two-electron Coulomb and hybrid integrals arising in relativistic and nonrelativistic ab initio calculations on molecules are evaluated. Compact, arbitrarily accurate expressions are obtained. They are expressed through molecular auxiliary functions and evaluated with the numerical Global-adaptive method for arbitrary values of parameters in the noninteger Slater-type orbitals. Highly accurate benchmark values are presented for these integrals. The convergence properties of new molecular auxiliary functions are investigated. The comparison for two-center two-electron integrals is made with results obtained from single center expansions by translation of the wave function to a single center with integer principal quantum numbers and results obtained from the Cuba numerical integration algorithm, respectively. The procedures discussed in this work are capable of yielding highly accurate two-center two-electron integrals for all ranges of orbital parameters.
Role of Interactions in Electronic Structure of a Two-Electron Quantum Dot Molecule
Institute of Scientific and Technical Information of China (English)
DONG Qing-Rui; XU Ying-Qiang; ZHANG Shi-Yong; NIU Zhi-Chuan
2004-01-01
@@ We have studied a two-electron quantum dot molecule in a magnetic field. The electron interaction is treated accurately by the direct diagonalization of the Hamiltonian matrix. We calculate two lowest energy levels of the two-electron quantum dot molecule in a magnetic field. Our results show that the electron interactions are significant, as they can change the total spin of the two-electron ground state of the system by adjusting the magnetic field between S = 0 and S = 1. The energy difference △E between the lowest S = 0 and S = 1 states is shown as a function of the axial magnetic field. We found that the energy difference between the lowest S = 0 and S = 1 states in the strong-B S = 0 state varies linearly. Our results provide a possible realization for a qubit to be fabricated by current growth techniques.
Quantum ballistic transport by interacting two-electron states in quasi-one-dimensional channels
Energy Technology Data Exchange (ETDEWEB)
Huang, Danhong [Air Force Research Laboratory, Space Vehicles Directorate, Kirtland Air Force Base, New Mexico 87117 (United States); Center for High Technology Materials, University of New Mexico, 1313 Goddard St SE, Albuquerque, New Mexico 87106 (United States); Gumbs, Godfrey [Center for High Technology Materials, University of New Mexico, 1313 Goddard St SE, Albuquerque, New Mexico 87106 (United States); Abranyos, Yonatan [Department of Physics and Astronomy, Hunter College of the City University of New York, 695 Park Avenue, New York, New York 10065 (United States); Pepper, Michael; Kumar, Sanjeev [Department of Electronic and Electrical Engineering, University College London, London, WC1E 7JE (United Kingdom); London Centre for Nanotechnology, 17-19 Gordon Street, London, WC1H 0AH (United Kingdom)
2015-11-15
For quantum ballistic transport of electrons through a short conduction channel, the role of Coulomb interaction may significantly modify the energy levels of two-electron states at low temperatures as the channel becomes wide. In this regime, the Coulomb effect on the two-electron states is calculated and found to lead to four split energy levels, including two anticrossing-level and two crossing-level states. Moreover, due to the interplay of anticrossing and crossing effects, our calculations reveal that the ground two-electron state will switch from one anticrossing state (strong confinement) to a crossing state (intermediate confinement) as the channel width gradually increases and then back to the original anticrossing state (weak confinement) as the channel width becomes larger than a threshold value. This switching behavior leaves a footprint in the ballistic conductance as well as in the diffusion thermoelectric power of electrons. Such a switching is related to the triple spin degeneracy as well as to the Coulomb repulsion in the central region of the channel, which separates two electrons away and pushes them to different channel edges. The conductance reoccurrence region expands from the weak to the intermediate confinement regime with increasing electron density.
Relaxation and Dephasing in a Two-Electron 13C Nanotube Double Quantum Dot
DEFF Research Database (Denmark)
Churchill, H O H; Kuemmeth, Ferdinand; Harlow, J W;
2009-01-01
We use charge sensing of Pauli blockade (including spin and isospin) in a two-electron 13C nanotube double quantum dot to measure relaxation and dephasing times. The relaxation time T1 first decreases with a parallel magnetic field and then goes through a minimum in a field of 1.4 T. We attribute...
Observation and spectroscopy of a two-electron Wigner molecule in an ultraclean carbon nanotube
DEFF Research Database (Denmark)
Pecker, S.; Kuemmeth, Ferdinand; Secchi, A.;
2013-01-01
Two electrons on a string form a simple model system where Coulomb interactions are expected to play an interesting role. In the presence of strong interactions, these electrons are predicted to form a Wigner molecule, separating to the ends of the string. This spatial structure is believed...
Calculation of differential cross section for dielectronic recombination with two-electron uranium
Lyashchenko, Konstantin N
2016-01-01
Calculation of the differential cross section for the dielectronic recombination with two-electron uranium within the framework of QED is presented. The polarization of the emitted photon is investigated. The contributions of the Breit interaction and the interference of the photon multipoles are studied.
Dimensionality effect on two-electron energy spectrum: A fractional-dimension-based formulation
Energy Technology Data Exchange (ETDEWEB)
Correa, R.; Gutiérrez, W.; Mikhailov, I. [Escuela de Física, Universidad Industrial de Santander, A.A. 678, Bucaramanga (Colombia); Fulla, M.R. [Escuela de Física, Universidad Nacional de Colombia, A.A. 3840, Medellín (Colombia); Marín, J.H., E-mail: jhmarin@unal.edu.co [Escuela de Física, Universidad Nacional de Colombia, A.A. 3840, Medellín (Colombia)
2015-07-17
We analyze the spectrum of two-electron quantum dot with anisotropic parabolic confinement by using the fractional-dimension formulation which allows us to reduce the two-particle problem to two equations for independent particles in an effective space with variable dimension, ranging between two and three for ellipsoidal-shaped quantum dots and between one and two for elliptical-shaped quantum disks. The dependencies of energy levels on the heterostructure sizes for quantum dots, disks and wires are presented. - Highlights: • We report the two-electron eigenenergies in a quantum dot with anisotropic parabolic confinement. • Our model is versatile enough to consider changes in the dimension space from 3 to 2 and 2 to 1. • The two-electron structure is calculated in integer and fractional dimensional spaces. • The two-electron energy structure is sensitive to the quantum dot size and morphology changes. • The electron–electron Coulomb interaction is strongly dependent on the space dimensionality.
Pseudospectral sampling of Gaussian basis sets as a new avenue to high-dimensional quantum dynamics
Heaps, Charles
. The pseudospectral sampling of Gaussian basis functions introduces a new and efficient means of calculating the underlying quantum mechanics associated with trajectory-guided basis sets. We also discuss the conceptual connections to the quantum trajectory method and the benefits of solving quantum mechanics on a discrete grid. We include a chapter studying the strengths and weaknesses of the parametric two-electron reduced-density-matrix (p2-RDM) method for systems susceptible to delocalization error. Density matrix methods are known to overestimate the energetic effects of electron delocalization, including severe effects such as diatomic dissociation to fractionally charged atoms. We consider the role of delocalization error in p2-RDM and demonstrate that the p2-RDM is resistant to delocalization error in challenging cases.
Highly accurate wavefunctions for two-electron systems using two parameteres
Chauhan, Rabeet Singh
2015-01-01
It is shown for two electron atoms that ground-state wavefunctions of the form $\\Psi(\\vec{r_{1}}, \\vec{r_{2}})=\\phi(\\vec{r_{1}})\\phi(\\vec{r_{2}})(\\cosh ar_{1}+\\cosh ar_{2})(1+0.5 r_{12}e^{-b r_{12}})$ where $\\vec{r_{1}}$ and $\\vec{r_{2}}$ are the coordinates of two electrons and $r_{12}=|\\vec{r_{1}}-\\vec{r_{2}}|$, can be made highly accurate by optimizing $a$, $b$ and $\\phi$. This is done by solving a variationally derived equation for $\\phi$ for a given $a$ and $b$ and finding $a$ and $b$ so that the expectation value of the Hamiltonian is minimum. For the set $\\{a, b, \\phi\\}$ the values for various quantities obtained from the above wavefunction are compared with those given by $204$-parameter wavefunction of Koga et al. and are found to be matching quite accurately(within ppm) with them.
Energy Technology Data Exchange (ETDEWEB)
King, Paul W [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Lubner, Carolyn E [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Mulder, David W [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Zhang, Peng [Duke University; Yuly, Jonathon [Duke University; Peters, John W. [Washington State University; Beratan, David N. [Duke University
2017-09-06
How can proteins drive two electrons from a redox active donor onto two acceptors at very different potentials and distances? And how can this transaction be conducted without dissipating very much energy or violating the laws of thermodynamics? Nature appears to have addressed these challenges by coupling thermodynamically uphill and downhill electron transfer reactions, using two-electron donor cofactors that have very different potentials for the removal of the first and second electron. Although electron bifurcation is carried out with near perfection from the standpoint of energy conservation and electron delivery yields, it is a biological energy transduction paradigm that has only come into focus recently. This Account provides an exegesis of the biophysical principles that underpin electron bifurcation.
Coulomb barrier and exchange interaction in dynamical two-electron systems
Gregoire, Maxwell; Lougovski, Pavel; Batelaan, Herman
2012-06-01
Recent electron sources can produce pulses containing multiple electrons that are confined both laterally and longitudinally. Given that the highest reported degeneracy for continuous sources of free electrons is about 10-4, it would be interesting to know the degeneracy for these pulsed sources. We previously studied one-dimensional two-electron degeneracy [1], and we now study three-dimensional two-electron degeneracy as a function of time. Our primary goal is to use this project as a necessary step to studying three-dimensional n-electron degeneracy. Our second goal is to develop a theory that predicts the outcome of Hasselbach's experiment demonstrating the Hanbury Brown-Twiss Effect [2] for free electrons.[4pt] [1] Lougovski P, and Batelaan H, Phys. Rev. A 84, 023417 (2011).[0pt] [2] Kiesel H, Renz A, and Hasselbach F, Nature. 418, 392-4 (2002).
A compact terahertz free-electron laser with two gratings driven by two electron-beams
Liu, Weihao; Lu, Yalin; Wang, Lin; Jia, Qika
2017-02-01
We proposed and investigated a novel terahertz free-electron laser, which is based on two gratings driven by two electron-beams. Two gratings are symmetrically arranged to form an open-cavity. Two electron-beams generate special Smith-Purcell radiations, respectively, from two gratings. When radiation interferes constructively, operation modes of the open-cavity are excited and then amplified by beam-wave interactions. By means of particle-in-cell simulations, we have shown that, with compact equipments and available electron-beams, this scheme can generate radiation with power and efficiency being higher than those of majority radiation sources in the vicinity region of 1 THz. It can promisingly be developed as a high-power, high-efficiency, and compact terahertz source for practice.
Fourier transform technique in variational treatment of two-electron parabolic quantum dot
Institute of Scientific and Technical Information of China (English)
S.(S)akiro(g)lu; A.Yildiz; (U).Dogan; K.Akgüng(o)r; H.Epik; Y.Ergün; H.Sarl; I.S(o)kmen
2009-01-01
In this work,we propose an efficient method of reducing the computational effort of variational calculation with a Hylleraas-like trial wavefunction.The method consists of introducing integral transforms for the terms as r12k exp (-λr12)which provide the calculation of the expectation value of energy and the relevant matrix elements to be done analytically over single-electron coordinates instead of Hylleraas coordinates.We have used this method to calculate the ground state energy of a two-electron system in a spherical dot and a disk-like quantum dot separately.Under parabolic confinement potential and within effective mass approximation size and shape effects of quantum dots on the ground state energy of two electrons have been investigated.The calculation shows that our results even with a small number of basis states axe in good agreement with previous theoretical results.
The structure of approximate two electron wavefunctions in intense laser driven ionization dynamics
Sato, Takeshi
2014-01-01
The structure of approximate two electron wavefunction is deeply investigated, both theoretically and numerically, in the strong-field driven ionization dynamics. Theoretical analyses clarify that for two electron singlet systems, the previously proposed time-dependent extended Hartree-Fock (TD-EHF) method [Phys. Rev. A 51, 3999 (1995)] is equivalent to the multiconfiguration time-dependent Hartree-Fock method with two occupied orbitals. The latter wavefunction is further transformed into the natural expansion form, enabling the direct propagation of the natural orbitals (NOs). These methods, as well as the conventional time-dependent Hartree-Fock (TDHF) method, are numerically assessed for the description of ionization dynamics of one-dimensional helium atom model. This numerical analysis (i) explains the reason behind the well-known failure of TDHF method to describe tunneling ionization, (ii) demonstrates the interpretive power of the TD-EHF wavefunction both in the original nonorthogonal and the NO-based ...
Computation of energy states of hydrogenic quantum dot with two-electrons
Yakar, Y.; Özmen, A.; ćakır, B.
2016-03-01
In this study we have investigated the electronic structure of the hydrogenic quantum dot with two electrons inside an impenetrable potential surface. The energy eigenvalues and wavefunctions of the ground and excited states of spherical quantum dot have been calculated by using the Quantum Genetic Algorithm (QGA) and Hartree-Fock Roothaan (HFR) method, and the energies are investigated as a function of dot radius. The results show that as dot radius increases, the energy of quantum dot decreases.
Quantum Size Effects on Two Electrons and Two Holes in Double-Layer Quantum Dots
Institute of Scientific and Technical Information of China (English)
XIE Wen-Fang; ZHU Wu
2002-01-01
We propose a procedure to solve exactly the Schrodinger equation for a system of two electrons and two holes in a double-layer quantum dot by using the method of few-body physics. The features of the low-lying spectra have been deduced based on symmetry. The binding energies of the ground state are obtained as a function of the electron-to-hole mass ratio σ for a few values of the quantum dot size.
Two-Electron Energy Spectrum in a Parabolic Quantum Dot Under a Magnetic Field
Institute of Scientific and Technical Information of China (English)
XIE Wen-Fang
2003-01-01
Two interacting electrons in a harmonic oscillator potential under the influence of a perpendicular homo-geneous magnetic field are considered. The energies of two-electron quantum dots with the electron-LO-phonon couplingas a function of magnetic field are calculated. Calculations are made by using the method of few-body physics withinthe effective-mass approximation. Our results show that the electron-LO-phonon coupling effect is very important insemiconductor quantum dots.
Frustrated double and single ionization in a two-electron triatomic molecule H$^+_3$
Chen, A; Price, H; Emmanouilidou, A
2016-01-01
Using a semi-classical model, we study the formation of highly excited neutral fragments during the fragmentation of $\\mathrm{H_3^+}$, a two-electron triatomic molecule, driven by an intense near-IR laser field. To do so, we first formulate a microcanonical distribution for arbitrary one-electron triatomic molecules. We then study frustrated double and single ionization in strongly-driven $\\mathrm{H_3^+}$ and compute the kinetic energy release of the nuclei for these two processes. Moreover, we investigate the dependence of frustrated ionization on the strength of the laser field as well as on the geometry of the initial molecular state.
Analytic derivatives for the Cholesky representation of the two-electron integrals.
Aquilante, Francesco; Lindh, Roland; Pedersen, Thomas Bondo
2008-07-21
We propose a formalism for calculating analytic derivatives of the electronic energy with respect to nuclear coordinates using Cholesky decomposition of the two-electron integrals. The formalism is derived by exploiting the equivalence of Cholesky decomposition and density fitting when a suitable auxiliary basis set is used for expanding atomic orbital product densities in the latter. An implementation of gradients at the nonhybrid density functional theory level is presented, and sample calculations demonstrate that the errors in equilibrium geometries due to the Cholesky representation of the integrals can be controlled by adjusting the decomposition threshold.
Effect of Coulomb Interaction on Dynamical Localization in a Two-Electron Quantum-Dot Molecule
Institute of Scientific and Technical Information of China (English)
WANG Li-Min; DUAN Su-Qing; ZHAO Xian-Geng; LIU Cheng-Shi
2004-01-01
The combined interaction of Coulomb interaction and ac fields with two electrons in a quantum dot molecule is studied respectively with numerical simulation, perturbation theory and the approximation of driven two-level model. The dynamical localization occurs with the ac field whose ratio of the amplitude to the angular frequency is a root of n-order Bessel functions, where n is determined by the Coulomb interaction energy. Such results are explained with either the driven two-level approximation or the degenerated three-level model and verified by the numerical simulations.
t-SURFF: Fully Differential Two-Electron Photo-Emission Spectra
Scrinzi, Armin
2012-01-01
The time dependent surface flux (t-SURFF) method is extended to single and double ionization of two electron systems. Fully differential double emission spectra by strong pulses at extreme UV and infrared wave length are calculated using simulation volumes that only accommodate the effective range of the atomic binding potential and the quiver radius of free electrons in the external field. For a model system we find pronounced dependence of shake-up and non-sequential double ionization on phase and duration of the laser pulse. Extension to fully three-dimensional calculations is discussed.
Theory of Square-Wave Voltammetry of Two-Electron Reduction with the Adsorption of Intermediate
Directory of Open Access Journals (Sweden)
Milivoj Lovric
2012-01-01
Full Text Available Thermodynamically unstable intermediate of fast and reversible two-electron electrode reaction can be stabilized by the adsorption to the electrode surface. In square-wave voltammetry of this reaction mechanism, the split response may appear if the electrode surface is not completely covered by the adsorbed intermediate. The dependence of the difference between the net peak potentials of the prepeak and postpeak on the square-wave frequency is analyzed theoretically. This relationship can be used for the estimation of adsorption constant.
Dynamic Localization Condition of Two Electrons in a Strong dc-ac Biased Quantum Dot Molecule
Institute of Scientific and Technical Information of China (English)
WANG Li-Min; DUAN Su-Qing; ZHAO Xian-Geng; LIU Cheng-Shi
2004-01-01
@@ We present a perturbation investigation of dynamic localization condition of two electrons in a strong dc-ac biased quantum dot molecule. By reducing the system to an Hubbard-type effective two-site model and by applying Floquet theory, we find that the dynamical localization phenomenon occurs under certain values of the large strength of the dc and ac field. This demonstrates the possibility of using appropriate dc-ac fields to manipulate dynamical localized states in mesoscopic devices, which is an essential component of practical schemes for quantum information processing. Our conclusion is instructive to the field of quantum function devices.
Two-electron Oxidation of a Twisted Non Anti-aromatic 40π Expanded Isophlorin
Indian Academy of Sciences (India)
PRACHI GUPTA; SANTOSH P PANCHAL; VENKATARAMANARAO G ANAND
2016-11-01
Expanded isophlorins are typical examples for stable anti-aromatic systems. Paratropic ring current effects are observed in their NMR spectra mainly due to their planar conformation. Herein we report the synthesis of the first twisted 40π expanded isophlorin and also its two-electron oxidation to a 38π dication. It sustains the twisted conformation for the 4nπ and (4n+2)π electrons. Due to the non-planar conformation, they do not display ring current effects in their respective 1H NMR spectrum. NICS calculations reveal the non-(anti)aromatic features for the neutral 40π and the 38π dication species.
Relaxation and Dephasing in a Two-Electron 13C Nanotube Double Quantum Dot
DEFF Research Database (Denmark)
Churchill, H O H; Kuemmeth, Ferdinand; Harlow, J W
2009-01-01
We use charge sensing of Pauli blockade (including spin and isospin) in a two-electron 13C nanotube double quantum dot to measure relaxation and dephasing times. The relaxation time T1 first decreases with a parallel magnetic field and then goes through a minimum in a field of 1.4 T. We attribute...... both results to the spin-orbit-modified electronic spectrum of carbon nanotubes, which at high field enhances relaxation due to bending-mode phonons. The inhomogeneous dephasing time T2* is consistent with previous data on hyperfine coupling strength in 13C nanotubes....
Comparative characterization of two-electron wavefunctions using information-theory measures
Energy Technology Data Exchange (ETDEWEB)
Howard, I.A., E-mail: ihoward@vub.ac.b [Department of Chemistry (ALGC), Free University of Brussels (VUB), B-1050, Brussels, Belgium/Member of the QCMM-Alliance Ghent-Brussels (Belgium); Borgoo, A.; Geerlings, P. [Department of Chemistry (ALGC), Free University of Brussels (VUB), B-1050, Brussels, Belgium/Member of the QCMM-Alliance Ghent-Brussels (Belgium); Sen, K.D. [School of Chemistry, University of Hyderabad, Hyderabad 500046 (India)
2009-08-31
Information-theory measures, in particular the Shannon entropy, Fisher information and statistical complexity, are used to discuss the variations among several commonly encountered model two-electron correlated wavefunctions. The Hookean, Moshinsky, and three-parameter Chandrasekhar wavefunctions are considered in real and momentum space, with further comparisons to the Hookean-Hartree-Fock (HF) wavefunction of Ragot, the numerical HF limit, and the hydrogenic (pure Coulomb) limit. The purpose of the study is to quantitatively analyze the effect of different models for inclusion of electron-electron correlation on information-theoretical measures, including statistical complexity, which characterize the electron distribution in position and momentum space.
Double ionization in R -matrix theory using a two-electron outer region
Wragg, Jack; Parker, J. S.; van der Hart, H. W.
2015-08-01
We have developed a two-electron outer region for use within R -matrix theory to describe double ionization processes. The capability of this method is demonstrated for single-photon double ionization of He in the photon energy region between 80 and 180 eV. The cross sections are in agreement with established data. The extended R -matrix with time dependence method also provides information on higher-order processes, as demonstrated by the identification of signatures for sequential double ionization processes involving an intermediate He+ state with n =2 .
Indian Academy of Sciences (India)
M Akbari-Moghanjoughi; N Ahmadzadeh-Khosroshahi
2011-08-01
Oblique interaction of small- but ﬁnite-amplitude KdV-type electron-acoustic solitary excitations is examined in an unmagnetized two-electron-populated degenerate quantum electron–ion plasma in the framework of quantum hydrodynamics model using the extended Poincaré–Lighthill–Kuo (PLK) perturbation method. Critical plasma parameter is found to distinguish the types of solitons and their interaction phase-shifts. It is shown that, depending on the critical quantum diffraction parameter cr, both compressive and rarefactive solitary excitations may exist in this plasma and their collision phase-shifts can be either positive or negative for the whole range of collision angles 0 < θ < .
Nonrelativistic structure calculations of two-electron ions in a strongly coupled plasma environment
Energy Technology Data Exchange (ETDEWEB)
Bhattacharyya, S.; Saha, J. K.; Mukherjee, T. K.
2015-04-01
In this work, the controversy between the interpretations of recent measurements on dense aluminum plasma created with the Linac coherent light source (LCLS) x-ray free electron laser (FEL) and the Orion laser has been addressed. In both kinds of experiments, heliumlike and hydrogenlike spectral lines are used for plasma diagnostics. However, there exist no precise theoretical calculations for He-like ions within a dense plasma environment. The strong need for an accurate theoretical estimate for spectral properties of He-like ions in a strongly coupled plasma environment leads us to perform ab initio calculations in the framework of the Rayleigh-Ritz variation principle in Hylleraas coordinates where an ion-sphere potential is used. An approach to resolve the long-drawn problem of numerical instability for evaluating two-electron integrals with an extended basis inside a finite domain is presented here. The present values of electron densities corresponding to the disappearance of different spectral lines obtained within the framework of an ion-sphere potential show excellent agreement with Orion laser experiments in Al plasma and with recent theories. Moreover, this method is extended to predict the critical plasma densities at which the spectral lines of H-like and He-like carbon and argon ions disappear. Incidental degeneracy and level-crossing phenomena are being reported for two-electron ions embedded in strongly coupled plasma. Thermodynamic pressure experienced by the ions in their respective ground states inside the ion spheres is also reported.
Giesbertz, K J H; Pernal, K; Gritsenko, O V; Baerends, E J
2009-03-21
Time-dependent density functional theory in its current adiabatic implementations exhibits three striking failures: (a) Totally wrong behavior of the excited state surface along a bond-breaking coordinate, (b) lack of doubly excited configurations, affecting again excited state surfaces, and (c) much too low charge transfer excitation energies. We address these problems with time-dependent density matrix functional theory (TDDMFT). For two-electron systems the exact exchange-correlation functional is known in DMFT, hence exact response equations can be formulated. This affords a study of the performance of TDDMFT in the TDDFT failure cases mentioned (which are all strikingly exhibited by prototype two-electron systems such as dissociating H(2) and HeH(+)). At the same time, adiabatic approximations, which will eventually be necessary, can be tested without being obscured by approximations in the functional. We find the following: (a) In the fully nonadiabatic (omega-dependent, exact) formulation of linear response TDDMFT, it can be shown that linear response (LR)-TDDMFT is able to provide exact excitation energies, in particular, the first order (linear response) formulation does not prohibit the correct representation of doubly excited states; (b) within previously formulated simple adiabatic approximations the bonding-to-antibonding excited state surface as well as charge transfer excitations are described without problems, but not the double excitations; (c) an adiabatic approximation is formulated in which also the double excitations are fully accounted for.
Simulation of molecular Auger spectra using a two-electron Dyson propagator
Energy Technology Data Exchange (ETDEWEB)
Hori, Y.; Nishida, M.; Lim, F.H.; Ida, T., E-mail: ida@se.kanazawa-u.ac.jp; Mizuno, M.
2016-02-15
Highlights: • Auger electron spectra (AES) simulation using a new two-electron Dyson propagator. • Double ionization potentials can be accurately and efficiently computed. • The proposal method is useful for belonging peaks in AES of molecule. - Abstract: In order to simulate Auger electron spectra (AES), we propose the use of the two-electron Dyson propagator with the shifted denominator approximation (SD2). The double ionization potentials (DIPs) of molecules calculated using the SD2 method have shown good agreement with experimental data. This method can be used to calculate each DIP separately, and reducing the matrix dimensionality into that of only a two-hole configurations. We carried out AES simulations of water (H{sub 2}O), ethylene (C{sub 2}H{sub 4}), and formaldehyde (H{sub 2}CO) molecules and compared with the observed spectra. Furthermore Auger line shapes of glycine and hydrated glycine molecules were simulated, it found out that the peaks of nitrogen K-LL Auger were broadened due to hydration. From these results, we conclude that the SD2 method is very useful for the calculation of DIPs to investigate the properties of a double ionized molecule.
Ion-acoustic solitons in negative ion plasma with two-electron temperature distributions
Energy Technology Data Exchange (ETDEWEB)
Mishra, M. K.; Tiwari, R. S.; Chawla, J. K. [Department of Physics, University of Rajasthan, Jaipur-302004 (India)
2012-06-15
Ion-acoustic solitons in a warm positive and negative ion species with different masses, concentrations, and charge states with two electron temperature distributions are studied. Using reductive perturbation method, Korteweg de-Vries (KdV) and modified-KdV (m-KdV) equations are derived for the system. The soliton solution of the KdV and m-KdV equations is discussed in detail. It is found that if the ions have finite temperatures, then there exist two types of modes, namely slow and fast ion-acoustic modes. It is also investigated that the parameter determining the nature of soliton (i.e., whether the system will support compressive or rarefactive solitons) is different for slow and fast modes. For the slow mode, the parameter is the relative temperature of the two ion species; whereas for the fast mode, it is the relative concentration of the two ion species. At a critical concentration of negative ions, both compressive and rarefactive solitons coexist. The amplitude and width of the solitons are discussed in detail at critical concentration for m-KdV solitons. The effect of the relative temperature of the two-electron and cold-electron concentration on the characteristics of the solitons are also discussed.
Two-electron electrochemical oxidation of quercetin and kaempferol changes only the flavonoid C-ring
DEFF Research Database (Denmark)
Jørgensen, Lars; Cornett, Claus; Justesen, Ulla
1998-01-01
Bulk electrolysis of the antioxidant flavonoids quercetin and kaempferol in acetonitrile both yield a single oxidation product in two-electron processes. The oxidation products are more polar than their parent compounds, with an increased molecular weight of 16g/mol, and were identified as 2......-(3,4-dihydroxybenzoyl)-2,4,6-trihydroxy-3 (2H)-benzofuranone and 2-(4-hydroxybenzoyl)-2,4,6-trihydroxy-3(2H)-benzofuranone for quercetin and kaempferol, respectively. Two-electron oxidation of the parent flavonoid is suggested to yield a 3,4-flavandione with unchanged substitution pattern in the A- and B-ring, which...... may rearrange to form the substituted 3(2H)-benzofuranone through the chalcan-trione ring-chain tautomer. The acidity of the 3-OH group is suggested to determine the fate of the flavonoid phenoxyl radical originally formed by one-electron oxidation, as no well-defined oxidation product of luteolin...
Observation of coherent population trapping in a V-type two-electron system
Singh, Alok K
2015-01-01
We observe coherent population trapping (CPT) in a two-electron atom---$^{174}$Yb---using the $\\rm {^1S_0,F=0} \\rightarrow {^3P_1,F'=1}$ transition. CPT is not possible for such a transition according to one-electron theory because the magnetic sublevels form a V-type system, but in a two-electron atom like Yb, the interaction of the electrons transforms the level structure into a $ \\Lambda $-type system, which allows the formation of a dark state and hence the observation of CPT. Since the two levels involved are degenerate, we use a magnetic field to lift the degeneracy. The single fluorescence dip then splits into five dips---the central unshifted one corresponds to coherent population oscillation, while the outer four are due to CPT. The linewidth of the CPT resonance is about 300 kHz and is limited by the natural linewidth of the excited state, which is to be expected because the excited state is involved in the formation of the dark state.
Quantum Interferometry and Correlated Two-Electron Wave-Packet Observation in Helium
Ott, Christian; Raith, Philipp; Meyer, Kristina; Laux, Martin; Zhang, Yizhu; Hagstotz, Steffen; Ding, Thomas; Heck, Robert; Pfeifer, Thomas
2012-01-01
The concerted motion of two or more bound electrons governs atomic and molecular non-equilibrium processes and chemical reactions. It is thus a long-standing scientific dream to measure the dynamics of two bound correlated electrons in the quantum regime. Quantum wave packets were previously observed for single-active electrons on their natural attosecond timescales. However, at least two active electrons and a nucleus are required to address the quantum three-body problem. This situation is realized in the helium atom, but direct time-resolved observation of two-electron wave-packet motion remained an unaccomplished challenge. Here, we measure a 1.2-femtosecond quantum beating among low-lying doubly-excited states in helium to evidence a correlated two-electron wave packet. Our experimental method combines attosecond transient-absorption spectroscopy at unprecedented high spectral resolution (20 meV near 60 eV) with an intensity-tuneable visible laser field to couple the quantum states from the perturbative ...
Çakır, Bekir; Yakar, Yusuf; Özmen, Ayhan
2015-02-01
Linear and nonlinear absorption coefficients of two-electron spherical quantum dot (QD) with parabolic potential are investigated in this paper. Wave functions and energy eigenvalues of the 1s2, 1s1p, 1s1d and 1s1f electronic states have been computed by using an optimization approach, which is a combination of Quantum Genetic Algorithm (QGA) and Hartree-Fock Roothaan (HFR) method. It is found that the strength of S→P transition is stronger than P→D and D→F transitions. Also the peak positions and amplitudes of the absorption coefficients are sensitive to the electron spin. It should be noted that the peak positions and amplitudes of absorption coefficients are strongly dependent on the parabolic potential. Additionally, dot radius, impurity charge, incident optical intensity and relaxation time have a great influence on the linear and nonlinear absorption coefficients.
Electronic structure of two-electron quantum dot with parabolic potential
Yakar, Yusuf; Çakır, Bekir; Özmen, Ayhan
2015-01-01
In this study, we investigate the parabolic potential effects on the ground and excited energy states of two-electron quantum dot with impurity inside an infinite spherical confining potential well. The wave function and energy eigenvalues were calculated using a modified variational optimization procedure based mainly on quantum genetic algorithm and Hartree-Fock-Roothaan method. The results show that the parabolic potential and impurity charge have a strong effect on the energy states and ionization energies. It is worth pointing out that as impurity charge increases, the ionization energy rises, but the ionization dot radius decreases. On the other hand, as parabolic potential increases, the ionization energy decreases, but the ionization dot radius increases.
Energy Technology Data Exchange (ETDEWEB)
Çakır, Bekir, E-mail: bcakir@selcuk.edu.tr [Physics Department, Faculty of Science, Selcuk University, Campus 42075, Konya (Turkey); Yakar, Yusuf, E-mail: yuyakar@yahoo.com [Physics Department, Faculty of Arts and Science, Aksaray University, Campus 68100, Aksaray (Turkey); Özmen, Ayhan [Physics Department, Faculty of Science, Selcuk University, Campus 42075, Konya (Turkey)
2015-02-01
Linear and nonlinear absorption coefficients of two-electron spherical quantum dot (QD) with parabolic potential are investigated in this paper. Wave functions and energy eigenvalues of the 1s{sup 2}, 1s1p, 1s1d and 1s1f electronic states have been computed by using an optimization approach, which is a combination of Quantum Genetic Algorithm (QGA) and Hartree–Fock Roothaan (HFR) method. It is found that the strength of S→P transition is stronger than P→D and D→F transitions. Also the peak positions and amplitudes of the absorption coefficients are sensitive to the electron spin. It should be noted that the peak positions and amplitudes of absorption coefficients are strongly dependent on the parabolic potential. Additionally, dot radius, impurity charge, incident optical intensity and relaxation time have a great influence on the linear and nonlinear absorption coefficients.
Ground State of a Two-Electron Quantum Dot with a Gaussian Confining Potential
Institute of Scientific and Technical Information of China (English)
XIE Wen-Fang
2006-01-01
We investigate the ground-state properties of a two-dimensional two-electron quantum dot with a Gaussian confining potential under the influence of perpendicular homogeneous magnetic field. Calculations are carried out by using the method of numerical diagonalization of Hamiltonian matrix within the effective-mass approximation. A ground-state behaviour (singlet→triplet state transitions) as a function of the strength of a magnetic field has been found. It is found that the dot radius R of the Gaussian potential is important for the ground-state transition and the feature of ground-state for the Gaussian potential quantum dot (QD), and the parabolic potential QDs are similar when R is larger. The larger the quantum dot radius, the smaller the magnetic field for the singlet-triplet transition of the ground-state of two interacting electrons in the Gaussian quantum dot.
Fast calculation of two-electron-repulsion integrals: a numerical approach
Lopes, Pedro E M
2016-01-01
An alternative methodology to evaluate two-electron-repulsion integrals based on numerical approximation is proposed. Computational chemistry has branched into two major fields with methodologies based on quantum mechanics and classical force fields. However, there are significant shadowy areas not covered by any of the available methods. Many relevant systems are often too big for traditional quantum chemical methods while being chemically too complex for classical force fields. Examples include systems in nanomedicine, studies of metalloproteins, etc. There is an urgent need to develop fast quantum chemical methods able to study large and complex systems. This work is a proof-of-concept on the numerical techniques required to develop accurate and computationally efficient algorithms for the fast calculation of electron-repulsion integrals, one of the most significant bottlenecks in the extension of quantum chemistry to large systems. All concepts and calculations were developed for the three-center integral...
Ab-initio calculations on two-electron ions in strongly coupled plasma environment
Bhattacharyya, S; Mukherjee, T K
2015-01-01
In this work, the controversy between the interpretations of recent measurements on dense aluminum plasma created with Linac coherent light sources (LCLS) X-ray free electron laser (FEL) and Orion laser has been addressed. In both kind of experiments, helium-like and hydrogen-like spectral lines are used for plasma diagnostics . However, there exist no precise theoretical calculations for He-like ions within dense plasma environment. The strong need for an accurate theoretical estimates for spectral properties of He-like ions in strongly coupled plasma environment leads us to perform ab initio calculations in the framework of Rayleigh-Ritz variation principle in Hylleraas coordinates where ion-sphere potential is used. An approach to resolve the long-drawn problem of numerical instability for evaluating two-electron integrals with extended basis inside a finite domain is presented here. The present values of electron densities corresponding to disappearance of different spectral lines obtained within the fram...
Katriel, Jacob; Bauer, Michael; Springborg, Michael; McCarthy, Shane P; Thakkar, Ajit J
2007-07-14
Reparametrization of Wigner's correlation energy density functional yields a very close fit to the correlation energies of the helium isoelectronic sequence. However, a quite different reparametrization is required to obtain an equally close fit to the isoelectronic sequence of Hooke's atom. In an attempt to avoid having to reparametrize the functional for different choices of the one-body potential, we propose a parametrization that depends on global characteristics of the ground-state electron density as quantified by scale-invariant combinations of expectation values of local one-body operators. This should be viewed as an alternative to the density-gradient paradigm, allowing one to introduce the nonlocal dependence of the density functional on the density in a possibly more effective way. Encouraging results are obtained for two-electron systems with one-body potentials of the form r(zeta) with zeta=-12,+12,1, which span the range between the Coulomb potential (zeta=-1) and the Hooke potential (zeta=2).
Spin-orbit coupled two-electron Fermi gases of ytterbium atoms
Song, Bo; Zhang, Shanchao; Zou, Yueyang; Haciyev, Elnur; Huang, Wei; Liu, Xiong-Jun; Jo, Gyu-Boong
2016-01-01
We demonstrate the spin-orbit coupling (SOC) in a two-electron Fermi gas of $^{173}$Yb atoms by coupling two hyperfine ground states via the two-photon Raman transition. Due to the SU($N$) symmetry of the $^1$S$_0$ ground-state manifold which is insensitive to external magnetic field, an optical AC Stark effect is applied to split the ground spin states and separate an effective spin-1/2 subspace out from other hyperfine levels for the realization of SOC. With a momentum-dependent spin-orbit gap being suddenly opened by switching on the Raman transition, the dephasing of spin dynamics is observed, as a consequence of the momentum-dependent Rabi oscillations. Moreover, the momentum asymmetry of the spin-orbit coupled Fermi gas is also examined after projection onto the bare spin state and the corresponding momentum distribution is measured for different two-photon detuning. The realization of SOC for Yb fermions may open a new avenue to the study of novel spin-orbit physics with alkaline-earth-like atoms.
Two-electron and one-photon transitions in highly charged nickel-like ions
Institute of Scientific and Technical Information of China (English)
Xie Lu-You; Dong Chen-Zhong; Jiang Jun; Wan Jian-Jie; Yan Jun
2008-01-01
This paper calculates the transition wavelengths and probabilities of the two-electron and one-photon(TEOP) transition from the(38-11/24dj)J:1,2 to(3p-13/24s1/2)J=1 and the(3p-11/2481/2)J=1 to(3d-1j4dj1)J=1,2 for highly charged Ni-like ions with atomic number Z in the range 47≤Z≤92.In the calculations,the multi-configuration Dirac-Fock method and corresponding program packages GRASP92 and REOS99 were used,and the relativistic effects,correlation effects and relaxation effects were considered systematically.It is found that the TEOP transitions are very sensitive to the correlation of electrons,and the probabilities will be enhanced sharply in some special Z regions along the isoelectronic sequence.The present TEOP transition wavelengths are compared with the available data from some previous publications,good agreement is obtained.
Spin-orbit-coupled two-electron Fermi gases of ytterbium atoms
Song, Bo; He, Chengdong; Zhang, Shanchao; Hajiyev, Elnur; Huang, Wei; Liu, Xiong-Jun; Jo, Gyu-Boong
2016-12-01
We demonstrate all-optical implementation of spin-orbit coupling (SOC) in a two-electron Fermi gas of 173Yb atoms by coupling two hyperfine ground states with a narrow optical transition. Due to the SU (N ) symmetry of the S10 ground-state manifold which is insensitive to external magnetic fields, an optical ac Stark effect is applied to split the ground spin states, which exhibits a high stability compared with experiments on alkali-metal and lanthanide atoms, and separate out an effective spin-1/2 subspace from other hyperfine levels for the realization of SOC. The dephasing spin dynamics when a momentum-dependent spin-orbit gap is suddenly opened and the asymmetric momentum distribution of the spin-orbit-coupled Fermi gas are observed as a hallmark of SOC. The realization of all-optical SOC for ytterbium fermions should offer a route to a long-lived spin-orbit-coupled Fermi gas and greatly expand our capability of studying spin-orbit physics with alkaline-earth-metal-like atoms.
Banerjee, Srijib; Furtmüller, Paul G; Obinger, Christian
2011-02-01
Lactoperoxidase (LPO), a member of the peroxidase-cyclooxygenase superfamily, is found in multiple human exocrine secretions and acts as a first line of defense against invading microorganisms by production of antimicrobial oxidants. Because of its ability to efficiently catalyze one- and two-electron oxidation reactions of inorganic and organic compounds, the heme peroxidase is widely used in food biotechnology, cosmetic industry, and diagnostic kits. In order to probe its structural integrity, conformational, and thermal stability, we have undertaken a comprehensive investigation by using complementary biophysical techniques including UV-Vis, circular dichroism and fluorescence spectroscopy as well as differential scanning calorimetry (DSC). The oxidoreductase exhibits a high chemical and thermal stability under oxidizing conditions but is significantly destabilized by addition of DTT. Due to its unique ester bonds between the prosthetic group and the protein as well as six intra-chain disulfides, unfolding of the central compact (-helical core occurs concomitantly with denaturation of the heme cavity. The corresponding enthalpic and entropic contributions to the free enthalpy of unfolding are presented. Together with spectroscopic data they will be discussed with respect to the known structure of bovine LPO and homologous myeloperoxidase as well as to its practical application.
In vivo accuracy of two electronic foramen locators based on different operation systems.
Vasconcelos, Bruno Carvalho de; Araújo, Rebeca Bastos Rocha; Silva, Francisco Cláudio Fernandes Alves e; Luna-Cruz, Suyane Maria; Duarte, Marco Antonio Hungaro; Fernandes, Carlos Augusto de Oliveira
2014-01-01
The aim of this study was to compare in vivo the accuracy of two electronic foramen locators (EFLs) based on different operation systems - Root ZX and Propex II. Ten healthy adult patients needing premolar extractions due to orthodontic reasons participated in the study, providing a sample of 17 noncarious, non-restored, vital teeth (n= 24 canals). After coronal access preparation and cervical preflaring and prior to tooth extraction, the root canal length was measured alternating the two EFLs. All measurements were performed with K-files well fitted to the canal diameter at the level that each EFL indicated the apical foramen in their display (APEX or 0.0). The last K-file were fixed in place with cyanoacrylate, the tooth was extracted, and the apical 4 mm of each root were resected to measure the distance between the file tip and the apical foramen. The mean errors based on the absolute values of discrepancies were 0.30 ± 0.29 mm (Root ZX) and 0.32 ± 0.27 mm (Propex II). Analysis by the Wilcoxon test for paired samples showed no statistically significant differences between the electronic canal measurements performed with the EFLs (p=0.587). The apical foramen was accurately located in 75% (Root ZX) and 66.7% (Propex II) of the cases, considering a ±0.5 mm error margin, with no statistically significant difference by the chi-square test. Despite having different measurement mechanisms, both EFLs were capable of locating the apical foramen with high accuracy in vivo. Under the tested clinical conditions, Root ZX and Propex II displayed similar results.
Green, Jennifer C; Green, Malcolm L H; Parkin, Gerard
2012-12-07
Although compounds that feature 3-centre 2-electron (3c-2e) bonds are well known, there has been no previous effort to classify the interactions according to the number of electrons that each atom contributes to the bond, in a manner analogous to the classification of 2-centre 2-electron (2c-2e) bonds as either normal covalent or dative covalent. This article provides an extension to the Covalent Bond Classification (CBC) method by categorizing 3c-2e interactions according to whether (i) the two electrons are provided by one or by two atoms and (ii) the central bridging atom provides two, one, or zero electrons. Class I 3c-2e bonds are defined as those in which two atoms each contribute one electron to the 3-centre orbital, while Class II 3c-2e bonds are defined as systems in which the pair of electrons are provided by a single atom. Class I and Class II 3c-2e interactions can be denoted by structure-bonding representations that employ the "half-arrow" notation, which also provides a convenient means to determine the electron count at a metal centre. In contrast to other methods of electron counting, this approach provides a means to predict metal-metal bond orders that are in accord with theory. For example, compounds that feature symmetrically bridging carbonyl ligands do not necessarily have to be described as "ketone derivatives" because carbon monoxide can also serve as an electron pair donor to two metal centres. This bonding description also provides a simple means to rationalize the theoretical predictions of the absence of M-M bonds in molecules such as Fe(2)(CO)(9) and [CpFe(CO)(2)](2), which are widely misrepresented in textbooks as possessing M-M bonds.
The case for synchrotron radiation studies of two-electron ions, atoms, and molecules at the ALS
Lubell, M. S.
1995-05-01
The theoretical description of two-electron systems has remained one of the most vexing problems in atomic physics since Bohr first introduced the concept of the quantized atom in 1913. Despite the diversity in approach, a degree of orthodoxy developed over the course of many years for characterizing and clasifying the discrete spectrum of two-electron states and for describing the features of the near-threshold double continuum. The last four years have seen this orthodoxy challenged both theoretically and experimentally. As a result, a strong need exists for additional experimental investigations of two-electron systems. We will first examine the long-held orthodox views and the recent challenges to them. We will then review the details and status of a new program at the Advanced Light Source (ALS) of Lawrence Berkeley Laboratory that has been developed by the NAU8 Collaboration to address this need.
Meier, Joseph; Kappadath, S Cheenu
2015-11-08
We characterized the energy response of personal dose equivalent (Hp(10) in mrem) and the contribution of backscatter to the readings of two electronic personal dosimeter (EPD) models with radionuclides commonly used in a nuclear medicine clinic. The EPD models characterized were the RADOS RAD-60R, and the SAIC PD-10i. The experimental setup and calculation of EPD energy response was based on ANSI/HPS N13.11-2009. Fifteen RAD-60R and 2 PD-10i units were irradiated using (99m)Tc, (131)I, and (18)F radionuclides with emission energies at 140 keV, 364 keV, and 511 keV, respectively. At each energy, the EPDs output in Hp(10) [mrem] were recorded with 15 inch thick PMMA to simulate backscatter form the torso. Simultaneous free-in-air exposure rate measurements were also performed using two Victoreen ionization survey meters to calculate the expected EPD Hp(10) values per ANSI/HPS N13.11-2009. The energy response was calculated by taking the ratio of the EPD Hp(10) readings with the expected Hp(10) readings and a two-tailed z-test was used to determine the significance of the ratio deviating away from unity. The contribution from backscatter was calculated by taking the ratio of the EPD Hp(10) readings with and without backscatter material. A paired, two-tailed t-test was used to determine the significance of change in EPD Hp(10) readings. The RAD-60R mean energy response at 140 keV was 0.85, and agreed to within 5% and 11% at 364 and 511 keV, respectively. The PD-10i mean energy response at 140 keV was 1.20, and agreed to within 5% at 364 and 511 keV, respectively. On average, in the presence of acrylic, RAD-60R values increased by 32%, 12%, and 14%, at 140, 364, and 511 keV, respectively; all increases were statistically significant. The PD-10i increased by 25%, 19%, and 10% at 140 keV, 364 keV, and 511 keV, respectively; however, only the 140 keV measurement was statistically significant. Although both EPD models performed within the manufacturers' specifications of
Directory of Open Access Journals (Sweden)
Julie A Law
2011-07-01
Full Text Available DNA methylation is an evolutionarily conserved epigenetic modification that is critical for gene silencing and the maintenance of genome integrity. In Arabidopsis thaliana, the de novo DNA methyltransferase, domains rearranged methyltransferase 2 (DRM2, is targeted to specific genomic loci by 24 nt small interfering RNAs (siRNAs through a pathway termed RNA-directed DNA methylation (RdDM. Biogenesis of the targeting siRNAs is thought to be initiated by the activity of the plant-specific RNA polymerase IV (Pol-IV. However, the mechanism through which Pol-IV is targeted to specific genomic loci and whether factors other than the core Pol-IV machinery are required for Pol-IV activity remain unknown. Through the affinity purification of nuclear RNA polymerase D1 (NRPD1, the largest subunit of the Pol-IV polymerase, we found that several previously identified RdDM components co-purify with Pol-IV, namely RNA-dependent RNA polymerase 2 (RDR2, CLASSY1 (CLSY1, and RNA-directed DNA methylation 4 (RDM4, suggesting that the upstream siRNA generating portion of the RdDM pathway may be more physically coupled than previously envisioned. A homeodomain protein, SAWADEE homeodomain homolog 1 (SHH1, was also found to co-purify with NRPD1; and we demonstrate that SHH1 is required for de novo and maintenance DNA methylation, as well as for the accumulation of siRNAs at specific loci, confirming it is a bonafide component of the RdDM pathway.
Peng, Bo; Kowalski, Karol
2017-09-12
The representation and storage of two-electron integral tensors are vital in large-scale applications of accurate electronic structure methods. Low-rank representation and efficient storage strategy of integral tensors can significantly reduce the numerical overhead and consequently time-to-solution of these methods. In this work, by combining pivoted incomplete Cholesky decomposition (CD) with a follow-up truncated singular vector decomposition (SVD), we develop a decomposition strategy to approximately represent the two-electron integral tensor in terms of low-rank vectors. A systematic benchmark test on a series of 1-D, 2-D, and 3-D carbon-hydrogen systems demonstrates high efficiency and scalability of the compound two-step decomposition of the two-electron integral tensor in our implementation. For the size of the atomic basis set, Nb, ranging from ∼100 up to ∼2,000, the observed numerical scaling of our implementation shows [Formula: see text] versus [Formula: see text] cost of performing single CD on the two-electron integral tensor in most of the other implementations. More importantly, this decomposition strategy can significantly reduce the storage requirement of the atomic orbital (AO) two-electron integral tensor from [Formula: see text] to [Formula: see text] with moderate decomposition thresholds. The accuracy tests have been performed using ground- and excited-state formulations of coupled cluster formalism employing single and double excitations (CCSD) on several benchmark systems including the C60 molecule described by nearly 1,400 basis functions. The results show that the decomposition thresholds can be generally set to 10(-4) to 10(-3) to give acceptable compromise between efficiency and accuracy.
2014-09-24
low-scaling 2-RDM method that scales computationally as O(r 4 ) where r is the number of orbitals in the one electron basis set. Further...to the foundation of 2-RDM quantum theory. Conditions beyond T2 will eventually allow for the computation of molecular quantum systems in...21. A. M. Sand and D. A. Mazziotti, “Effect of molecular - orbital rotations on ground-state energies in the parametric two-electron reduced density
Adiabatic potential energy curves of long-range Rydberg molecules: Two-electron R-matrix approach
Tarana, Michal
2016-01-01
We introduce a computational method developed for study of long-range molecular Rydberg states of such systems that can be approximated by two electrons in a model potential of the atomic cores. Only diatomic molecules are considered. The method is based on a two-electron \\rmath approach inside a sphere centered on one of the atoms. The wave function is then connected to a Coulomb region outside the sphere via multichannel version of the Coulomb Green's function. This approach is put into a test by its application to a study of Rydberg states of the hydrogen molecule for internuclear distances $R$ from 20 to 400 bohrs and energies corresponding to $n$ from 3 to 22. The results are compared with previous quantum chemical calculations (lower quantum numbers $n$) and computations based on contact potential models (higher quantum numbers $n$).
Fossgård, Eirik; Ruud, Kenneth
2006-02-01
We describe the implementation of a parallel, in-core, integral-direct Hartree-Fock and density functional theory code for the efficient calculation of Hartree-Fock wave functions and density functional theory. The algorithm is based on a parallel master-slave algorithm, and the two-electron integrals calculated by a slave are stored in available local memory. To ensure the greatest computational savings, the master node keeps track of all integral batches stored on the different slaves. The code can reuse undifferentiated two-electron integrals both in the wave function optimization and in the evaluation of second-, third-, and fourth-order molecular properties. Superlinear scaling is achieved in a series of test examples, with speedups of up to 55 achieved for calculations run on medium-sized molecules on 16 processors with respect to the time used on a single processor.
Energy Technology Data Exchange (ETDEWEB)
Noguchi, Yoshifumi [Department of Physics, Graduate School of Engineering, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501 (Japan); Computational Materials Science Center, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047 (Japan)], E-mail: NOGUCHI.Yoshifumi@nims.go.jp; Ishii, Soh; Ohno, Kaoru [Department of Physics, Graduate School of Engineering, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501 (Japan)
2007-05-15
Short-range electron correlation plays a very important role in small systems and significantly affects the double ionization energy (DIE) spectra and the two-electron distribution functions of a CO molecule, for example. In our calculations, the local density approximation (LDA) of the density functional theory is chosen as a starting point, the GW approximation (GWA) is performed in a next step, and finally the Bethe-Salpeter equation for the T-matrix, describing the particle-particle ladder diagrams up to the infinite order, is solved via the eigenvalue problem. The calculated DIE spectra, which are directly given by the eigenvalues, reflect the short-range electron correlation and are in good agreement with the experiment. We confirm that the Coulomb hole appears in the two-electron distribution function constructed from the eigenfunction.
Institute of Scientific and Technical Information of China (English)
CAI Liang; ZHANG Ping; YANG Tao; PAN Xiao-Yin
2011-01-01
By using the path integral approach, we investigate the problem of Hooke's atom (two electrons interacting with Coulomb potential in an external harmonic-oscillator potential) in an arbitrary time-dependent electric field. For a certain infinite set of discrete oscillator frequencies, we obtain the analytical solutions. The ground state polarization of the atom is then calculated. The same result is also obtained through linear response theory.
Coulomb Repulsion Effect in Two-electron Non-adiabatic Tunneling through a One-level redox Molecule
DEFF Research Database (Denmark)
Medvedev, Igor M.; Kuznetsov, Alexander M.; Ulstrup, Jens
2009-01-01
is representative of electrochemical scanning tunneling microscopy or a pair of electrochemical nanoscale electrodes. The two-electron transfer molecular system also represents redox molecules with three electrochemically accessible oxidation states, rather than only two states such as comprehensively studied...... conductance/bias voltage correlation can have up to four peaks even for a single-level redox molecule. The peak position, height, and width are determined by the oxidized and reduced states of both the ionization and affinity levels of the molecule and depend crucially on the Debye screening of the electric...
Becker, A; Faisal, F
2001-03-26
Recently observed momentum distribution of doubly charged recoil-ions of atoms produced by femtosecond infrared laser pulses is analyzed using the so-called intense-field many-body S-matrix theory. Observed characteristics of the momentum distributions, parallel and perpendicular to the polarization axis, are reproduced by the theory. It is shown that correlated energy-sharing between the two electrons in the intermediate state and their 'Volkov-dressing' in the final state, can explain the origin of these characteristics.
Energy Technology Data Exchange (ETDEWEB)
Errea, L.F.; Mendez, L.; Riera, A.
1983-06-01
In a previous paper we have pointed out that the common-translation-factor (CTF) method is the only one which, at present, and within the framework of the molecular model of atomic collisions, can be shown to be both convergent and computationally fast, even for many-electron systems. In this Communication we check that this second statement is correct, presenting, for the first time, a molecular calculation involving two-electron translation factors, for He/sup +/ + H collisions. A careful study of the sensitivity of the calculated cross sections to the choice of the CTF is performed, and conclusions on that sensitivity are drawn, for several types of processes.
Institute of Scientific and Technical Information of China (English)
胡义镇; 安静仪; 蒋丽金
1994-01-01
In this study the spectroscopic characteristics of a water-soluble derivative of hypocrellin A (HA), 14-dehydroxy-15-deacetyl-hypocrellin A-13-sulfonate(13-SO3Na-DDHA),and its one- and two-electron reduction products have been investigated. From the changes in absorbance with pH it was observed that the two phenolic hydroxy groups at C-3 and C-10 positions of 13-SO3Na-DDHA or HA dissociated stepwise with increase of pH values. The pKa values for 13-SO3Na-DDHA and HA were determined using an effective method established in this study. Attempts were also made to use absorption and ESR spectroscopies to study the photoreduction of 13-SO3Na-DDHA. It was found that 13-SO3Na-DDHA was directly reduced to its two-electron reduction product in buffered aqueous solution (pH 7. 7). However, in DMF-buffer (1 :1/ v : v,pH 7. 7), it proceeded with one-electron reduction to generate its semiquinone radical anions. The semiquinone radical anions decayed according to second-order kinetics. indicating that the terminatio
Tarana, Michal; Čurík, Roman
2016-05-01
We introduce a computational method developed for study of long-range molecular Rydberg states of such systems that can be approximated by two electrons in a model potential of the atomic cores. The method is based on a two-electron R-matrix approach inside a sphere centered on one of the atoms. The wave function is then connected to a Coulomb region outside the sphere via a multichannel version of the Coulomb Green's function. This approach is applied to a study of Rydberg states of Rb2 for internuclear separations R from 40 to 320 bohrs and energies corresponding to n from 7 to 30. We report bound states associated with the low-lying 3Po resonance and with the virtual state of the rubidium atom that turn into ion-pair-like bound states in the Coulomb potential of the atomic Rydberg core. The results are compared with previous calculations based on single-electron models employing a zero-range contact-potential and short-range modele potential. Czech Science Foundation (Project No. P208/14-15989P).
Cleaves, Peter A; King, David M; Kefalidis, Christos E; Maron, Laurent; Tuna, Floriana; McInnes, Eric J L; McMaster, Jonathan; Lewis, William; Blake, Alexander J; Liddle, Stephen T
2014-09-22
Two-electron reductive carbonylation of the uranium(VI) nitride [U(Tren(TIPS))(N)] (2, Tren(TIPS)=N(CH2CH2NSiiPr3)3) with CO gave the uranium(IV) cyanate [U(Tren(TIPS))(NCO)] (3). KC8 reduction of 3 resulted in cyanate dissociation to give [U(Tren(TIPS))] (4) and KNCO, or cyanate retention in [U(Tren(TIPS))(NCO)][K(B15C5)2] (5, B15C5=benzo-15-crown-5 ether) with B15C5. Complexes 5 and 4 and KNCO were also prepared from CO and the uranium(V) nitride [{U(Tren(TIPS))(N)K}2] (6), with or without B15C5, respectively. Complex 5 can be prepared directly from CO and [U(Tren(TIPS))(N)][K(B15C5)2] (7). Notably, 7 reacts with CO much faster than 2. This unprecedented f-block reactivity was modeled theoretically, revealing nucleophilic attack of the π* orbital of CO by the nitride with activation energy barriers of 24.7 and 11.3 kcal mol(-1) for uranium(VI) and uranium(V), respectively. A remarkably simple two-step, two-electron cycle for the conversion of azide to nitride to cyanate using 4, NaN3 and CO is presented.
Silva, Franck; Reiter, Maud; Mills-Webb, Rebecca; Sawicki, Marcin; Klär, Daniel; Bensel, Nicolas; Wagner, Alain; Gouverneur, Véronique
2006-10-27
A novel palladium(II)-catalyzed oxy-carbopalladation process was developed allowing for the orchestrated union of hydroxy ynones with ethyl acrylate, two electron-deficient reactants. With beta-hydroxy ynones, this cascade Wacker-Heck process gave access to highly functionalized tri- or tetrasubstituted dihydropyranones featuring an unusual dienic system. For diastereomerically pure and for enantioenriched beta-hydroxyynones, these reactions proceed without affecting the stereochemical integrity of the existing stereocenters. In addition, tetrasubstituted furanones can be prepared when alpha-hydroxyynones and ethyl acrylate are used as starting materials. The dihydropyranones and furanones obtained upon cyclization are novel compounds, but structurally related carbohydrate derivatives featuring a similar dienic system have been used as starting materials for the construction of polyannulated products, suggesting that these cascade Pd(II)-mediated oxidative heterocyclizations are of value for various synthetic applications.
Serov, Vladislav V; Sergeeva, Tatiana A; Vinitsky, Sergue I
2012-01-01
A review of some recently developed methods of calculating multiple differential cross-sections of photoionization and electron impactionization of atoms and molecules having two active electrons is presented. The methods imply original approaches to calculating three-particle Coulomb wave functions. The external complex scaling method and the formalism of the Schroedinger equation with a source in the right-hand side are considered. Efficiency of the time-dependent approaches to the scattering problem, such as the paraxial approximation and the time-dependent scaling, is demonstrated. An original numerical method elaborated by the authors for solving the 6D Schroedinger equation for an atom with two active electrons, based on the Chang-Fano transformation and the discrete variable representation, is formulated. Basing on numerical simulations, the threshold behavior of angular distributions of two-electron photoionization of the negative hydrogen ion and helium atom, and multiple differential cross-sections ...
Directory of Open Access Journals (Sweden)
A. Rejo Jeice
2013-09-01
Full Text Available The combined effect of hydrostatic pressure and temperature on correlation energy in a triplet state of two electron spherical quantum dot with square well potential is computed. The result is presented taking GaAs dot as an example. Our result shows the correlation energies are inegative in the triplet state contrast to the singlet state ii it increases with increase in pressure iiifurther decreases due to the application of temperature iv it approaches zero as dot size approaches infinity and v it contribute 10% decrement in total confined energy to the narrow dots. All the calculations have been carried out with finite models and the results are compared with existing literature.
[Cu13 {S2 CN(n) Bu2 }6 (acetylide)4 ](+) : A Two-Electron Superatom.
Chakrahari, Kiran Kumarvarma; Liao, Jian-Hong; Kahlal, Samia; Liu, Yu-Chiao; Chiang, Ming-Hsi; Saillard, Jean-Yves; Liu, C W
2016-11-14
The first structurally characterized copper cluster with a Cu13 centered cuboctahedral arrangement, a model of the bulk copper fcc structure, was observed in [Cu13 (S2 CN(n) Bu2 )6 (C≡CR)4 ](PF6 ) (R=C(O)OMe, C6 H4 F) nanoclusters. Four of the eight triangular faces of the cuboctahedron are capped by acetylide groups in μ3 fashion, and each of the six square faces is bridged by a dithiolate ligand in μ2 ,μ2 fashion, which leads to a truncated tetrahedron of twelve sulfur atoms. DFT calculations are fully consistent with the description of these Cu13 clusters as two-electron superatoms, that is, a [Cu13 ](11+) core passivated by ten monoanionic ligands, with an a1 HOMO containing two 1S jellium electrons.
Role of two-electron processes in the excitation-ionization of lithium atoms by fast ion impact
Kirchner, T; Gulyás, L
2015-01-01
We study excitation and ionization in the 1.5 MeV/amu O$^{8+}$-Li collision system, which was the subject of a recent reaction-microscope-type experiment [Fischer \\textit{et al.}, Phys. Rev. Lett. \\textbf{109}, 113202 (2012)]. Starting from an independent-electron model based on determinantal wave functions and using single-electron basis generator method and continuum distorted-wave with eikonal initial-state calculations we show that pure single ionization of a lithium $K$-shell electron is too weak a process to explain the measured single differential cross section. Rather, our analysis suggests that two-electron excitation-ionization processes occur and have to be taken into account when comparing with the data. Good agreement is obtained only if we replace the independent-electron calculation by an independent-event model for one of the excitation-ionization processes and also take a shake-off process into account.
Energy Technology Data Exchange (ETDEWEB)
Giesbertz, Klaas J. H. [Theoretical Chemistry, Faculty of Exact Sciences, VU University, De Boelelaan 1083, 1081 HV Amsterdam (Netherlands); Leeuwen, Robert van [Department of Physics, Nanoscience Center, University of Jyväskylä, P.O. Box 35, 40014 Jyväskylä, Survontie 9, Jyväskylä (Finland)
2014-05-14
Electron correlations in molecules can be divided in short range dynamical correlations, long range Van der Waals type interactions, and near degeneracy static correlations. In this work, we analyze for a one-dimensional model of a two-electron system how these three types of correlations can be incorporated in a simple wave function of restricted functional form consisting of an orbital product multiplied by a single correlation function f (r{sub 12}) depending on the interelectronic distance r{sub 12}. Since the three types of correlations mentioned lead to different signatures in terms of the natural orbital (NO) amplitudes in two-electron systems, we make an analysis of the wave function in terms of the NO amplitudes for a model system of a diatomic molecule. In our numerical implementation, we fully optimize the orbitals and the correlation function on a spatial grid without restrictions on their functional form. Due to this particular form of the wave function, we can prove that none of the amplitudes vanishes and moreover that it displays a distinct sign pattern and a series of avoided crossings as a function of the bond distance in agreement with the exact solution. This shows that the wave function ansatz correctly incorporates the long range Van der Waals interactions. We further show that the approximate wave function gives an excellent binding curve and is able to describe static correlations. We show that in order to do this the correlation function f (r{sub 12}) needs to diverge for large r{sub 12} at large internuclear distances while for shorter bond distances it increases as a function of r{sub 12} to a maximum value after which it decays exponentially. We further give a physical interpretation of this behavior.
Anusevicius, Zilvinas; Miseviciene, Lina; Medina, Milagros; Martinez-Julvez, Marta; Gomez-Moreno, Carlos; Cenas, Narimantas
2005-05-15
Flavoenzymes may reduce quinones in a single-electron, mixed single- and two-electron, and two-electron way. The mechanisms of two-electron reduction of quinones are insufficiently understood. To get an insight into the role of flavin semiquinone stability in the regulation of single- vs. two-electron reduction of quinones, we studied the reactions of wild type Anabaena ferredoxin:NADP(+)reductase (FNR) with 48% FAD semiquinone (FADH*) stabilized at the equilibrium (pH 7.0), and its Glu301Ala mutant (8% FADH* at the equilibrium). We found that Glu301Ala substitution does not change the quinone substrate specificity of FNR. However, it confers the mixed single- and two-electron mechanism of quinone reduction (50% single-electron flux), whereas the wild type FNR reduces quinones in a single-electron way. During the oxidation of fully reduced wild type FNR by tetramethyl-1,4-benzoquinone, the first electron transfer (formation of FADH*) is about 40 times faster than the second one (oxidation of FADH*). In contrast, the first and second electron transfer proceeded at similar rates in Glu301Ala FNR. Thus, the change in the quinone reduction mechanism may be explained by the relative increase in the rate of second electron transfer. This enabled us to propose the unified scheme of single-, two- and mixed single- and two-electron reduction of quinones by flavoenzymes with the central role of the stability of flavin/quinone ion-radical pair.
Propagating two-particle reduced density matrices without wavefunctions
Lackner, Fabian; Sato, Takeshi; Ishikawa, Kenichi L; Burgdörfer, Joachim
2014-01-01
Describing time-dependent many-body systems where correlation effects play an important role remains a major theoretical challenge. In this paper we develop a time-dependent many-body theory that is based on the two-particle reduced density matrix (2-RDM). We develop a closed equation of motion for the 2-RDM employing a novel reconstruction functional for the three-particle reduced density matrix (3-RDM) that preserves norm, energy, and spin symmetries during time propagation. We show that approximately enforcing $N$-representability during time evolution is essential for achieving stable solutions. As a prototypical test case which features long-range Coulomb interactions we employ the one-dimensional model for lithium hydride (LiH) in strong infrared laser fields. We probe both one-particle observables such as the time-dependent dipole moment and two-particle observables such as the pair density and mean electron-electron interaction energy. Our results are in very good agreement with numerically exact solu...
Energy Technology Data Exchange (ETDEWEB)
Lobayan, Rosana M., E-mail: rmlb@exa.unne.edu.ar [Departamento de Física, Facultad de Ciencias Exactas, Naturales y Agrimensura, Universidad Nacional del Nordeste, 3400, Corrientes (Argentina); Bochicchio, Roberto C., E-mail: rboc@df.uba.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, and IFIBA, CONICET, Ciudad Universitaria, 1428, Buenos Aires (Argentina)
2014-05-07
Two-electron three-center bonding interactions in organic ions like methonium (CH{sub 5}{sup +}), ethonium (C{sub 2}H{sub 7}{sup +}), and protonated alkanes n−C{sub 4}H{sub 11}{sup +} isomers (butonium cations) are described and characterized within the theoretical framework of the topological analysis of the electron density decomposition into its effectively paired and unpaired contributions. These interactions manifest in some of this type of systems as a concentration of unpaired electron cloud around the bond paths, in contrast to the well known paradigmatic boron hydrids in which it is not only concentrated close to the atomic nucleus and the bond paths but out of them and over the region defined by the involved atoms as a whole. This result permits to propose an attempt of classification for these interactions based in such manifestations. In the first type, it is called as interactions through bonds and in the second type as interactions through space type.
Rehman, Momin A.; Mishra, M. K.
2016-01-01
The ion-acoustic solitons in collisionless plasma consisting of warm adiabatic ions, isothermal positrons, and two temperature distribution of electrons have been studied. Using reductive perturbation method, Korteweg-de Vries (K-dV), the modified K-dV (m-KdV), and Gardner equations are derived for the system. The soliton solution of the Gardner equation is discussed in detail. It is found that for a given set of parameter values, there exists a critical value of β=Tc/Th, (ratio of cold to hot electron temperature) below which only rarefactive KdV solitons exist and above it compressive KdV solitons exist. At the critical value of β, both compressive and rarefactive m-KdV solitons co-exist. We have also investigated the soliton in the parametric regime where the KdV equation is not valid to study soliton solution. In this region, it is found that below the critical concentration the system supports rarefactive Gardner solitons and above it compressive Gardner solitons are found. The effects of temperature ratio of two-electron species, cold electron concentration, positron concentration on the characteristics of solitons are also discussed.
Gumberidze, A; Stöhlker, Th; Banaś, D; Beckert, K; Beller, P; Beyer, H F; Bosch, F; Cai, X; Hagmann, S; Kozhuharov, C; Liesen, D; Nolden, F; Ma, X; Mokler, P H; Orsić-Muthig, A; Steck, M; Sierpowski, D; Tashenov, S; Warczak, A; Zou, Y
2004-05-21
Radiative recombination transitions into the ground state of cooled bare and hydrogenlike uranium ions were measured at the storage ring ESR. By comparing the corresponding x-ray centroid energies, this technique allows for a direct measurement of the electron-electron contribution to the ionization potential in the heaviest He-like ions. For the two-electron contribution to the ionization potential of He-like uranium we obtain a value of 2248+/-9 eV. This represents the most accurate determination of two-electron effects in the domain of high-Z He-like ions, and the accuracy reaches already the size of the specific two-electron radiative QED corrections.
Banerji, N.; Hayes, S. C.; Knorr, Fritz J.; Melamen, Deborah J.; Mchale, Jeanne L.; Marchioro, Arianna; Moser, Jacques-Edouard
2014-01-01
The plant pigment betanin is investigated as a dye-sensitizer on TiO2 with regard to its potential to undergo two- electron oxidation following one-photon excitation. Electrochemical, spectroelectrochemical and transient absorption measurements provide evidence for two-electron proton-coupled photo-oxidation leading to a quinone methide interme- diate which rearranges to 2-decarboxy-2,3-dehydrobetanin. Time-resolved spectroscopy measurements of betanin on nanocrystalline TiO2 and ZrO2 films w...
Knorr, Fritz J.; Malamen, Deborah J.; Mchale, Jeanne L.; Marchioro, Arianna; Moser, Jacques-Edouard
2014-01-01
The plant pigment betanin is investigated as a dye-sensitizer on TiO2 with regard to its potential to undergo two-electron oxidation following one-photon excitation. Electrochemical, spectroelectrochemical and transient absorption measurements provide evidence for two-electron proton-coupled photo-oxidation leading to a quinone methide intermediate which rearranges to 2-decarboxy-2,3-dehydrobetanin. Time-resolved spectroscopy measurements of betanin on nanocrystalline TiO2 and ZrO2 films were...
Stevenson, Gareth P; Lee, Chong-Yong; Kennedy, Gareth F; Parkin, Alison; Baker, Ruth E; Gillow, Kathryn; Armstrong, Fraser A; Gavaghan, David J; Bond, Alan M
2012-06-26
A detailed analysis of the cooperative two-electron transfer of surface-confined cytochrome c peroxidase (CcP) in contact with pH 6.0 phosphate buffer solution has been undertaken. This investigation is prompted by the prospect of achieving a richer understanding of this biologically important system via the employment of kinetically sensitive, but background devoid, higher harmonic components available in the large-amplitude Fourier transform ac voltammetric method. Data obtained from the conventional dc cyclic voltammetric method are also provided for comparison. Theoretical considerations based on both ac and dc approaches are presented for cases where reversible or quasi-reversible cooperative two-electron transfer involves variation in the separation of their reversible potentials, including potential inversion (as described previously for solution phase studies), and reversibility of the electrode processes. Comparison is also made with respect to the case of a simultaneous two-electron transfer process that is unlikely to occur in the physiological situation. Theoretical analysis confirms that the ac higher harmonic components provide greater sensitivity to the various mechanistic nuances that can arise in two-electron surface-confined processes. Experimentally, the ac perturbation with amplitude and frequency of 200 mV and 3.88 Hz, respectively, was employed to detect the electron transfer when CcP is confined to the surface of a graphite electrode. Simulations based on cooperative two-electron transfer with the employment of reversible potentials of 0.745 ± 0.010 V, heterogeneous electron transfer rate constants of between 3 and 10 s(-1) and charge transfer coefficients of 0.5 for both processes fitted experimental data for the fifth to eighth ac harmonics. Imperfections in theory-experiment comparison are consistent with kinetic and thermodynamic dispersion and other nonidealities not included in the theory used to model the voltammetry of surface
Energy Technology Data Exchange (ETDEWEB)
Amovilli, C., E-mail: amovilli@dcci.unipi.it [Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via Risorgimento 35, 56126 Pisa (Italy); March, N.H. [Department of Physics, University of Antwerp, Antwerp (Belgium); University of Oxford, Oxford (United Kingdom)
2014-05-01
Though density functional theory is already developed in useful practical numerical forms, no explicit simple ground-state energy density functional exists. Here, towards establishing such a theory, we present the ground-state energy of the Crandall et al.'s two-electron spin-compensated model atom in terms of ∇{sup 2}ρ(r)/ρ(r) evaluated at r=0, where ρ(r) is the electron density.
Amovilli, C.; March, N. H.
2014-05-01
Though density functional theory is already developed in useful practical numerical forms, no explicit simple ground-state energy density functional exists. Here, towards establishing such a theory, we present the ground-state energy of the Crandall et al.'s two-electron spin-compensated model atom in terms of ∇2ρ(r)/ρ(r) evaluated at r=0, where ρ(r) is the electron density.
Energy Technology Data Exchange (ETDEWEB)
March, N.H
2002-12-30
The first-order density matrix {gamma}(r{sub 1},r{sub 2}) for the ground-state of a model two-electron atom is explicitly constructed from the electron density {rho}(r). The model has harmonic confinement plus interparticle harmonic interactions. {gamma}(r{sub 1},r{sub 2}) and {rho}(r) are related non-locally, even though no density gradients and no quadratures appear.
Aratani, Yusuke; Suenobu, Tomoyoshi; Ohkubo, Kei; Yamada, Yusuke; Fukuzumi, Shunichi
2017-03-25
The photocatalytic production of hydrogen peroxide from water and dioxygen under visible light irradiation was made possible by using polymeric cyano-bridged heteronuclear metal complexes (M(II)[Ru(II)(CN)4(bpy)]; M(II) = Ni(II), Fe(II) and Mn(II)), where the photocatalytic two-electron reduction of O2 and water oxidation were catalysed by the Ru and M(II) moieties, respectively.
Li, Rongbao; Bianchet, Mario A.; Talalay, Paul; Amzel, L. Mario
1995-09-01
Quinone reductase [NAD(P)H:(quinone acceptor) oxidoreductase, EC 1.6.99.2], also called DT diaphorase, is a homodimeric FAD-containing enzyme that catalyzes obligatory NAD(P)H-dependent two-electron reductions of quinones and protects cells against the toxic and neoplastic effects of free radicals and reactive oxygen species arising from one-electron reductions. These two-electron reductions participate in the reductive bioactivation of cancer chemotherapeutic agents such as mitomycin C in tumor cells. Thus, surprisingly, the same enzymatic reaction that protects normal cells activates cytotoxic drugs used in cancer chemotherapy. The 2.1-Å crystal structure of rat liver quinone reductase reveals that the folding of a portion of each monomer is similar to that of flavodoxin, a bacterial FMN-containing protein. Two additional portions of the polypeptide chains are involved in dimerization and in formation of the two identical catalytic sites to which both monomers contribute. The crystallographic structures of two FAD-containing enzyme complexes (one containing NADP^+, the other containing duroquinone) suggest that direct hydride transfers from NAD(P)H to FAD and from FADH_2 to the quinone [which occupies the site vacated by NAD(P)H] provide a simple rationale for the obligatory two-electron reductions involving a ping-pong mechanism.
Zhang, Min; E, Wenbo; Ohkubo, Kei; Sanchez-Garcia, David; Yoon, Dae-Wi; Sessler, Jonathan L; Fukuzumi, Shunichi; Kadish, Karl M
2008-02-21
Electron-transfer interconversion between the four-electron oxidized form of a quaterpyrrole (abbreviated as P4 for four pyrroles) and the two-electron oxidized form (P4H2) as well as between P4H2 and its fully reduced form (P4H4) bearing analogous substituents in the alpha- and beta-pyrrolic positions was studied by means of cyclic voltammetry and UV-visible spectroelectrochemistry combined with ESR and laser flash photolysis measurements. The two-electron oxidized form, P4H2, acts as both an electron donor and an electron acceptor. The radical cation (P4H2*+) and radical anion (P4H2*-) are both produced by photoinduced electron transfer from dimeric 1-benzyl-1,4-dihydronicotinamide to P4H2, whereas the cation radical form of the compound is also produced by electron-transfer oxidation of P4H2 with [Ru(bpy)3]3+. The ESR spectra of P4H2*+ and P4H2*- were recorded at low temperature and exhibit spin delocalization over all four pyrrole units. Thus, the two-electron oxidized form of the quaterpyrrole (P4H2) displays redox and electronic features analogous to those seen in the case of porphyrins and may be considered as a simple, open-chain model of this well-studied tetrapyrrolic macrocycle. The dynamics of deprotonation from P4H2*+ and disproportionation of P4H2 were examined by laser flash photolysis measurements of photoinduced electron-transfer oxidation and reduction of P4H2, respectively.
Dyall, Kenneth G.
1992-01-01
The effect of omission of two-electron integrals involving basis functions for the small component of the wavefunction on the eigenvalue spectrum in the Dirac-Hartree-Fock problem is studied. From an analysis of the Fock matrix it is shown that omission of these integrals moves the negative-energy states down, not up. Their complete omission does not give rise to intruder states. The appearance of intruder states occurs when only some of the core integrals are omitted, due to the nature of particular contraction schemes used for the core basis functions. Use of radially localized functions rather than atomic functions alleviates the intruder state problem.
DEFF Research Database (Denmark)
Vesborg, Peter Christian Kjærgaard; Seger, Brian
2016-01-01
Solar-drivenreduction of CO2 to solar fuels as an alternative to H2 via water splitting is an intriguing proposition. We modelthe solar-to-fuel (STF) efficiencies using realistic parameters basedon recently reported CO2 reduction catalysts with a highperformance tandem photoabsorber structure. CO...... and formate, whichare both two-electron reduction products, offer STF efficiencies (20.0%and 18.8%) competitively close to that of solar H2 (21.8%)despite markedly worse reduction catalysis. The slightly lower efficiencytoward carbon products is mainly due to electrolyte resistance, notoverpotential. Using...... a cell design where electrolyte resistance isminimized makes formate the preferred product from an efficiency standpoint(reaching 22.7% STF efficiency). On the other hand, going beyond a2 electron reduction reaction, the more highly reduced products seemunviable with presently available electrocatalysts...
Chu, John C K; Dalton, Derek M; Rovis, Tomislav
2015-04-08
We report a catalytic asymmetric synthesis of piperidines through [4 + 2] cycloaddition of 1-azadienes and nitro-alkenes. The reaction uses earth abundant Zn as catalyst and is highly diastereo- and regioselective. A novel BOPA ligand (F-BOPA) confers high reactivity and enantioselectivity in the process. The presence of ortho substitution on the arenes adjacent to the bis(oxazolines) was found to be particularly impactful, due to limiting the undesired coordination of 1-azadiene to the Lewis acid and thus allowing the reaction to be carried out at lower temperature. A series of secondary kinetic isotope effect studies using a range of ligands implicates a stepwise mechanism for the transformation, involving an initial Michael-type addition of the imine to the nitro-alkene followed by a cyclization event. The stepwise mechanism obviates the electronic requirement inherent to a concerted mechanism, explaining the successful cycloaddition between two electron-deficient partners.
Yang, Yang; Dominguez, Adriel; Zhang, Du; Lutsker, Vitalij; Niehaus, Thomas A; Frauenheim, Thomas; Yang, Weitao
2017-03-28
The particle-particle random phase approximation (pp-RPA) is a promising method for studying charge transfer(CT) excitations. Through a detailed analysis on two-electron deficient systems, we show that the pp-RPA is always able to recover the long-distance asymptotic -1/R trend for CT excitations as a result of the concerted effect between orbital energies and the pp-RPA kernel. We also provide quantitative results for systems with relatively short donor-acceptor distances. With conventional hybrid or range-separated functionals, the pp-RPA performs much better than time-dependent density functional theory (TDDFT), although it still gives underestimated results which are not as good as TDDFT with system-dependent tuned functionals. For pp-RPA, there remain three great challenges in dealing with CT excitations. First, the delocalized frontier orbitals in strongly correlated systems often lead to difficulty with self-consistent field convergence as well as an incorrect picture with about half an electron transferred. Second, the commonly used density functionals often underestimate the energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital (LUMO) for the two-electron deficient species, resulting in systems with delocalized orbitals. Third, the performance of pp-RPA greatly depends on the energy difference between the LUMO and a higher virtual orbital. However, the meaning of the orbital energies for higher virtual orbitals is still not clear. We also discuss the performance of an approximate pp-RPA scheme that uses density functional tight binding (pp-DFTB) as reference and demonstrate that the aforementioned challenges can be overcome by adopting suitable range-separated hybrid functionals. The pp-RPA and pp-DFTB are thus promising general approaches for describing charge transfer excitations.
Shimada, Tetsuya; Kumagai, Akihiro; Funyu, Shigeaki; Takagi, Shinsuke; Masui, Dai; Nabetani, Yu; Tachibana, Hiroshi; Tryk, Donald A; Inoue, Haruo
2012-01-01
The reaction mechanism of the highly efficient (phi = 0.60), selective photochemical epoxidation of alkenes sensitized by CO-coordinated tetra(2,4,6-trimethyl)phenylporphyrinatoruthenium(II) (Ru(II)TMP(CO)), with water acting both as an electron and oxygen atom donor, was investigated. The steady-state light irradiation of the reaction mixture indicated the formation of the Ru(II)TMP (CO) cation radical under neutral conditions, which was effectively trapped by an hydroxide ion to regenerate the starting sensitizer. By means of a laser flash photolysis experiment, the formation of the cation radical as the primary process from the triplet excited state of Ru(II)TMP(CO) was clearly observed. Four kinds of transients were detected in completely different ranges of the delay time: the excited triplet state of Ru(II)TMP(CO) [delay time region reaction mechanism was revealed that involves RuTMP(CO) cation radical formation from the triplet excited state of the sensitizer, followed by attack of an hydroxide ion to form an hydroxyl-coordinated Ru-porphyrin (Intermediate [I]) and subsequent reaction with cyclohexene to form Intermediate [II]. The kinetics for each step of the successive processes was carefully analyzed and their rate constants were determined. The two-electron oxidation of water by one-photon irradiation, as revealed in the photochemical epoxidation, is proposed to be one of the more promising candidates to get through the bottleneck of water oxidation in artificial photosynthesis.
Sharp, P. M.; D'Amico, I.
2016-02-01
We consider a model system of two electrons confined in a two-dimensional harmonic oscillator potential, with the electrons interacting via an α / r2 potential, and subject to a magnetic field applied perpendicular to the plane of confinement. Our results show that variations in the strength of the electron-electron interaction generate a "band structure" in ground state metric spaces, which shares many characteristics with those generated as a result of varying the confinement potential. In particular, the metric spaces for wavefunctions, particle densities, and paramagnetic current densities all exhibit distinct "bands" and "gaps". The behavior of the polar angle of the bands also shares traits with that obtained by varying the confinement potential, but the behavior of the arc lengths of the bands on the metric space spheres can be seen to be different for the two cases and opposite for a large range of angular momentum values. The findings here and in Refs. [1,2] demonstrate that the "band structure" that arises in ground state metric spaces when a magnetic field is applied is a robust feature.
Trifonov, Alexander A; Borovkov, Ivan A; Fedorova, Elena A; Fukin, Georgii K; Larionova, Joulia; Druzhkov, Nikolai O; Cherkasov, Vladimir K
2007-01-01
Ytterbocene [Yb(C(5)MeH(4))(2)(thf)(2)] reacts with diazabutadiene 2,6-iPr(2)C(6)H(3)-N=CH-CH=N-C(6)H(3)iPr(2)-2,6 (DAD) as a one-electron reductant to afford a bis(cyclopentadienyl) Yb(III) derivative containing a DAD radical anion [Yb(C(5)MeH(4))(2)(dad(-.))]. However, ytterbocenes [YbCp*(2)(thf)(2)] (Cp*=C(5)Me(5), C(5)Me(4)H) coordinated by sterically demanding cyclopentadienyl ligands act as two-electron reductants in their reactions with DAD. These reactions occur by abstraction of one Cp* ring and result in the formation of novel Yb(III) mixed-ligand bent-sandwich complexes, [YbCp*(dad)(thf)], in which the dianion of DAD has an uncommon terminal eta(4)-coordination to the ytterbium atom. The variable-temperature magnetic measurements of complex [Yb(C(5)Me(5))(dad)(thf)] suggest the existence of redox tautomerism for this compound.
Energy Technology Data Exchange (ETDEWEB)
Reuschl, Regina
2008-07-01
Experiments on the 1s Lamb-shift in heavy H-like ions and on the intra-shell transitions in heavy He-like systems have been performed. These investigations are of particular interest to verify the validity of quantum electrodynamics (QED) in extremely strong Coulomb fields. In addition, in heavy systems not only QED but also relativistic effects start to play a key role. The experiments have been performed at the gas-jet target of the experimental storage ring (ESR) at GSI. In an experiment with He-like uranium we were able to directly measure the intra-shell transition 2{sup 3}P{sub 2}{yields}2{sup 3}S{sub 1}, in a high-Z system for the very first time. This has been achieved by combining the results from a high-resolution Bragg crystal-spectrometer and a standard planar Germanium detector. A fit of the experimental spectrum with data obtained from a simulation shows, the theoretical predictions describe the transition dynamics very well in this two-electron system. Another experiment has been performed on H-like lead to investigate the 1s Lamb-shift in heavy H-like systems. Here, a high-resolution Laue crystal-spectrometer has been commissioned together with novel high-resolution two dimensional micro-strip Ge-detectors. The combination of both instruments is a very promising tool for future high-precision X-ray experiments. (orig.)
Florens, Serge; Freyn, Axel; Roch, Nicolas; Wernsdorfer, Wolfgang; Balestro, Franck; Roura-Bas, Pablo; Aligia, A A
2011-06-22
We review here some universal aspects of the physics of two-electron molecular transistors in the absence of strong spin-orbit effects. Several recent quantum dot experiments have shown that an electrostatic backgate could be used to control the energy dispersion of magnetic levels. We discuss how the generally asymmetric coupling of the metallic contacts to two different molecular orbitals can indeed lead to a gate-tunable Hund's rule in the presence of singlet and triplet states in the quantum dot. For gate voltages such that the singlet constitutes the (non-magnetic) ground state, one generally observes a suppression of low voltage transport, which can yet be restored in the form of enhanced cotunneling features at finite bias. More interestingly, when the gate voltage is controlled to obtain the triplet configuration, spin S = 1 Kondo anomalies appear at zero bias, with non-Fermi liquid features related to the underscreening of a spin larger than 1/2. Finally, the small bare singlet-triplet splitting in our device allows fine-tuning with the gate between these two magnetic configurations, leading to an unscreening quantum phase transition. This transition occurs between the non-magnetic singlet phase, where a two-stage Kondo effect occurs, and the triplet phase, where the partially compensated (underscreened) moment is akin to a magnetically 'ordered' state. These observations are put theoretically into a consistent global picture by using new numerical renormalization group simulations, tailored to capture sharp finite-voltage cotunneling features within the Coulomb diamonds, together with complementary out-of-equilibrium diagrammatic calculations on the two-orbital Anderson model. This work should shed further light on the complicated puzzle still raised by multi-orbital extensions of the classic Kondo problem.
Sturm, Erica J.
Strong correlation due to multi-referenced electronic states of quantum chemical systems are crucial for a proper understanding of important phenomena including excited states, bond breakage and formation, singlet fission and biological transport. By solving for the 2-electron reduced density matrix (2-RDM) directly via the anti-Hermitian contracted Schrodinger equation (ACSE) we provide a balanced treatment of single and multi-referenced correlation effects without utilizing the N-electron wave function. This significantly reduces the computational expense while still maintaining near full configuration interaction accuracy when available. When provided with an initial 2-RDM guess from an active-space multi-configuration self consistent field wave function the ACSE scales as [special characters omitted] where ra is the number of active molecular orbitals (MOs) and ra is the number of external MOs. This work demonstrates the energetic accuracy of ACSE calculations with several small multi-referenced systems and presents a novel approach for investigating intermolecular interactions, using a simple dimer test case. In this monomer-optimized basis set approach we compute each monomer's properties in isolation and obtain a set of natural orbitals that best describe the monomer. We then remove or truncate orbitals deemed excessive as a function of occupation number, defining a monomer molecular orbital basis uniquely suited to that monomer. Combining two such monomers yields a super-system expressed in the monomer basis which we then rotate to a dimer basis at a desired geometry before creating a new initial 2-RDM for the final optimization by an ACSE calculation. It is found that the intermolecular properties calculated in this fashion from larger atomic basis sets maintain their high accuracy but at a fraction of the computational cost. Furthermore this basis set optimization is free of basis set superposition error, circumventing the need for an expensive
Energy Technology Data Exchange (ETDEWEB)
Lappin, A.G.; Osvath, P.; Baral, S.
1987-09-23
The kinetics and mechanism of the two-electron oxidation of the sexidentate bis(oxime-imine) complex of nickel(II), (Ni/sup II/L) (I), by bromine have been investigated in bromide ion media over the pH range 3.1-7.6 at 25/sup 0/C and 1.0 M ionic strength. In the presence of an excess of bromine or nickel(II), oxidation is monophasic, and the initial product is (Ni/sup IV/L)/sup 2 +/, a formal nickel(IV) species that undergoes subsequent reactions to give an unknown oxidation product with excess bromine at pH > 6 or to give (Ni/sup III/L)/sup +/ by comproportionation with excess nickel(II) at pH > 5. The sole kinetically important oxidant is Br/sub 2/, and second-order rate constants for reaction of (Ni/sup II/L) and its protonated form (Ni/sup II/LH)/sup +/ are 2.1 x 10/sup 7/ and 7.1 x 10/sup 5/ M/sup -1/ s/sup -1/, respectively. These rate constants are in line with a rate-determining single-electron-transfer reaction, and the proposed mechanism involves formation of a transient ion pair (Ni/sup III/L/sup +/,Br/sub 2//sup -/ in which the rate of subsequent electron transfer is comparable with the rate of ion-pair dissociation. In addition, the pulse-radiolysis technique has been used to investigate the reactions of nickel(II) with Br/sub 2//sup -/ to give (Ni/sup III/L)/sup +/, and rate constants for (Ni/sup II/L) and (Ni/sup II/LH)/sup +/ are 8.5 x 10/sup 8/ and 2.7 x 10/sup 8/ M/sup -1/ S/sup -1/, respectively, at 21/sup 0/C. 34 references, 3 figures, 3 tables.
Energy Technology Data Exchange (ETDEWEB)
Bordenave-Montesquieu, A.; Benoit-Cattin, P.; Gleizes, A.; Marrakchi, A.I.; Dousson, S.; Hitz, D.
1985-07-01
Singly differential cross sections for two-electron capture into autoionising states (nl,n'l') with n=2,3,4 and n'>=n in Nsup(q+) (q=6,7) on He and H/sub 2/ collisions have been measured at 10,5q ke V collision energy and an observation angle thetasub(lab)=11.6/sup 0/. Total cross sections are estimated assuming isotropic angular distributions. (orig.).
Variables Affecting Two Electron Transport System Assays
Burton, G. Allen; Lanza, Guy R.
1986-01-01
Several methodological variables were critical in two commonly used electron transport activity assays. The dehydrogenase assay based on triphenyl formazan production exhibited a nonlinear relationship between formazan production (dehydrogenase activity) and sediment dilution, and linear formazan production occurred for 1 h in sediment slurries. Activity decreased with increased time of sediment storage at 4°C. Extraction efficiencies of formazan from sediment varied with alcohol type; methan...
McCann, Scott D; Stahl, Shannon S
2015-06-16
Selective oxidation reactions have extraordinary value in organic chemistry, ranging from the conversion of petrochemical feedstocks into industrial chemicals and polymer precursors to the introduction of heteroatom functional groups into pharmaceutical and agrochemical intermediates. Molecular oxygen (O2) would be the ideal oxidant for these transformations. Whereas many commodity-scale oxidations of simple hydrocarbon feedstocks employ O2 as an oxidant, methods for selective oxidation of more complex molecules bearing diverse functional groups are often incompatible with existing aerobic oxidation methods. The latter limitation provides the basis for our interest in the development of new catalytic transformations and the elucidation of mechanistic principles that underlie selective aerobic oxidation reactions. One challenge inherent in such methods is the incommensurate redox stoichiometry associated with the use of O2, a four-electron oxidant, in reactions that achieve two-electron oxidation of organic molecules. This issue is further complicated by the use of first-row transition-metal catalysts, which tend to undergo facile one-electron redox steps. In recent years, we have been investigating Cu-catalyzed aerobic oxidation reactions wherein the complexities just noted are clearly evident. This Account surveys our work in this area, which has emphasized three general classes of reactions: (1) single-electron-transfer reactions for oxidative functionalization of electron-rich substrates, such as arenes and heterocycles; (2) oxidative carbon-heteroatom bond-forming reactions, including C-H oxidations, that proceed via organocopper(III) intermediates; and (3) methods for aerobic oxidation of alcohols and amines that use Cu(II) in combination with an organic redox-active cocatalyst to dehydrogenate the carbon-heteroatom bond. These reaction classes demonstrate three different pathways to achieve two-electron oxidation of organic molecules via the cooperative
Sheng, Hua; Frei, Heinz
2016-08-10
In the search for the two-electron-reduced intermediate of the tetraaza catalyst [Co(II)N4H(MeCN)](2+) (N4H = 2,12-dimethyl-3,7,11,17-tetraazabicyclo[11.3.1]heptadeca-1(17),2,11,13,15-pentaene) for CO2 reduction and elementary steps that result in the formation of CO product, rapid-scan FT-IR spectroscopy of the visible-light-sensitized catalysis, using Ir(ppy)3 in wet acetonitrile (CD3CN) solution, led to the observation of two sequential intermediates. The initially formed one-electron-reduced [Co(I)N4H](+)-CO2 adduct was converted by the second electron to a transient [Co(I)N4H](+)-CO2(-) complex that spontaneously converted CO2 to CO in a rate-limiting step on the second time scale in the dark under regeneration of the catalyst (room temperature). The macrocycle IR spectra of the [Co(I)N4H](+)-CO2(-) complex and the preceding one-electron [Co(I)N4H](+)-CO2 intermediate show close similarity but distinct differences in the carboxylate modes, indicating that the second electron resides mainly on the CO2 ligand. Vibrational assignments are corroborated by (13)C isotopic labeling. The structure and stability of the two-electron-reduced intermediate derived from the time-resolved IR study are in good agreement with recent predictions by DFT electronic structure calculations. This is the first observation of an intermediate of a molecular catalyst for CO2 reduction during the bond-breaking step producing CO. The reaction pathway for the Co tetraaza catalyst uncovered here suggests that the competition between CO2 reduction and proton reduction of a macrocyclic multi-electron catalyst is steered toward CO2 activation if the second electron is directly captured by an adduct of CO2 and the one-electron-reduced catalyst intermediate.
Energy Technology Data Exchange (ETDEWEB)
Fleming, Barry D. [School of Chemistry, Monash University, Wellington Rd, Clayton, Victoria 3800 (Australia)], E-mail: barry.fleming@sci.monash.edu.au; Bond, Alan M. [School of Chemistry, Monash University, Wellington Rd, Clayton, Victoria 3800 (Australia)], E-mail: alan.bond@sci.monash.edu.au
2009-04-01
The free-base porphyrin, 5,10,15,20-tetrakis(1-methyl-4-pyridyl)-21H,23H-porphine (H{sub 2}TMPyP), adsorbs onto a basal-plane graphite electrode. Under DC cyclic voltammetric conditions, the fully protonated dication, [H{sub 4}TMPyP(0)]{sup 2+}, undergoes an apparently close to ideal surface-confined two-electron reduction to the neutral [H{sub 4}TMPyP(-II)] species when the supporting electrolyte consists of aqueous 1 M HCl and 1 M NaCl and coverages are sub-monolayer. The reversible potential calculated from the average of the oxidation and reduction peak potentials is 0.138 {+-} 0.002 V (vs Ag/AgCl, 3 M NaCl) whilst their separation {delta}E{sub p}, approaches 0 mV at slow scan rates, as expected theoretically for an ideal surface-confined electron transfer process. Comparisons of simulated and experimental data imply that the increase in {delta}E{sub p} observed at scan rates above 10 V s{sup -1} is consistent with uncompensated Ohmic IR{sub u} drop effects, and not limitations imposed by electron transfer kinetics. Analysis of fundamental and higher harmonic components derived from large-amplitude sine-wave AC voltammetry is consistent with a very fast electron transfer rate constant, k{sup 0}, in excess of 10{sup 6} s{sup -1} for the overall two-electron process. However, careful comparison with AC theory highlights minor levels of non-ideality not attributable to purely capacitative background or uncompensated resistance effects. These are particularly evident when greater than monolayer surface coverages are employed. It is likely that subtle contributions from heterogeneity in the adsorbed layer and complexities in the reaction mechanism are present in this close to ideal surface-confined process, but they are more readily detected under conditions of large-amplitude Fourier transformed AC cyclic voltammetry than with the conventionally used DC cyclic format.
Patil, Mahendra P; Sunoj, Raghavan B
2006-11-07
A systematic investigation on the cycloreversion reaction of the cycloadduct formed between substituted cyclopentadiene and p-benzoquinone (1-19) is reported at the B3LYP/6-311+G**//B3LYP/6-31G* level of theory. The computed activation barrier exhibits a fairly high sensitivity to the nature of substituents at the C7-position. Gibbs free energy of activation for 1 and 19 are found to be 20.3 and 30.1 kcal mol(-1), respectively, compared to 7, which is estimated to be 24.7 kcal mol(-1). Quantitative analysis of the electronic effects operating in both the cycloadduct as well as the corresponding transition state for the retro Diels-Alder (rDA) reaction performed using the natural bond orbital (NBO) and atoms in molecule (AIM) methods have identified important two-electron stabilizing interactions. Among four major delocalizations, sigma(C7-X) to sigma*(C1-C5) [and to sigma*(C2-C6)] is identified as the key contributing factor responsible for ground state C1-C5 bond elongation, which in turn is found to be crucial in promoting the rDA reaction. A good correlation between the population of antibonding orbital [sigma*(C1-C5)] of the ground state cycloadduct and Gibbs free energy of activation is observed. The importance of factors that modulate ground state structural features in controlling the energetics of rDA reaction is described.
Institute of Scientific and Technical Information of China (English)
祁家能
2012-01-01
After going through the rising,developing and perfecting stages,the development of electronic reading rooms in college libraries now faces many new difficulties.So it is necessary to reconsider and reform the construction of the electronic reading room.It is advised to divide two electronic reading rooms into three areas which can offer free service,information retrieval service and special service respectively,so as to implement three kinds of management modes to meet the demands of different readers.The method is helpful to solve the development dilemma of the electronic reading rooms and give full play to the resources and facilities of the library.%高校图书馆电子阅览室从兴起、快速发展、成熟完善,到现在面临的诸多困境,促使我们对电子阅览室的建设要重新认识和进行理念创新。应该把两个电子阅览室分成辅助教学及读者自主学习区,信息检索学习区和个性化特色服务区三个区域,实行三种管理模式,满足不同读者的需求,走出电子阅览室发展的困境,使图书馆资源和设备发挥最大作用。
Kakuda, Saya; Peterson, Ryan L; Ohkubo, Kei; Karlin, Kenneth D; Fukuzumi, Shunichi
2013-05-01
A copper complex, [(PV-tmpa)Cu(II)](ClO4)2 (1) [PV-tmpa = bis(pyrid-2-ylmethyl){[6-(pivalamido)pyrid-2-yl]methyl}amine], acts as a more efficient catalyst for the four-electron reduction of O2 by decamethylferrocene (Fc*) in the presence of trifluoroacetic acid (CF3COOH) in acetone as compared with the corresponding copper complex without a pivalamido group, [(tmpa)Cu(II)](ClO4)2 (2) (tmpa = tris(2-pyridylmethyl)amine). The rate constant (k(obs)) of formation of decamethylferrocenium ion (Fc*(+)) in the catalytic four-electron reduction of O2 by Fc* in the presence of a large excess CF3COOH and O2 obeyed first-order kinetics. The k(obs) value was proportional to the concentration of catalyst 1 or 2, whereas the k(obs) value remained constant irrespective of the concentration of CF3COOH or O2. This indicates that electron transfer from Fc* to 1 or 2 is the rate-determining step in the catalytic cycle of the four-electron reduction of O2 by Fc* in the presence of CF3COOH. The second-order catalytic rate constant (k(cat)) for 1 is 4 times larger than the corresponding value determined for 2. With the pivalamido group in 1 compared to 2, the Cu(II)/Cu(I) potentials are -0.23 and -0.05 V vs SCE, respectively. However, during catalytic turnover, the CF3COO(-) anion present readily binds to 2 shifting the resulting complex's redox potential to -0.35 V. The pivalamido group in 1 is found to inhibit anion binding. The overall effect is to make 1 easier to reduce (relative to 2) during catalysis, accounting for the relative k(cat) values observed. 1 is also an excellent catalyst for the two-electron two-proton reduction of H2O2 to water and is also more efficient than is 2. For both complexes, reaction rates are greater than for the overall four-electron O2-reduction to water, an important asset in the design of catalysts for the latter.
Energy Technology Data Exchange (ETDEWEB)
Bouri, C
2007-04-15
This work presents a study of the {sup 1}P{sup 0} excited states of He that can be reached by absorption of a single photon carrying an energy close to the double ionization threshold (DIT) (79 eV). Above the DIT, these states are the double continuum states; below, they are the double excited states. These two types of states are tightly coupled to the single continuum states with or without excitation of the residual ion He{sup +}, owing to their degeneracy in energy. In a one-photon process, these states can only be formed owing to the electronic correlations in the system which must be well described to obtain quantitative good results. Our study is a part of the work which aims at a united description of all these doubly excited, ionized-excited, and double continuum states. We use the Hyperspherical R-Matrix with Semiclassical Outgoing Waves (HRM-SOW) method, initially dedicated to double photoionization studies. We extend it to extract information on the single continuum. This extension allows us to compute cross sections of single photoionization with or without excitation up to n 50 for an excess of 100 meV just above the double ionization threshold. A deep insight into this process is given by a partial waves analysis. The results obtained shed light on the key role of angular and radial correlations. The numerous data we obtain on double and single ionization allow us to establish a continuity relation between these two processes. We show that single ionization with an infinite excitation of the residual ion merges into double photoionization when the excess energy is redistributed between the two electrons. It appears that this relation is valid not only for low but also for high photon energies. Since the HRM-SOW can produce the integrated cross section for double photoionization with high accuracy in the low energy domain, we check the Wannier threshold law. The parameters extracted support strongly this threshold law, and are in good agreement with
Energy Technology Data Exchange (ETDEWEB)
Bordenave-Montesquieu, A.; Benoit-Cattin, P.; Gleizes, A.; Marrakchi, A.I.; Dousson, S.; Hitz, D.
1984-04-14
Double electron transfer into autoionising states N/sup 4 +/(1snln'l'), with n = 2,3,4 and n' >= n has been observed in a collision between a one-electron highly charged N/sup 6 +/(1s) ion and a two-electron target (He or H/sub 2/), by electron spectrometry. The same configurations are excited in the two collisional systems but with very different probabilities. Electron capture mainly occurs into 1s2ln'l' in He-systems whereas transfer into 1s3ln'l' is stronger in H/sub 2/ systems.
Internal Conversion Process of Chlorophyll a in Solvents in Femtosecond Pump-Probe Laser Fields
Institute of Scientific and Technical Information of China (English)
Kai Niu; Li-qing Dong; Shu-lin Cong
2008-01-01
The internal conversion (IC) processes of chlorophyll a (chl-a) in solvents are studied based on the reduced density matrix theory. The IC times can be obtained by simulating the experimental fluorescence depletion spectra (FDS). The calculated IC times of chl-a in ethyl acetate, tetrahydrofuran and dimethyl formamide are 141, 147, and 241 fs, respectively. The oscillation feature of the FDS results from the forward and backward transfer of the population between coupled electronic states. The effects of diabatic coupling between two electronic states on the IC time and the FDS are described. The influence of molecule-reservoir coupling on the IC time is also investigated.
Quantification of entanglement entropy in helium by the Schmidt-Slater decomposition method
Lin, Chien-Hao
2014-01-01
In this work, we present an investigation on the spatial entanglement entropies in the helium atom by using highly correlated Hylleraas functions to represent the S-wave states. Singlet-spin 1sns 1Se states (with n = 1 to 6) and triplet-spin 1sns 3Se states (with n = 2 to 6) are investigated. As a measure on the spatial entanglement, von Neumann entropy and linear entropy are calculated. Furthermore, we apply the Schmidt-Slater decomposition method on the two-electron wave functions, and obtain eigenvalues of the one-particle reduced density matrix, from which the linear entropy and von Neumann entropy can be determined.
Atomic-batched tensor decomposed two-electron repulsion integrals
Schmitz, Gunnar; Madsen, Niels Kristian; Christiansen, Ove
2017-04-01
We present a new integral format for 4-index electron repulsion integrals, in which several strategies like the Resolution-of-the-Identity (RI) approximation and other more general tensor-decomposition techniques are combined with an atomic batching scheme. The 3-index RI integral tensor is divided into sub-tensors defined by atom pairs on which we perform an accelerated decomposition to the canonical product (CP) format. In a first step, the RI integrals are decomposed to a high-rank CP-like format by repeated singular value decompositions followed by a rank reduction, which uses a Tucker decomposition as an intermediate step to lower the prefactor of the algorithm. After decomposing the RI sub-tensors (within the Coulomb metric), they can be reassembled to the full decomposed tensor (RC approach) or the atomic batched format can be maintained (ABC approach). In the first case, the integrals are very similar to the well-known tensor hypercontraction integral format, which gained some attraction in recent years since it allows for quartic scaling implementations of MP2 and some coupled cluster methods. On the MP2 level, the RC and ABC approaches are compared concerning efficiency and storage requirements. Furthermore, the overall accuracy of this approach is assessed. Initial test calculations show a good accuracy and that it is not limited to small systems.
Sturmian bases for two-electron systems in hyperspherical coordinates
Abdouraman, A; Hamido, A; Mota-Furtado, F; O'Mahony, P F; Mitnik, D; Gasaneo, G; Piraux, B
2016-01-01
We give a detailed account of an $\\it{ab}$ $\\it{initio}$ spectral approach for the calculation of energy spectra of two active electron atoms in a system of hyperspherical coordinates. In this system of coordinates, the Hamiltonian has the same structure as the one of atomic hydrogen with the Coulomb potential expressed in terms of a hyperradius and the nuclear charge replaced by an angle dependent effective charge. The simplest spectral approach consists in expanding the hyperangular wave function in a basis of hyperspherical harmonics. This expansion however, is known to be very slowly converging. Instead, we introduce new hyperangular sturmian functions. These functions do not have an analytical expression but they treat the first term of the multipole expansion of the electron-electron interaction potential, namely the radial electron correlation, exactly. The properties of these new functions are discussed in detail. For the basis functions of the hyperradius, several choices are possible. In the present...
Sturmian bases for two-electron systems in hyperspherical coordinates
Abdouraman, A.; Frapiccini, A. L.; Hamido, A.; Mota-Furtado, F.; O'Mahony, P. F.; Mitnik, D.; Gasaneo, G.; Piraux, B.
2016-12-01
We give a detailed account of an ab initio spectral approach for the calculation of energy spectra of two active electron atoms in a system of hyperspherical coordinates. In this system of coordinates, the Hamiltonian has the same structure as the one of atomic hydrogen with the Coulomb potential expressed in terms of a hyperradius and the nuclear charge replaced by an angle dependent effective charge. The simplest spectral approach consists in expanding the hyperangular wave function in a basis of hyperspherical harmonics. This expansion however, is known to be very slowly converging. Instead, we introduce new hyperangular Sturmian functions. These functions do not have an analytical expression but they treat the first term of the multipole expansion of the electron-electron interaction potential, namely the radial electron correlation, exactly. The properties of these new functions are discussed in detail. For the basis functions of the hyperradius, several choices are possible. In the present case, we use Coulomb-Sturmian functions of half integer angular momentum. We show that, in the case of H-, the accuracy of the energy and the width of the resonance states obtained through a single diagonalization of the Hamiltonian, is comparable to the values given by state-of-the-art methods while using a much smaller basis set. In addition, we show that precise values of the electric-dipole oscillator strengths for {{S}}\\to {{P}} transitions in helium are obtained thereby confirming the accuracy of the bound state wave functions generated with the present method.
ATLAS Experiment
2011-01-01
Proton Collision Event with 2 Electrons & 2 Muons (Actual Event) An animation of an actual ATLAS proton collision event in 2011. The two muons are detailed as long blue tracks, the two electrons as short blue tracks matching green clusters of energy in the calorimeters which lie outside the inner tracking detector. source: http://www.atlas.ch/multimedia/2-electron-2-muon-event.html
Density functional theory: Foundations reviewed
Energy Technology Data Exchange (ETDEWEB)
Kryachko, Eugene S., E-mail: eugene.kryachko@ulg.ac.be [Bogolyubov Institute for Theoretical Physics, Kiev, 03680 (Ukraine); Ludeña, Eduardo V., E-mail: popluabe@yahoo.es [Centro de Química, Instituto Venezolano de Investigaciones Científicas, IVIC, Apartado 21827, Caracas 1020-A (Venezuela, Bolivarian Republic of); Prometheus Program, Senescyt (Ecuador); Grupo Ecuatoriano para el Estudio Experimental y Teórico de Nanosistemas, GETNano, USFQ, N104-E, Quito (Ecuador); Escuela Politécnica Superior del Litoral, ESPOL, Guayaquil (Ecuador)
2014-11-10
Guided by the above motto (quotation), we review a broad range of issues lying at the foundations of Density Functional Theory, DFT, a theory which is currently omnipresent in our everyday computational study of atoms and molecules, solids and nano-materials, and which lies at the heart of modern many-body computational technologies. The key goal is to demonstrate that there are definitely the ways to improve DFT. We start by considering DFT in the larger context provided by reduced density matrix theory (RDMT) and natural orbital functional theory (NOFT), and examine the implications that N-representability conditions on the second-order reduced density matrix (2-RDM) have not only on RDMT and NOFT but, also, by extension, on the functionals of DFT. This examination is timely in view of the fact that necessary and sufficient N-representability conditions on the 2-RDM have recently been attained. In the second place, we review some problems appearing in the original formulation of the first Hohenberg–Kohn theorem which is still a subject of some controversy. In this vein we recall Lieb’s comment on this proof and the extension to this proof given by Pino et al. (2009), and in this context examine the conditions that must be met in order that the one-to-one correspondence between ground-state densities and external potentials remains valid for finite subspaces (namely, the subspaces where all Kohn–Sham solutions are obtained in practical applications). We also consider the issue of whether the Kohn–Sham equations can be derived from basic principles or whether they are postulated. We examine this problem in relation to ab initio DFT. The possibility of postulating arbitrary Kohn–Sham-type equations, where the effective potential is by definition some arbitrary mixture of local and non-local terms, is discussed. We also deal with the issue of whether there exists a universal functional, or whether one should advocate instead the construction of problem
Giesbertz, Klaas J H; Baerends, Evert Jan
2013-01-01
Recently, we have demonstrated that the problems finding a suitable adiabatic approximation in time-dependent one-body reduced density matrix functional theory can be remedied by introducing an additional degree of freedom to describe the system: the phase of the natural orbitals [Phys. Rev. Lett. 105, 013002 (2010), J. Chem. Phys. 133, 174119 (2010)]. In this article we will show in detail how the frequency-dependent response equations give the proper static limit ($\\omega\\to0$), including the perturbation in the chemical potential, which is required in static response theory to ensure the correct number of particles. Additionally we show results for the polarizability for H$_2$ and compare the performance of two different two-electron functionals: the phase-including L\\"owdin-Shull functional and the density matrix form of the L\\"owdin-Shull functional.
White, Bonnie Roe
1991-01-01
Seven 5-minute, straight-copy timed writings administered to 87 college students revealed that (1) use of the print and return features of electronic typewriters does not automatically heighten speed or accuracy; and (2) students do not necessarily choose the best combination of features for enhancing performance. (SK)
Adaptive low rank wavelet methods and applications to two-electron Schrödinger equations
2012-01-01
In this work, we develop methods for the numerical approximation of higher-dimensional functions, given as solutions of linear elliptic operator equations or as eigenfunctions of such operators. The approximations of these functions are generated by iterative schemes, where iterates are represented in a multiplicatively nonlinear tensor decomposition of their wavelet coefficients. As a concrete application problem, we consider the stationary electronic Schrödinger equation, the fundamental eq...
Full two-electron calculations of antiproton collisions with molecular hydrogen
DEFF Research Database (Denmark)
Lühr, Armin Christian; Saenz, Alejandro
2010-01-01
Total cross sections for single ionization and excitation of molecular hydrogen by antiproton impact are presented over a wide range of impact energies from 1 keV to 6.5 MeV. A nonperturbative time-dependent close-coupling method is applied to fully treat the correlated dynamics of the electrons....
Dynamical Localization in a Two-Electron Quantum Dot Molecule Biased by a dc Voltage
Institute of Scientific and Technical Information of China (English)
王立民; 段素青; 赵宪庚; 刘承师; 马本堃
2003-01-01
We study the dynamics of two interacting electrons in a coupled-quantum-dot system with a time-dependent external electric field. The numerical results of the two-particle states reveal that the dynamical localization still exists under appropriate dc and ac voltage amplitudes. Such localization is different from the stationary localization phenomenon. Our conclusion is instructive for the field of quantum function devices.
Two-electron time-delay interference in atomic double ionization by attosecond pulses
Energy Technology Data Exchange (ETDEWEB)
Rescigno, Thomas N
2009-10-04
A two-color two-photon atomic double ionization experiment using subfemtosecond UV pulses can be designed such that the sequential two-color process dominates and one electron is ejected by each pulse. Nonetheless, ab initio calculations show that, for sufficiently short pulses, a prominent interference pattern in the joint energy distribution of the sequentially ejected electrons can be observed that is due to their indistinguishability and the exchange symmetry of the wave function.
In vivo comparison of the accuracy of two electronic apex locators.
Silveira, Luiz F M; Petry, Fernanda V; Martos, Josué; Neto, João B C
2011-08-01
The aim of this study was to analyse in vivo the accuracy of two apex locators, Root ZX and Novapex, to determine the position of the apical constriction. Twenty-three human single-rooted teeth to be extracted for periodontal reasons constituted the experiment. Endodontic access was obtained and the apical constriction was determined by one of the apex locators after initial crown-down preparation. When the electronic marker indicated that the tip of the endodontic file was at the apical constriction, the teeth were filled with composite and then surgically removed. The presence of the endodontic file tip at the apical constriction was evaluated stereomicroscopically (30×) and confirming radiographs were exposed. The accuracy of Root ZX and Novapex was 91.7% and 81.8% respectively. Within the limits of this study, the evaluated apex locators have a similar clinical performance for the apical constriction location.
Two-electron reduction of nitroaromatic compounds by flavin mononucleotide. DFT computational study
Directory of Open Access Journals (Sweden)
Liudmyla K. Sviatenko
2016-08-01
Full Text Available The mechanism for reduction of nitroaromatic compounds by flavin mononucleotide (FMN was examined at MPWB1K/tzvp level. The solvent effects were calculated using a PCM(Pauling and SMD(Pauling solvation models for ions and neutral molecules, respectively. Calculated thermodynamics of the reduction of nitro group to nitroso group suggests consequtive four-steps’ process (electron–proton–electron–proton transfer where the first proton comes from solution, while the second one – from FMN. Water molecule releases during fourth step of the process. Electron attachment to nitrocompound and electron lose by reduced FMN facilitate the breaking of N–O bond and proton release, respectively. Calculations show that reduction of nitro group to nitroso group in studied nitrocompounds is a thermodynamically feasible with 56–59 kcal/mol Gibbs free energy release. The most easy electron transfer proceeds for TNT (2,4,6-trinitrotoluene and NTO (5-nitro-2,4-dihydro-3H-1,2,4-triazol-3-one. While the most energy release occurs during proton transfer in case of ANTA (5-amino-3-nitro-1H-1,2,4-triazole.
Simulations of one- and two-electron systems by Bead-Fourier path integral molecular dynamics
Ivanov, Sergei D.; Lyubartsev, Alexander P.
2005-07-01
The Bead-Fourier path integral molecular dynamics technique introduced earlier [S. D. Ivanov, A. P. Lyubartsev, and A. Laaksonen, Phys. Rev. E 67 066710 (2003)] is applied for simulation of electrons in the simplest molecules: molecular hydrogen, helium atom, and their ions. Special attention is paid to the correct description of electrons in the core region of a nucleus. In an attempt to smooth the Coulomb potential at small distances, a recipe is suggested. The simulation results are in excellent agreement with the analytical solution for the "harmonic helium atom", as well as with the vibrational potential of the H2 molecule and He ionization energies. It is demonstrated, that the Bead-Fourier path integral molecular dynamics technique is able to provide the accuracy required for the description of electron structure and chemical bonds in cases when electron exchange effects need not be taken into account.
Electron transfer by excited benzoquinone anions: slow rates for two-electron transitions.
Zamadar, Matibur; Cook, Andrew R; Lewandowska-Andralojc, Anna; Holroyd, Richard; Jiang, Yan; Bikalis, Jin; Miller, John R
2013-09-05
Electron transfer (ET) rate constants from the lowest excited state of the radical anion of benzoquinone, BQ(-•)*, were measured in THF solution. Rate constants for bimolecular electron transfer reactions typically reach the diffusion-controlled limit when the free-energy change, ΔG°, reaches -0.3 eV. The rate constants for ET from BQ(-•)* are one-to-two decades smaller at this energy and do not reach the diffusion-controlled limit until -ΔG° is 1.5-2.0 eV. The rates are so slow probably because a second electron must also undergo a transition to make use of the energy of the excited state. Similarly, ET, from solvated electrons to neutral BQ to form the lowest excited state, is slow, while fast ET is observed at a higher excited state, which can be populated in a transition involving only one electron. A simple picture based on perturbation theory can roughly account for the control of electron transfer by the need for transition of a second electron. The picture also explains how extra driving force (-ΔG°) can restore fast rates of electron transfer.
Applications of Adiabatic Approximation to One- and Two-electron Phenomena in Strong Laser Fields
Bondar, Denys
2010-01-01
The adiabatic approximation is a natural approach for the description of phenomena induced by low frequency laser radiation because the ratio of the laser frequency to the characteristic frequency of an atom or a molecule is a small parameter. Since the main aim of this work is the study of ionization phenomena, the version of the adiabatic approximation that can account for the transition from a bound state to the continuum must be employed. Despite much work in this topic, a universally accepted adiabatic approach of bound-free transitions is lacking. Hence, based on Savichev's modified adiabatic approximation [Sov. Phys. JETP 73, 803 (1991)], we first of all derive the most convenient form of the adiabatic approximation for the problems at hand. Connections of the obtained result with the quasiclassical approximation and other previous investigations are discussed. Then, such an adiabatic approximation is applied to single-electron ionization and non-sequential double ionization of atoms in a strong low fr...
Observation and spectroscopy of a two-electron Wigner molecule in an ultraclean carbon nanotube
DEFF Research Database (Denmark)
Pecker, S.; Kuemmeth, Ferdinand; Secchi, A.;
2013-01-01
to be clearly imprinted on the energy spectrum, yet so far a direct measurement of such a spectrum in a controllable one-dimensional setting is still missing. Here we use an ultraclean carbon nanotube to realize this system in a tunable potential. Using tunnelling spectroscopy we measure the addition spectra...
Shannon Information Entropy in Position Space for Two-Electron Atomic Systems
Lin, Chien-Hao
2015-01-01
Entropic measures provide analytic tools to help us understand correlation in quantum systems. In our previous work, we calculated linear entropy and von Neumann entropy as entanglement measures for the ground state and lower lying excited states in helium-like systems. In this work, we adopt another entropic measure, Shannon entropy, to probe the nature of correlation effects. Besides the results of the Shannon entropy in coordinate space for the singlet ground states of helium-like systems including positronium negative ion, hydrogen negative ion, helium atom, and lithium positive ion, we also show results for systems with nucleus charge around the ionization threshold.
Modified Korteweg-de Vries solitons at supercritical densities in two-electron temperature plasmas
Verheest, Frank; Hereman, Willy A
2016-01-01
The supercritical composition of a plasma model with cold positive ions in the presence of a two-temperature electron population is investigated, initially by a reductive perturbation approach, under the combined requirements that there be neither quadratic nor cubic nonlinearities in the evolution equation. This leads to a unique choice for the set of compositional parameters and a modified Korteweg-de Vries equation (mKdV) with a quartic nonlinear term. The conclusions about its one-soliton solution and integrability will also be valid for more complicated plasma compositions. Only three polynomial conservation laws can be obtained. The mKdV equation with quartic nonlinearity is not completely integrable, thus precluding the existence of multi-soliton solutions. Next, the full Sagdeev pseudopotential method has been applied and this allows for a detailed comparison with the reductive perturbation results. This comparison shows that the mKdV solitons have slightly larger amplitudes and widths than those obta...
Two-electron rearrangement K x-ray transitions in Na, Mg, and Al metals
Energy Technology Data Exchange (ETDEWEB)
Aberg, T.; Reinikainen, K.; Keski-Rahkonen, O.
1981-01-01
One-photon KL/sup n//sub 2,3/ (n=1,2) radiative electron rearrangement (KL/sup n/ RER) x-ray transitions have been observed in sodium, magnesium, and aluminum metals following electron-impact excitation. The structure of the KL/sup n/ RER transitions has been separated from the KLL and KL/sub 1/V radiative Auger (RA) structure and their intensity relative to the KL/sup n//sub 2,3/-L/sup n/+1/sub 2,3/ transitions has been determined. No significant discrepancy between the experimental and calulated KL/sup 1/ RER branching ratios has been found in contrast to recent ion-impact results of Jamison et al. for aluminum and silicon. Our KL/sup 2/ RER results also agree with theoretical predictions.
Lim, Hwei Mian; Chee, Hengleng; Kandiah, Mirnalini; Shamsuddin, Khadijah; Jamaluddin, Jamilah; Nordin, Noranitamegat; Shuib, Rashidah
2003-09-01
This study was a cross-sectional survey conducted among 122 women workers employed in the electronics factories in the Ulu Klang Free Trade Zone (FTZ) and the Bangi FTZ, Selangor, Peninsular Malaysia. The purpose of the study was to examine the problem of overweight (>25.0 kg/m2) among this group of women, and factors (socio-demographic, work, exercise, and dietary) associated with overweight, and, to study the food intake pattern of the women in both the overweight and non-overweight groups. Data was collected using a set of questionnaires, while anthropometric measurements were obtained to calculate body mass index (BMI) and waist hip ratio (WHR). The results of the study indicated that 64.0% of the women were overweight (29.5% pre-obese, 34.5% obese). About one-tenth of the women (11.5%) had a WHR of above 0.85. From the bivariate analysis, it was found that women who were older, ever married, had lower educational level, had higher salary, not living in the hostel, involved in shiftwork, and trying to lose weight were more likely to be overweight. After adjusting for age, each of the above factors, except for educational level, remained significantly associated with overweight. Women's diet was found to be monotonous and lacking in variety as accessibility to and availability of a variety of food was a problem for them due to the nature of their work. They also had a sedentary lifestyle. Therefore, further research focusing on changing the poor dietary habits and sedentary lifestyle of the women workers is necessary to address the problem of overweight.
One- or Two-Electron Water Oxidation, Hydroxyl Radical, or H2O2 Evolution.
Siahrostami, Samira; Li, Guo-Ling; Viswanathan, Venkatasubramanian; Nørskov, Jens K
2017-02-27
Electrochemical or photoelectrochemcial oxidation of water to form hydrogen peroxide (H2O2) or hydroxyl radicals ((•)OH) offers a very attractive route to water disinfection, and the first process could be the basis for a clean way to produce hydrogen peroxide. A major obstacle in the development of effective catalysts for these reactions is that the electrocatalyst must suppress the thermodynamically favored four-electron pathway leading to O2 evolution. We develop a thermochemical picture of the catalyst properties that determine selectivity toward the one, two, and four electron processes leading to (•)OH, H2O2, and O2.
A two-electron shell game: Intermediates of the extradiol-cleaving catechol dioxygenases
Fielding, Andrew J.
2014-01-01
Extradiol catechol ring-cleaving dioxygenases function by binding both the organic substrate and O2 at a divalent metal center in the active site. They have proven to be a particularly versatile group of enzymes with which to study the O2 activation process. Here, recent studies of homoprotocatechuate 2,3-dioxygenase (HPCD) are summarized with the objective of showing how Nature can utilize the enzyme structure and the properties of the metal and the substrate to select among many possible chemical paths to achieve both specificity and efficiency. Possible intermediates in the mechanism have been trapped by swapping active site metals, introducing active site amino acid substituted variants, and using substrates with different electron donating capacities. While each of these intermediates could form part of a viable reaction pathway, kinetic measurements significantly limit the likely candidates. Structural, kinetic, spectroscopic and computational analysis of the various intermediates shed light on how catalytic efficiency can be achieved. PMID:24615282
Slowly moving test charge in two-electron component non-Maxwellian plasma
Energy Technology Data Exchange (ETDEWEB)
Ali, S. [National Centre for Physics (NCP), Quaid-e-Azam University Campus, Shahdra Valley Road, Islamabad 44000 (Pakistan); Eliasson, B. [SUPA, Physics Department, University of Strathclyde, Glasgow G4 0NG, Scotland (United Kingdom)
2015-08-15
Potential distributions around a slowly moving test charge are calculated by taking into account the electron-acoustic waves in an unmagnetized plasma. Considering a neutralizing background of static positive ions, the supra-thermal hot and cold electrons are described by the Vlasov equations to account for the Kappa (power-law in velocity space) and Maxwell equilibrium distributions. Fourier analysis further leads to the derivation of electrostatic potential showing the impact of supra-thermal hot electrons. The test charge moves slowly in comparison with the hot and cold electron thermal speeds and is therefore shielded by the electrons. This gives rise to a short-range Debye-Hückel potential decaying exponentially with distance and to a far field potential decaying as inverse third power of the distance from the test charge. The results are relevant for both laboratory and space plasmas, where supra-thermal hot electrons with power-law distributions have been observed.
Slowly moving test charge in two-electron component non-Maxwellian plasma
Ali, S.; Eliasson, B.
2015-08-01
Potential distributions around a slowly moving test charge are calculated by taking into account the electron-acoustic waves in an unmagnetized plasma. Considering a neutralizing background of static positive ions, the supra-thermal hot and cold electrons are described by the Vlasov equations to account for the Kappa (power-law in velocity space) and Maxwell equilibrium distributions. Fourier analysis further leads to the derivation of electrostatic potential showing the impact of supra-thermal hot electrons. The test charge moves slowly in comparison with the hot and cold electron thermal speeds and is therefore shielded by the electrons. This gives rise to a short-range Debye-Hückel potential decaying exponentially with distance and to a far field potential decaying as inverse third power of the distance from the test charge. The results are relevant for both laboratory and space plasmas, where supra-thermal hot electrons with power-law distributions have been observed.
Liu, C; Liu, J; Yao, Y X; Wu, P; Wang, C Z; Ho, K M
2016-10-11
We recently proposed the correlation matrix renormalization (CMR) theory to treat the electronic correlation effects [Phys. Rev. B 2014, 89, 045131 and Sci. Rep. 2015, 5, 13478] in ground state total energy calculations of molecular systems using the Gutzwiller variational wave function (GWF). By adopting a number of approximations, the computational effort of the CMR can be reduced to a level similar to Hartree-Fock calculations. This paper reports our recent progress in minimizing the error originating from some of these approximations. We introduce a novel sum-rule correction to obtain a more accurate description of the intersite electron correlation effects in total energy calculations. Benchmark calculations are performed on a set of molecules to show the reasonable accuracy of the method.
Effect of pre-flaring and file size on the accuracy of two electronic apex locators
Directory of Open Access Journals (Sweden)
Manoel Brito-Júnior
2012-10-01
Full Text Available OBJECTIVE: This ex vivo study evaluated the effect of pre-flaring and file size on the accuracy of the Root ZX and Novapex electronic apex locators (EALs. MATERIAL AND METHODS: The actual working length (WL was set 1 mm short of the apical foramen in the palatal root canals of 24 extracted maxillary molars. The teeth were embedded in an alginate mold, and two examiners performed the electronic measurements using #10, #15, and #20 K-files. The files were inserted into the root canals until the "0.0" or "APEX" signals were observed on the LED or display screens for the Novapex and Root ZX, respectively, retracting to the 1.0 mark. The measurements were repeated after the preflaring using the S1 and SX Pro-Taper instruments. Two measurements were performed for each condition and the means were used. Intra-class correlation coefficients (ICCs were calculated to verify the intra- and inter-examiner agreement. The mean differences between the WL and electronic length values were analyzed by the three-way ANOVA test (p0.8 and the results demonstrated a similar accuracy for both EALs (p>0.05. Statistically significant accurate measurements were verified in the pre-flared canals, except for the Novapex using a #20 K-file. CONCLUSIONS: The tested EALs showed acceptable accuracy, whereas the pre-flaring procedure revealed a more significant effect than the used file size.
Correlated Two-Electron Capture by Ion with Emission of Photon
Mikhailov, A. I.
2005-05-01
The correlated double electron capture into the K shell of bare ions with emission of a single photon is considered. The process is treated as a time-reversed atomic double photoionization. For ten years of experimental investigations there is no evidence of existence of the reaction. There is a theoretical prediction (Phys. Rev. A 55 (1997) 1952), that a probability of the process grows rapidly with the ion charge due to relativistic effects and that the cross section does not depend on target atoms. However the recent experiment (GSI Scien.Rep., ISSN 174 (2001) 98) failed to observe this process under the recommended conditions. The present work reveals an incorrectness of those theoretical predictions and provides an expression to determine optimal experimental conditions for observing the process. We suggest to use ion beams slower than those in the experiment (NIM B98 (1995)303), and do not recommend to use heavy ions. We show that the cross section can increase significantly for solid-state targets and decelerated ion beams. The novel technique of deceleration of multicharged ions planned at GSI can be applied to perform such experiments.
Evaluation of Two-center One- and Two-electron Integrals over Slater Type Orbitals
Institute of Scientific and Technical Information of China (English)
YAKAR Yusuf; (O)ZMEN Ayhan; ATAV (U)lfet
2006-01-01
A formulation previously presented by the authors for coulomb integrals was generalized to other two-center integrals, except exchange integral. Within this frame, molecular integrals were expressed in terms of some new functions closely related to the well-known incomplete gamma functions and these functions recursively evaluated.Special issues arising in the case of hybrid integrals were addressed, and the results were compared with the ones found in the literature.
Energy Technology Data Exchange (ETDEWEB)
Olivier, C. P., E-mail: colivier@sansa.org.za; Maharaj, S. K., E-mail: smaharaj@sansa.org.za [South African National Space Agency (SANSA) Space Science, P. O. Box 32, Hermanus 7200 (South Africa); Bharuthram, R., E-mail: rbharuthram@uwc.ac.za [University of the Western Cape, Robert Sobukwe Road, Bellville 7535 (South Africa)
2015-08-15
The polarity of ion-acoustic solitons that arise in a plasma with two (same mass, different temperature) ion species and two (different temperature) electron species is investigated. Two different fluid models are compared. The first model treats all species as adiabatic fluids, while the second model treats the ion species as adiabatic, and the electron species as isothermal. Nonlinear structures are analysed via the reductive perturbation analysis and pseudo-potential analysis. Each model supports both slow and fast ion-acoustic solitons, associated with the two (slow and fast) ion-acoustic speeds. The models support both positive and negative polarity solitons associated with the slow ion-acoustic speed. Moreover, results are in good agreement, and both models support positive and negative polarity double layers. For the fast ion-acoustic speed, the first model supports only positive polarity solitons, while the second model supports solitons of both polarity, coexistence of positive and negative polarity solitons, double layers and supersolitons. A novel feature of our analysis is the evaluation of nonlinear structures at critical number densities where polarity changes occur. This analysis shows that solitons that occur at the acoustic speed are neither a necessary nor a sufficient condition for the phenomenon of coexistence. The relationship between the existence regions of supersolitons and soliton polarity is also discussed.
Energy Technology Data Exchange (ETDEWEB)
Modesto-Costa, Lucas; Canuto, Sylvio [Instituto de Física, Universidade de São Paulo, CP 66318, 05314-970 São Paulo (Brazil); Mukherjee, Prasanta K., E-mail: profpkmukherjee@gmail.com [Department of Physics, Ramakrishna Mission Vivekananda University, P.O. Belur Math, Howrah, West Bengal 711202 (India)
2015-03-15
A detailed investigation of the magnetic dipolar and quadrupolar excitation energies and transition probabilities of helium isoelectronic He, Be{sup 2+}, C{sup 4+}, and O{sup 6+} have been performed under exponential cosine screened Coulomb potential generated in a plasma environment. The low-lying excited states 1s{sup 2}:{sup 1}S{sup e} → 1sns:{sup 3}S{sup e}{sub 0}, and 1snp:{sup 3}P{sup o}{sub 2} (n = 2, 3, 4, and 5) are considered. The variational time-dependent coupled Hartree-Fock scheme has been used. The effect of the confinement produced by the potential on the structural properties is investigated for increasing coupling strength of the plasma. It is noted that there is a gradual destabilization of the energy of the system with the reduction of the ionization potential and the number of excited states. The effect of the screening enhancement on the excitation energies and transition probabilities has also been investigated and the results compared with those available for the free systems and under the simple screened Coulomb potential.
Fourier-Legendre expansion of the one-electron density-matrix of ground-state two-electron atoms
Ragot, Sebastien; Ruiz, Maria Belen
2009-01-01
The density-matrix rho(r, r') of a spherically symmetric system can be expanded as a Fourier-Legendre series of Legendre polynomials Pl(cos(theta) = r.r'/rr'). Application is here made to harmonically trapped electron pairs (i.e. Moshinsky's and Hooke's atoms), for which exact wavefunctions are known, and to the helium atom, using a near-exact wavefunction. In the present approach, generic closed form expressions are derived for the series coefficients of rho(r, r'). The series expansions are...
Institute of Scientific and Technical Information of China (English)
M.N.S.Qureshi; S.Sehar; H.A.Shah; J.B.Cao
2013-01-01
In many physical situations where a laser or electron beam passes through a dense plasma,hot low-density electron populations can be generated,resulting in a particle distribution function consisting of a dense cold population and a small hot population.Presence of such low-density electron distributions can alter the wave damping rate.A kinetic model is employed to study the Landau damping of Langmuir waves when a small hot electron population is present in the dense cold electron population with non-Maxwellian distribution functions.Departure of plasma from Maxwellian distributions significantly alters the damping rates as compared to the Maxwellian plasma.Strong damping is found for highly non-Maxwellian distributions as well as plasmas with a higher density and hot electron population.Existence of weak damping is also established when the distribution contains broadened flat tops at the low energies or tends to be Maxwellian.These results may be applied in both experimental and space physics regimes.
Kiernicki, John J; Fanwick, Phillip E; Bart, Suzanne C
2014-08-01
Exposure of the uranium(IV) complex, Cp(P)U((Mes)PDI(Me)) (1) ((Mes)PDI(Me) = 2,6-((Mes)N=CMe)2–C5H3N; Mes = 2,4,6-trimethylphenyl; Cp(P) = 1-(7,7-dimethylbenzyl)cyclopentadienyl), which contains a [(Mes)PDI(Me)](3−) chelate, to I2, Cl2, PhSeCl, and PhEEPh (E = S, Se, Te) results in oxidative addition to form the uranium(IV) family, Cp(P)U(XX′)((Mes)PDI(Me)) (X = X′ = I, Cl, EPh; X = SePh, X′ = Cl). Spectroscopic and structural studies support products with [(Mes)PDI(Me)](1−), indicating the reducing equivalents derive from this redox-active chelate.
Lesiuk, Michał
2014-01-01
In this paper, which constitutes the first part of the series, we consider calculation of two-centre Coulomb and hybrid integrals over Slater-type orbitals (STOs). General formulae for these integrals are derived with no restrictions on the values of the quantum numbers and nonlinear parameters. Direct integration over the coordinates of one of the electrons leaves us with the set of overlap-like integrals which are evaluated by using two distinct methods. The first one is based on the transformation to the ellipsoidal coordinates system and the second utilises a recursive scheme for consecutive increase of the angular momenta in the integrand. In both methods simple one-dimensional numerical integrations are used in order to avoid severe digital erosion connected with the straightforward use of the alternative analytical formulae. It is discussed that the numerical integration does not introduce a large computational overhead since the integrands are well-behaved functions, calculated recursively with decent...
Jain, Saru; Kapur, Ravi
2012-01-01
Context: The establishment of appropriate working length is one of the most critical steps in endodontic therapy. Electronic apex locators have been introduced to determine the working length. The development of electronic apex locators has helped make the assessment of the working length more accurate and predictable, along with reduction in treatment time and radiation dose. Objectives: The aim of this study was to compare the efficacy of electronic apex locators after cleansing and shaping of the root canals and whether there was any alteration in accuracy when used in the presence of irrigants. Materials and Methods: Seventy extracted human permanent molars with mature apices were selected. Equal number of maxillary and mandibular permanent molars (35 each) were sectioned at the cemento-enamel junction. Access opening was done and only the mesiobuccal root canal was studied for the purpose of standardization. Electronic working length measurements were taken before and after preparation of the mesiobuccal canal with Root ZX and ProPex II using various irrigants. Statistical Analysis Used: The data were statistically analyzed using a paired t-test at 0.05 level of significance. Results: P-values for actual and final canal lengths for Root ZX employing NaoCl(0.001), CHX(0.006), LA(0.020) and for ProPex II was (0.001) respectively. When the data were compared, results were statistically significant (P locator and CHX as irrigant matched more precisely with the actual canal length measurements. PMID:23230349
Directory of Open Access Journals (Sweden)
Saru Jain
2012-01-01
Full Text Available Context: The establishment of appropriate working length is one of the most critical steps in endodontic therapy. Electronic apex locators have been introduced to determine the working length. The development of electronic apex locators has helped make the assessment of the working length more accurate and predictable, along with reduction in treatment time and radiation dose. Objectives: The aim of this study was to compare the efficacy of electronic apex locators after cleansing and shaping of the root canals and whether there was any alteration in accuracy when used in the presence of irrigants. Materials and Methods: Seventy extracted human permanent molars with mature apices were selected. Equal number of maxillary and mandibular permanent molars (35 each were sectioned at the cemento-enamel junction. Access opening was done and only the mesiobuccal root canal was studied for the purpose of standardization. Electronic working length measurements were taken before and after preparation of the mesiobuccal canal with Root ZX and ProPex II using various irrigants. Statistical Analysis Used: The data were statistically analyzed using a paired t-test at 0.05 level of significance. Results: P-values for actual and final canal lengths for Root ZX employing NaoCl(0.001, CHX(0.006, LA(0.020 and for ProPex II was (0.001 respectively. When the data were compared, results were statistically significant (P < 0.05. Conclusion: Within the limitations of this study Root ZX can be considered to be an accurate electronic apex locator and CHX as irrigant matched more precisely with the actual canal length measurements.
Two-electron bound state formation in the t-J-U model for exchange-coupled planes
Morriss-Andrews, A.; Gooding, R. J.
2007-01-01
An anisotropic t-J-U model Hamiltonian is used to model electron behaviour in quasi-2d materials in the dilute limit, and as a highly simplified representation of the weakly coupled CuO2 planes of the high-Tc cuprates we model the very poor out-of-plane conductivity via the complete suppression of interplanar hopping. However, we do include the very weak interplanar superexchange, and are thus considering a model of exchange-coupled planes. For an isotropic three-dimensional system in the dil...
Bevers, L.E.; Hagen, W.R.
2009-01-01
Reversible binding of the tetrahedral oxoanions MoO4 2- and WO4 2- to two carboxylato ligands of the soluble scavenger protein WtpA from the hyperthermophilic archaeon Pyrococcus furiosus enforces a quasi-octahedral MO6 coordination in which the +VI oxidation state is destabilized.
Effects of bias on dynamics of an AC-driven two-electron quantum-dot molecule
Institute of Scientific and Technical Information of China (English)
Wang Li-Min; Duan Su-Qing; Zhao Xian-Geng; Liu Cheng-Shi
2005-01-01
The effects of bias on the dynamical localization of two interacting electrons in a pair of coupled quantum dots driven by external AC fields have been numerically investigated. With an effective two-site model and Floquet formalism,the time-dependent Schrodinger equation is numerically solved and the Pmin, the minimum of the population evolution of the initial state within a certain time period, is used to quantify the degree of the dynamical localization. Results indicate that the bias can change the energy of the initial state and break the dynamical symmetry of the system with a pure AC field. And the amplitude of the AC field with dynamical localization phenomenon changes with bias. All the numerical results are explained by the perturbation theory and two-level approximation.
Hu, X; Hu, Xuedong
2000-01-01
We study theoretically a double quantum dot hydrogen molecule in the GaAs conduction band as the basic elementary gate for a quantum computer with the electron spins in the dots serving as qubits. Such a two-dot system provides the necessary two-qubit entanglement required for quantum computation. We determine the excitation spectrum of two horizontally coupled quantum dots with two confined electrons, and study its dependence on an external magnetic field. In particular, we focus on the splitting of the lowest singlet and triplet states, the double occupation probability of the lowest states, and the relative energy scales of these states. We point out that at zero magnetic field it is difficult to have both a vanishing double occupation probability for a small error rate and a sizable exchange coupling for fast gating. On the other hand, finite magnetic fields may provide finite exchange coupling for quantum computer operations with small errors. We critically discuss the applicability of the envelope funct...
Two-electron transfer and ionization mechanism in 80-keV/u Ne8 + on He collisions
Zhang, R. T.; Feng, W. T.; Zhu, X. L.; Zhang, S. F.; Guo, D. L.; Gao, Y.; Qian, D. B.; Xu, S.; Yan, S. C.; Zhang, P.; Huang, Z. K.; Wang, H. B.; Hai, B.; Zhao, D. M.; Ma, X.
2016-03-01
Autoionization decay from doubly excited states of Ne6 +[1 s23 l n l (n =3 ,4 ,5 )] (symmetric configurations) as well as the Coster-Kronig transition from doubly excited states of Ne6 +[1 s22 p n l (n ⩾7 ) ] (asymmetric configurations) are observed in the transfer ionization reaction channel of 80 keV/u Ne8 +-He collisions. It has been predicted that the formation of symmetric configurations results from uncorrelated double-electron capture processes [Z. Chen and C. D. Lin, Phys. Rev. A 48, 1298 (1993), 10.1103/PhysRevA.48.1298], and the formation of asymmetric configurations probably results from correlated double-electron capture caused by the dynamical electron-correlation effects which are attributed to small internuclear distances. However, previous experimental measurements were not able to obtain information about the dependence on internuclear distance which can be reflected in the transversal recoil-ion momentum. In this work, we measure the recoil-ion momentum in coincidence with the ejected electron velocity and find that the observed transverse recoil-ion momentum is smaller for the formation of symmetric Ne6 +[1 s23 l n l (n =3 ,4 ,5 ) ] states than the formation of asymmetric Ne6 +[1 s22 p n l (n ⩾7 ) ] states. Since large momentum transfer occurs for small internuclear distances (strong electron-electron interactions) and small momentum transfer occurs for large internuclear distances (weak electron-electron interactions), the results indicate that dynamical electron correlation is important for the formation of the asymmetric states.
Directory of Open Access Journals (Sweden)
Farouk Rashwan
2005-01-01
Full Text Available The Electrochemical Impedance Spectroscopic techniques (EIS were used to investigate the behavior of some dye compounds (quinoid systems characterized with 2e-transfer processes. For this purpose, Alizarin Red S (ARS, Alizarin Cyanine (AC, Alizarin Viridin (AV and carminic acid were chosen for the measurements. The EIS experiments were performed using a small AC amplitude (10 mV p-p in addition to a relatively wide frequency range (0.01 Hz â¤ f â¤ 105 Hz. The investigations were carried out at room temperature in aqueous media (HClO4, NaClO4 and KNO3 on the Hanging Mercury Drop Electrode (HMDE and for comparison one experiment only was measured in aprotic solvent (DMF on the Pt-disc electrode. The EIS diagrams of these systems were characterized in the complex plane by two fundamental observations, the first of which is a straight line crossing the real axis at an angle of 45Â° (or at least nearly so and the second one is two semicircles beside each other corresponding to high-frequency and low-frequency regions, which are implying the presence of well-separated time constants. The EIS characteristic parameters for these dye systems were calculated and discussed.
Energy Technology Data Exchange (ETDEWEB)
Giesbertz, K. J. H., E-mail: k.j.h.giesbertz@vu.nl [Section Theoretical Chemistry, VU University, De Boelelaan 1083, 1081 HV Amsterdam (Netherlands); Gritsenko, O. V. [Section Theoretical Chemistry, VU University, De Boelelaan 1083, 1081 HV Amsterdam (Netherlands); Pohang University of Science and Technology, Department of Chemistry, San 31, Hyojadong, Namgu, Pohang 790-784 (Korea, Republic of); Baerends, E. J. [Section Theoretical Chemistry, VU University, De Boelelaan 1083, 1081 HV Amsterdam (Netherlands); Pohang University of Science and Technology, Department of Chemistry, San 31, Hyojadong, Namgu, Pohang 790-784 (Korea, Republic of); Department of Chemistry, Faculty of Science, King Abdulaziz University, Jeddah 21589 (Saudi Arabia)
2014-05-14
Recently, we have demonstrated that the problems finding a suitable adiabatic approximation in time-dependent one-body reduced density matrix functional theory can be remedied by introducing an additional degree of freedom to describe the system: the phase of the natural orbitals [K. J. H. Giesbertz, O. V. Gritsenko, and E. J. Baerends, Phys. Rev. Lett. 105, 013002 (2010); K. J. H. Giesbertz, O. V. Gritsenko, and E. J. Baerends, J. Chem. Phys. 133, 174119 (2010)]. In this article we will show in detail how the frequency-dependent response equations give the proper static limit (ω → 0), including the perturbation in the chemical potential, which is required in static response theory to ensure the correct number of particles. Additionally we show results for the polarizability for H{sub 2} and compare the performance of two different two-electron functionals: the phase-including Löwdin–Shull functional and the density matrix form of the Löwdin–Shull functional.
Giesbertz, K. J. H.; Gritsenko, O. V.; Baerends, E. J.
2014-05-01
Recently, we have demonstrated that the problems finding a suitable adiabatic approximation in time-dependent one-body reduced density matrix functional theory can be remedied by introducing an additional degree of freedom to describe the system: the phase of the natural orbitals [K. J. H. Giesbertz, O. V. Gritsenko, and E. J. Baerends, Phys. Rev. Lett. 105, 013002 (2010); K. J. H. Giesbertz, O. V. Gritsenko, and E. J. Baerends, J. Chem. Phys. 133, 174119 (2010)]. In this article we will show in detail how the frequency-dependent response equations give the proper static limit (ω → 0), including the perturbation in the chemical potential, which is required in static response theory to ensure the correct number of particles. Additionally we show results for the polarizability for H2 and compare the performance of two different two-electron functionals: the phase-including Löwdin-Shull functional and the density matrix form of the Löwdin-Shull functional.
Giesbertz, K J H; Gritsenko, O V; Baerends, E J
2014-05-14
Recently, we have demonstrated that the problems finding a suitable adiabatic approximation in time-dependent one-body reduced density matrix functional theory can be remedied by introducing an additional degree of freedom to describe the system: the phase of the natural orbitals [K. J. H. Giesbertz, O. V. Gritsenko, and E. J. Baerends, Phys. Rev. Lett. 105, 013002 (2010); K. J. H. Giesbertz, O. V. Gritsenko, and E. J. Baerends, J. Chem. Phys. 133, 174119 (2010)]. In this article we will show in detail how the frequency-dependent response equations give the proper static limit (ω → 0), including the perturbation in the chemical potential, which is required in static response theory to ensure the correct number of particles. Additionally we show results for the polarizability for H2 and compare the performance of two different two-electron functionals: the phase-including Löwdin-Shull functional and the density matrix form of the Löwdin-Shull functional.
Quantum entropy and special relativity.
Peres, Asher; Scudo, Petra F; Terno, Daniel R
2002-06-10
We consider a single free spin- 1 / 2 particle. The reduced density matrix for its spin is not covariant under Lorentz transformations. The spin entropy is not a relativistic scalar and has no invariant meaning.
CMS Higgs Search in 2011 and 2012 data: candidate ZZ event (8 TeV) with two electrons and two muons
McCauley, T
2012-01-01
Event recorded with the CMS detector in 2012 at a proton-proton centre of mass energy of 8 TeV. The event shows characteristics expected from the decay of the SM Higgs boson to a pair of Z bosons, one of which subsequently decays to a pair of electrons (green lines and green towers) and the other Z decays to a pair of muons (red lines). The event could also be due to known standard model background processes.
Haque, Q.; Mirza, Arshad M.; Iqbal, Javed
2016-04-01
Linear and nonlinear characteristics of electrostatic waves in a multicomponent magnetoplasma comprising of Boltzmann distributed electrons, Cairn's distributed hot electrons, and cold dynamic ions are studied. It is found that the effect of superthermal electrons, ion-neutral collisions, and ion shear flow modifies the propagation of ion-acoustic and drift waves. The growth rate of the ion shear flow instability varies with the addition of Cairn's distributed hot electrons. It is also investigated that the behavior of different type of vortices changes with the inclusion of superthermal hot electrons. The relevance of this investigation in space plasmas such as in auroral region and geomagnetic tail is also pointed out.
Álvarez-Rodríguez, Lucía; Cabeza, Javier A; García-Álvarez, Pablo; Pérez-Carreño, Enrique; Polo, Diego
2015-03-16
The reactivity of ruthenium carbonyl with amidinatogermylenes of the type Ge(R2bzam)(t)Bu (R2bzam = N,N'-disubstituted benzamidinate) was studied for R = (t)Bu (1tBu) and (i)Pr (1iPr). The mono-, bi-, and/or trinuclear derivatives [Ru(1R)(CO)4], [Ru(1R)2(CO)3], [Ru2(1iPr)(CO)7], [Ru3(1tBu)(CO)11], [Ru3(1tBu)2(CO)10], and [Ru3(1R)3(CO)9] (R = (t)Bu, (i)Pr) were isolated in yields that depend upon the reactant ratio and the reaction temperature. The experimental data are consistent with the proposal that, at room temperature, the trinuclear complexes [Ru3(CO)12], [Ru3(1R)(CO)11], and [Ru3(1R)2(CO)10] form an adduct with the germylene 1R that may evolve through two different reaction pathways, (a) releasing a CO ligand (thus leading to the corresponding trinuclear CO-substituted product) and/or (b) cleaving the cluster framework (thus leading to mononuclear germylene-containing products). At 90 °C, additional processes are also possible, such as the reactions of 1R with [Ru(1R)(CO)4] or [Ru3(1R)3(CO)9], which both give [Ru(1R)2(CO)3], or the reactions of [Ru(1tBu)(CO)4] and [Ru(1iPr)(CO)4] with [Ru3(CO)12], which give [Ru3(1tBu)(CO)11] and [Ru2(1iPr)(CO)7], respectively. This wide reaction panorama helps rationalize previously reported outcomes of reactions of [Ru3(CO)12] with other reagents of high basicity, such as trialkylphosphines or N-heterocyclic carbenes, including results for which no satisfactory explanation has been hitherto provided.
Energy Technology Data Exchange (ETDEWEB)
Maharaj, S. K. [South African National Space Agency (SANSA) Space Science, P.O. Box 32, Hermanus 7200 (South Africa); Bharuthram, R. [University of the Western Cape, Modderdam Road, Bellville 7530 (South Africa); Singh, S. V. [Indian Institute of Geomagnetism, New Panvel (West), Navi Mumbai 410218 (India); School of Physics, University of KwaZulu-Natal, Private Bag X54001, Durban 4000 (South Africa); Lakhina, G. S. [Indian Institute of Geomagnetism, New Panvel (West), Navi Mumbai 410218 (India)
2012-07-15
Using the Sagdeev pseudopotential technique, the existence of large amplitude ion-acoustic solitons is investigated for a plasma composed of ions, and hot and cool electrons. Not only are all species treated as adiabatic fluids but the model for which inertial effects of the hot electrons is neglected whilst retaining inertia and pressure for the ions and cool electrons has also been considered. The focus of this investigation has been on identifying the admissible Mach number ranges for large amplitude nonlinear ion-acoustic soliton structures. The lower Mach number limit yields a minimum velocity for the existence of ion-acoustic solitons. The upper Mach number limit for positive potential solitons is found to coincide with the limiting value of the potential (positive) beyond which the ion number density ceases to be real valued, and ion-acoustic solitons can no longer exist. Small amplitude solitons having negative potentials are found to be supported when the temperature of the cool electrons is negligible.
Energy Technology Data Exchange (ETDEWEB)
Maharaj, S. K. [South African National Space Agency (SANSA) Space Science, P.O. Box 32, Hermanus 7200 (South Africa); Bharuthram, R. [University of the Western Cape, Modderdam Road, Bellville 7530 (South Africa); Singh, S. V. [Indian Institute of Geomagnetism, New Panvel (West), Navi Mumbai 410218 (India); School of Chemistry and Physics, University of KwaZulu-Natal, Private Bag X54001, Durban 4000 (South Africa); Lakhina, G. S. [Indian Institute of Geomagnetism, New Panvel (West), Navi Mumbai 410218 (India)
2012-12-15
A three-component plasma model composed of ions, cool electrons, and hot electrons is adopted to investigate the existence of large amplitude electron-acoustic solitons not only for the model for which inertia and pressure are retained for all plasma species which are assumed to be adiabatic but also neglecting inertial effects of the hot electrons. Using the Sagdeev potential formalism, the Mach number ranges supporting the existence of large amplitude electron-acoustic solitons are presented. The limitations on the attainable amplitudes of electron-acoustic solitons having negative potentials are attributed to a number of different physical reasons, such as the number density of either the cool electrons or hot electrons ceases to be real valued beyond the upper Mach number limit, or, alternatively, a negative potential double layer occurs. Electron-acoustic solitons having positive potentials are found to be supported only if inertial effects of the hot electrons are retained and these are found to be limited only by positive potential double layers.
Hernandez, Penni; Podchiyska, Tanya; Weber, Susan; Ferris, Todd; Lowe, Henry
2009-11-14
The Stanford Translational Research Integrated Database Environment (STRIDE) clinical data warehouse integrates medication information from two Stanford hospitals that use different drug representation systems. To merge this pharmacy data into a single, standards-based model supporting research we developed an algorithm to map HL7 pharmacy orders to RxNorm concepts. A formal evaluation of this algorithm on 1.5 million pharmacy orders showed that the system could accurately assign pharmacy orders in over 96% of cases. This paper describes the algorithm and discusses some of the causes of failures in mapping to RxNorm.
Energy Technology Data Exchange (ETDEWEB)
Abrashkevich, A.G.; Shapiro, M. [Weizmann Inst. of Science, Rehovoth (Israel). Dept. of Chemical Physics and Structural Chemistry
1996-02-28
Theory of one-photon ionization of atoms by intense light pulses is developed. The infinite set of coupled first-order differential equations, derived from the time-dependent Schroedinger equation, is reduced to a single integro-differential equation. This equation is solved both numerically and in closed form by invoking the slowly varying continuum approximation (SVCA). Comparisons of the SVCA with the numerical solutions are used to delimit the range of validity of this approximation. The time-evolution of wavepackets composed of scattering states prepared by short laser pulses is studied as a function of the pulse intensity. We predict a transient `freezing` of the wavepacket during its build-up phase. Temporal saturation and power broadening of the wavepacket by the strong field are also studied. Our method is used to performing exact numerical calculations of the real-time strong-pulse one-photon ionization of He and the photodetachment of H{sup -}. (author).
Abrashkevich, Alexander G.; Shapiro, Moshe
1996-02-01
Theory of one-photon ionization of atoms by intense light pulses is developed. The infinite set of coupled first-order differential equations, derived from the time-dependent Schrödinger equation, is reduced to a single integro-differential equation. This equation is solved both numerically and in closed form by invoking the slowly varying continuum approximation (SVCA). Comparisons of the SVCA with the numerical solutions are used to delimit the range of validity of this approximation. The time-evolution of wavepackets composed of scattering states prepared by short laser pulses is studied as a function of the pulse intensity. We predict a transient `freezing' of the wavepacket during its build-up phase. Temporal saturation and power broadening of the wavepacket by the strong field are also studied. Our method is used to performing exact numerical calculations of the real-time strong-pulse one-photon ionization of He and the photodetachment of 0953-4075/29/4/006/img2.
Chu, John C. K.; Dalton, Derek M.; Rovis, Tomislav
2015-01-01
We report a catalytic asymmetric synthesis of piperidines through [4+2] cycloaddition of 1-azadienes and nitroalkenes. The reaction uses earth abundant Zn as catalyst, and is highly diastereo- and regio-selective. A novel BOPA ligand (F-BOPA) confers high reactivity and enantioselectivity in the process. The presence of ortho substitution on the arenes adjacent to the bis(oxazolines) was found to be particularly impactful, due to limiting the undesired coordination of 1-azadiene to the Lewis ...
Lesiuk, Michał; Musiał, Monika; Jeziorski, Bogumił; Moszynski, Robert
2014-01-01
In this paper we present results of ab-initio calculations for the beryllium dimer with basis set of Slater-type orbitals (STOs). Nonrelativistic interaction energy of the system is determined using the frozen-core full configuration interaction calculations combined with high-level coupled cluster correction for inner-shell effects. Newly developed STOs basis sets, ranging in quality from double to sextuple zeta, are used in these computations. Principles of their construction are discussed and several atomic benchmarks are presented. Relativistic effects of order ${\\alpha}^2$ are calculated perturbatively by using the Breit-Pauli Hamiltonian and are found to be significant. We also estimate the leading-order QED effects. Influence of the adiabatic correction is found to be negligible. Finally, the interaction energy of the beryllium dimer is determined to be 929.0$\\,\\pm\\,$1.9 $cm^{-1}$, in a very good agreement with the recent experimental value. The results presented here appear to be the most accurate ab-...
Fromager, Emmanuel; Jensen, Hans Jørgen Aa
2011-07-21
Range-separated density-functional theory combines wave function theory for the long-range part of the two-electron interaction with density-functional theory for the short-range part. When describing the long-range interaction with non-variational methods, such as perturbation or coupled-cluster theories, self-consistency effects are introduced in the density functional part, which for an exact solution requires iterations. They are generally assumed to be small but no detailed study has been performed so far. Here, the authors analyze self-consistency when using Møller-Plesset-type (MP) perturbation theory for the long range interaction. The lowest-order self-consistency corrections to the wave function and the energy, that enter the perturbation expansions at the second and fourth order, respectively, are both expressed in terms of the one-electron reduced density matrix. The computational implementation of the latter is based on a Neumann series which, interestingly, even though the effect is small, usually diverges. A convergence technique, which perhaps can be applied in other uses of Neumann series in perturbation theory, is proposed. The numerical results thus obtained show that, in weakly bound systems, self-consistency can be neglected since the long-range correlation does not affect the density significantly. Although MP is not adequate for multireference systems, it can still be used as a reliable analysis tool. Though the density change is not negligible anymore in such cases, self-consistency effects are found to be much smaller than long-range correlation effects (less than 10% for the systems considered). For that reason, a sensible approximation might be to update the short-range energy functional term while freezing its functional derivative, namely, the short-range local potential, in the wave function optimization. The accuracy of such an approximation still needs to be assessed.
Impact of quantum entanglement on spectrum of cosmological fluctuations
Energy Technology Data Exchange (ETDEWEB)
Kanno, Sugumi, E-mail: sugumi.kanno@uct.ac.za [Laboratory for Quantum Gravity and Strings and Astrophysics, Cosmology and Gravity Center, Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag, Rondebosch 7701 (South Africa)
2014-07-01
We investigate the effect of entanglement between two causally separated open charts in de Sitter space on the spectrum of vacuum fluctuations. We consider a free massive scalar field, and construct the reduced density matrix by tracing out the vacuum state for one of the open charts, as recently derived by Maldacena and Pimentel. We formulate the mean-square vacuum fluctuations by using the reduced density matrix and show that the scale invariant spectrum of massless scalar field is realized on small scales. On the other hand, we find that the quantum entanglement affects the shape of the spectrum on large scales comparable to or greater than the curvature radius.
Impact of quantum entanglement on spectrum of cosmological fluctuations
Kanno, Sugumi
2014-01-01
We investigate the effect of entanglement between two causally separated open charts in de Sitter space on the spectrum of vacuum fluctuations. We consider a free massive scalar field, and construct the reduced density matrix by tracing out the vacuum state for one of the open charts, as recently derived by Maldacena and Pimentel. We formulate the mean-square vacuum fluctuations by using the reduced density matrix and show that the scale invariant spectrum of massless scalar field is realized on small scales. On the other hand, we find that the quantum entanglement affects the shape of the spectrum on large scales comparable to or greater than the curvature radius.
Quantum Lévy Processes and Fractional Kinetics
Kusnezov, D; Dang, G D; Kusnezov, Dimitri; Bulgac, Aurel; Dang, Giu Do
1999-01-01
Exotic stochastic processes are shown to emerge in the quantum evolution of complex systems. Using influence function techniques, we consider the dynamics of a system coupled to a chaotic subsystem described through random matrix theory. We find that the reduced density matrix can display dynamics given by fractional kinetic equations. In particular we derive a fractional extension of Kramers equation.
Interpretation of the triad orientations in loop quantum cosmology
Kiefer, Claus
2012-01-01
Loop quantum cosmology allows for arbitrary superpositions of the triad variable. We show here how these superpositions can become indistinguishable from a classical mixture by the interaction with fermions. We calculate the reduced density matrix for a locally rotationally symmetric Bianchi I model and show that the purity factor for the triads decreases by decoherence. In this way, the Universe assumes a definite orientation.
Origin of the Canonical Ensemble : Thermalization with Decoherence
Yuan, Shengjun; Katsnelson, Mikhail I.; De Raedt, Hans
We solve the time-dependent Schrodinger equation for the combination of a spin system interacting with a spin bath environment. In particular, we focus on the time development of the reduced density matrix of the spin system. Under normal circumstances we show that the environment drives the reduced
Zhong, Zai-Zhe
2004-01-01
The partial separability of multipartite qubit density matrixes is strictly defined. We give a reduction way from N-partite qubit density matrixes to bipartite qubit density matrixes, and prove a necessary condition that a N-partite qubit density matrix to be partially separable is its reduced density matrix to satisfy PPT condition.
Zhong, Zai-Zhe
2004-01-01
The partial separability of multipartite qubit density matrixes is strictly defined. We give a reduction way from N-partite qubit density matrixes to bipartite qubit density matrixes, and prove a necessary condition that a N-partite qubit density matrix to be partially separable is its reduced density matrix to satisfy PPT condition.
Origin of the Canonical Ensemble : Thermalization with Decoherence
Yuan, Shengjun; Katsnelson, Mikhail I.; De Raedt, Hans
2009-01-01
We solve the time-dependent Schrodinger equation for the combination of a spin system interacting with a spin bath environment. In particular, we focus on the time development of the reduced density matrix of the spin system. Under normal circumstances we show that the environment drives the reduced
Approach to Equilibrium in Nano-scale Systems at Finite Temperature
Jin, Fengping; De Raedt, Hans; Yuan, Shengjun; Katsnelson, Mikhail I.; Miyashita, Seiji; Michielsen, Kristel
2010-01-01
We study the time evolution of the reduced density matrix of a system of spin-1/2 particles interacting with an environment of spin-1/2 particles. The initial state of the composite system is taken to be a product state of a pure state of the system and a pure state of the environment. The latter pu
Estimating purity in terms of correlation functions
Prosen, T; Znidaric, M; Prosen, Tomaz; Seligman, Thomas H.; Znidaric, Marko
2003-01-01
We prove a rigorous inequality estimating the purity of a reduced density matrix of a composite quantum system in terms of cross-correlation of the same state and an arbitrary product state. Various immediate applications of our result are proposed, in particular concerning Gaussian wave-packet propagation under classically regular dynamics.
Estimation of purity in terms of correlation functions
Prosen, Tomaž; Seligman, Thomas H.; Žnidarič, Marko
2003-06-01
We prove a rigorous inequality that estimates the purity of a reduced density matrix of a composite quantum system in terms of cross correlation of the same state and an arbitrary product state. Various immediate applications of our result are proposed, in particular, concerning Gaussian wave-packet propagation under classically regular dynamics.
Estimation for Entanglement Negativity of Free Fermions
Herzog, Christopher P
2016-01-01
In this letter we study the negativity of one dimensional free fermions. We derive the general form of the $\\mathbb{Z}_{N}$ symmetric term in moments of the partial transposed (reduced) density matrix, which is an algebraic function of the end points of the system. Such a path integral turns out to be a convenient tool for making estimations for the negativity.
Taras K. Antal; Sarvikas, Päivi; Tyystjärvi, Esa
2009-01-01
The oxygen-evolving complex of Photosystem II cycles through five oxidation states (S0–S4), and dark incubation leads to 25% S0 and 75% S1. This distribution cannot be reached with charge recombination reactions between the higher S states and the electron acceptor QB−. We measured flash-induced oxygen evolution to understand how S3 and S2 are converted to lower S states when the electron required to reduce the manganese cluster does not come from QB−. Thylakoid samples preconditioned to make...
McCauley, T
2012-01-01
Event recorded with the CMS detector in 2012 at a proton-proton centre of mass energy of 8 TeV. The event shows characteristics expected from the decay of the SM Higgs boson to a pair of Z bosons, one of which subsequently decays to a pair of electrons (green lines and green towers) and the other Z decays to a pair of muons (red lines). The event could also be due to known standard model background processes.
Rueda, M.; Sluyters-Rehbach, M.; Sluyters, J.H.
1987-01-01
A critical evaluation is presented of the analysis of impedance or admittance data in the case of an electrode reaction proceeding by two consecutive one-electron transfers with a stable, solution-soluble intermediate. It is shown that the expression for this case, as derived by Armstrong and
Buck, Henk M.
We have studied carbon transfer reactions following an SN2 reaction profile. With ab initio calculations and experimental geometries concerning the nature of the various complexes indicated as stable, intermediate, and transition state we were able to show the additional value of van't Hoff's tetrahedral configuration by changing its geometry via a trigonal pyramid into a trigonal bipyramid. The ratio of the apical bond and corresponding tetrahedral bond distances is then nearly 1.333. The relevance of this approach has also been shown for identity proton-(hydrogen atom-, and hydride-) in-line reactions. The use of this geometrical transmission will be demonstrated for the hydrogen bonding distances in e.g., DNA duplexes and other biological (supra) molecular systems.
Khachatryan, Vardan; Tumasyan, Armen; Adam, Wolfgang; Bergauer, Thomas; Dragicevic, Marko; Erö, Janos; Friedl, Markus; Fruehwirth, Rudolf; Ghete, Vasile Mihai; Hartl, Christian; Hörmann, Natascha; Hrubec, Josef; Jeitler, Manfred; Kiesenhofer, Wolfgang; Knünz, Valentin; Krammer, Manfred; Krätschmer, Ilse; Liko, Dietrich; Mikulec, Ivan; Rabady, Dinyar; Rahbaran, Babak; Rohringer, Herbert; Schöfbeck, Robert; Strauss, Josef; Treberer-Treberspurg, Wolfgang; Waltenberger, Wolfgang; Wulz, Claudia-Elisabeth; Mossolov, Vladimir; Shumeiko, Nikolai; Suarez Gonzalez, Juan; Alderweireldt, Sara; Bansal, Monika; Bansal, Sunil; Cornelis, Tom; De Wolf, Eddi A; Janssen, Xavier; Knutsson, Albert; Lauwers, Jasper; Luyckx, Sten; Ochesanu, Silvia; Rougny, Romain; Van De Klundert, Merijn; Van Haevermaet, Hans; Van Mechelen, Pierre; Van Remortel, Nick; Van Spilbeeck, Alex; Blekman, Freya; Blyweert, Stijn; D'Hondt, Jorgen; Daci, Nadir; Heracleous, Natalie; Keaveney, James; Lowette, Steven; Maes, Michael; Olbrechts, Annik; Python, Quentin; Strom, Derek; Tavernier, Stefaan; Van Doninck, Walter; Van Mulders, Petra; Van Onsem, Gerrit Patrick; Villella, Ilaria; Caillol, Cécile; Clerbaux, Barbara; De Lentdecker, Gilles; Dobur, Didar; Favart, Laurent; Gay, Arnaud; Grebenyuk, Anastasia; Léonard, Alexandre; Mohammadi, Abdollah; Perniè, Luca; Randle-conde, Aidan; Reis, Thomas; Seva, Tomislav; Thomas, Laurent; Vander Velde, Catherine; Vanlaer, Pascal; Wang, Jian; Zenoni, Florian; Adler, Volker; Beernaert, Kelly; Benucci, Leonardo; Cimmino, Anna; Costantini, Silvia; Crucy, Shannon; Dildick, Sven; Fagot, Alexis; Garcia, Guillaume; Mccartin, Joseph; Ocampo Rios, Alberto Andres; Ryckbosch, Dirk; Salva Diblen, Sinem; Sigamani, Michael; Strobbe, Nadja; Thyssen, Filip; Tytgat, Michael; Yazgan, Efe; Zaganidis, Nicolas; Basegmez, Suzan; Beluffi, Camille; Bruno, Giacomo; Castello, Roberto; Caudron, Adrien; Ceard, Ludivine; Da Silveira, Gustavo Gil; Delaere, Christophe; Du Pree, Tristan; Favart, Denis; Forthomme, Laurent; Giammanco, Andrea; Hollar, Jonathan; Jafari, Abideh; Jez, Pavel; Komm, Matthias; Lemaitre, Vincent; Nuttens, Claude; Pagano, Davide; Perrini, Lucia; Pin, Arnaud; Piotrzkowski, Krzysztof; Popov, Andrey; Quertenmont, Loic; Selvaggi, Michele; Vidal Marono, Miguel; Vizan Garcia, Jesus Manuel; Beliy, Nikita; Caebergs, Thierry; Daubie, Evelyne; Hammad, Gregory Habib; Aldá Júnior, Walter Luiz; Alves, Gilvan; Brito, Lucas; Correa Martins Junior, Marcos; Dos Reis Martins, Thiago; Mora Herrera, Clemencia; Pol, Maria Elena; Rebello Teles, Patricia; Carvalho, Wagner; Chinellato, Jose; Custódio, Analu; Melo Da Costa, Eliza; De Jesus Damiao, Dilson; De Oliveira Martins, Carley; Fonseca De Souza, Sandro; Malbouisson, Helena; Matos Figueiredo, Diego; Mundim, Luiz; Nogima, Helio; Prado Da Silva, Wanda Lucia; Santaolalla, Javier; Santoro, Alberto; Sznajder, Andre; Tonelli Manganote, Edmilson José; Vilela Pereira, Antonio; Bernardes, Cesar Augusto; Dogra, Sunil; Tomei, Thiago; De Moraes Gregores, Eduardo; Mercadante, Pedro G; Novaes, Sergio F; Padula, Sandra; Aleksandrov, Aleksandar; Genchev, Vladimir; Hadjiiska, Roumyana; Iaydjiev, Plamen; Marinov, Andrey; Piperov, Stefan; Rodozov, Mircho; Sultanov, Georgi; Vutova, Mariana; Dimitrov, Anton; Glushkov, Ivan; Litov, Leander; Pavlov, Borislav; Petkov, Peicho; Bian, Jian-Guo; Chen, Guo-Ming; Chen, He-Sheng; Chen, Mingshui; Cheng, Tongguang; Du, Ran; Jiang, Chun-Hua; Plestina, Roko; Romeo, Francesco; Tao, Junquan; Wang, Zheng; Asawatangtrakuldee, Chayanit; Ban, Yong; Li, Qiang; Liu, Shuai; Mao, Yajun; Qian, Si-Jin; Wang, Dayong; Zou, Wei; Avila, Carlos; Cabrera, Andrés; Chaparro Sierra, Luisa Fernanda; Florez, Carlos; Gomez, Juan Pablo; Gomez Moreno, Bernardo; Sanabria, Juan Carlos; Godinovic, Nikola; Lelas, Damir; Polic, Dunja; Puljak, Ivica; Antunovic, Zeljko; Kovac, Marko; Brigljevic, Vuko; Kadija, Kreso; Luetic, Jelena; Mekterovic, Darko; Sudic, Lucija; Attikis, Alexandros; Mavromanolakis, Georgios; Mousa, Jehad; Nicolaou, Charalambos; Ptochos, Fotios; Razis, Panos A; Bodlak, Martin; Finger, Miroslav; Finger Jr, Michael; Assran, Yasser; Elgammal, Sherif; Mahmoud, Mohammed; Radi, Amr; Kadastik, Mario; Murumaa, Marion; Raidal, Martti; Tiko, Andres; Eerola, Paula; Fedi, Giacomo; Voutilainen, Mikko; Härkönen, Jaakko; Karimäki, Veikko; Kinnunen, Ritva; Kortelainen, Matti J; Lampén, Tapio; Lassila-Perini, Kati; Lehti, Sami; Lindén, Tomas; Luukka, Panja-Riina; Mäenpää, Teppo; Peltola, Timo; Tuominen, Eija; Tuominiemi, Jorma; Tuovinen, Esa; Wendland, Lauri; Talvitie, Joonas; Tuuva, Tuure; Besancon, Marc; Couderc, Fabrice; Dejardin, Marc; Denegri, Daniel; Fabbro, Bernard; Faure, Jean-Louis; Favaro, Carlotta; Ferri, Federico; Ganjour, Serguei; Givernaud, Alain; Gras, Philippe; Hamel de Monchenault, Gautier; Jarry, Patrick; Locci, Elizabeth; Malcles, Julie; Rander, John; Rosowsky, André; Titov, Maksym; Baffioni, Stephanie; Beaudette, Florian; Busson, Philippe; Charlot, Claude; Dahms, Torsten; Dalchenko, Mykhailo; Dobrzynski, Ludwik; Filipovic, Nicolas; Florent, Alice; Granier de Cassagnac, Raphael; Mastrolorenzo, Luca; Miné, Philippe; Mironov, Camelia; Naranjo, Ivo Nicolas; Nguyen, Matthew; Ochando, Christophe; Paganini, Pascal; Regnard, Simon; Salerno, Roberto; Sauvan, Jean-Baptiste; Sirois, Yves; Veelken, Christian; Yilmaz, Yetkin; Zabi, Alexandre; Agram, Jean-Laurent; Andrea, Jeremy; Aubin, Alexandre; Bloch, Daniel; Brom, Jean-Marie; Chabert, Eric Christian; Collard, Caroline; Conte, Eric; Fontaine, Jean-Charles; Gelé, Denis; Goerlach, Ulrich; Goetzmann, Christophe; Le Bihan, Anne-Catherine; Skovpen, Kirill; Van Hove, Pierre; Gadrat, Sébastien; Beauceron, Stephanie; Beaupere, Nicolas; Boudoul, Gaelle; Bouvier, Elvire; Brochet, Sébastien; Carrillo Montoya, Camilo Andres; Chasserat, Julien; Chierici, Roberto; Contardo, Didier; Depasse, Pierre; El Mamouni, Houmani; Fan, Jiawei; Fay, Jean; Gascon, Susan; Gouzevitch, Maxime; Ille, Bernard; Kurca, Tibor; Lethuillier, Morgan; Mirabito, Laurent; Perries, Stephane; Ruiz Alvarez, José David; Sabes, David; Sgandurra, Louis; Sordini, Viola; Vander Donckt, Muriel; Verdier, Patrice; Viret, Sébastien; Xiao, Hong; Tsamalaidze, Zviad; Autermann, Christian; Beranek, Sarah; Bontenackels, Michael; Edelhoff, Matthias; Feld, Lutz; Heister, Arno; Hindrichs, Otto; Klein, Katja; Ostapchuk, Andrey; Raupach, Frank; Sammet, Jan; Schael, Stefan; Weber, Hendrik; Wittmer, Bruno; Zhukov, Valery; Ata, Metin; Brodski, Michael; Dietz-Laursonn, Erik; Duchardt, Deborah; Erdmann, Martin; Fischer, Robert; Güth, Andreas; Hebbeker, Thomas; Heidemann, Carsten; Hoepfner, Kerstin; Klingebiel, Dennis; Knutzen, Simon; Kreuzer, Peter; Merschmeyer, Markus; Meyer, Arnd; Millet, Philipp; Olschewski, Mark; Padeken, Klaas; Papacz, Paul; Reithler, Hans; Schmitz, Stefan Antonius; Sonnenschein, Lars; Teyssier, Daniel; Thüer, Sebastian; Weber, Martin; Cherepanov, Vladimir; Erdogan, Yusuf; Flügge, Günter; Geenen, Heiko; Geisler, Matthias; Haj Ahmad, Wael; Hoehle, Felix; Kargoll, Bastian; Kress, Thomas; Kuessel, Yvonne; Künsken, Andreas; Lingemann, Joschka; Nowack, Andreas; Nugent, Ian Michael; Perchalla, Lars; Pooth, Oliver; Stahl, Achim; Aldaya Martin, Maria; Asin, Ivan; Bartosik, Nazar; Behr, Joerg; Behrens, Ulf; Bell, Alan James; Bethani, Agni; Borras, Kerstin; Burgmeier, Armin; Cakir, Altan; Calligaris, Luigi; Campbell, Alan; Choudhury, Somnath; Costanza, Francesco; Diez Pardos, Carmen; Dolinska, Ganna; Dooling, Samantha; Dorland, Tyler; Eckerlin, Guenter; Eckstein, Doris; Eichhorn, Thomas; Flucke, Gero; Garay Garcia, Jasone; Geiser, Achim; Gunnellini, Paolo; Hauk, Johannes; Hempel, Maria; Jung, Hannes; Kalogeropoulos, Alexis; Kasemann, Matthias; Katsas, Panagiotis; Kieseler, Jan; Kleinwort, Claus; Korol, Ievgen; Krücker, Dirk; Lange, Wolfgang; Leonard, Jessica; Lipka, Katerina; Lobanov, Artur; Lohmann, Wolfgang; Lutz, Benjamin; Mankel, Rainer; Marfin, Ihar; Melzer-Pellmann, Isabell-Alissandra; Meyer, Andreas Bernhard; Mittag, Gregor; Mnich, Joachim; Mussgiller, Andreas; Naumann-Emme, Sebastian; Nayak, Aruna; Ntomari, Eleni; Perrey, Hanno; Pitzl, Daniel; Placakyte, Ringaile; Raspereza, Alexei; Ribeiro Cipriano, Pedro M; Roland, Benoit; Ron, Elias; Sahin, Mehmet Özgür; Salfeld-Nebgen, Jakob; Saxena, Pooja; Schoerner-Sadenius, Thomas; Schröder, Matthias; Seitz, Claudia; Spannagel, Simon; Vargas Trevino, Andrea Del Rocio; Walsh, Roberval; Wissing, Christoph; Blobel, Volker; Centis Vignali, Matteo; Draeger, Arne-Rasmus; Erfle, Joachim; Garutti, Erika; Goebel, Kristin; Görner, Martin; Haller, Johannes; Hoffmann, Malte; Höing, Rebekka Sophie; Junkes, Alexandra; Kirschenmann, Henning; Klanner, Robert; Kogler, Roman; Lange, Jörn; Lapsien, Tobias; Lenz, Teresa; Marchesini, Ivan; Ott, Jochen; Peiffer, Thomas; Perieanu, Adrian; Pietsch, Niklas; Poehlsen, Jennifer; Pöhlsen, Thomas; Rathjens, Denis; Sander, Christian; Schettler, Hannes; Schleper, Peter; Schlieckau, Eike; Schmidt, Alexander; Seidel, Markus; Sola, Valentina; Stadie, Hartmut; Steinbrück, Georg; Troendle, Daniel; Usai, Emanuele; Vanelderen, Lukas; Vanhoefer, Annika; Barth, Christian; Baus, Colin; Berger, Joram; Böser, Christian; Butz, Erik; Chwalek, Thorsten; De Boer, Wim; Descroix, Alexis; Dierlamm, Alexander; Feindt, Michael; Frensch, Felix; Giffels, Manuel; Gilbert, Andrew; Hartmann, Frank; Hauth, Thomas; Husemann, Ulrich; Katkov, Igor; Kornmayer, Andreas; Kuznetsova, Ekaterina; Lobelle Pardo, Patricia; Mozer, Matthias Ulrich; Müller, Thomas; Müller, Thomas; Nürnberg, Andreas; Quast, Gunter; Rabbertz, Klaus; Röcker, Steffen; Simonis, Hans-Jürgen; Stober, Fred-Markus Helmut; Ulrich, Ralf; Wagner-Kuhr, Jeannine; Wayand, Stefan; Weiler, Thomas; Wolf, Roger; Anagnostou, Georgios; Daskalakis, Georgios; Geralis, Theodoros; Giakoumopoulou, Viktoria Athina; Kyriakis, Aristotelis; Loukas, Demetrios; Markou, Athanasios; Markou, Christos; Psallidas, Andreas; Topsis-Giotis, Iasonas; Agapitos, Antonis; Kesisoglou, Stilianos; Panagiotou, Apostolos; Saoulidou, Niki; Stiliaris, Efstathios; Aslanoglou, Xenofon; Evangelou, Ioannis; Flouris, Giannis; Foudas, Costas; Kokkas, Panagiotis; Manthos, Nikolaos; Papadopoulos, Ioannis; Paradas, Evangelos; Strologas, John; Bencze, Gyorgy; Hajdu, Csaba; Hidas, Pàl; Horvath, Dezso; Sikler, Ferenc; Veszpremi, Viktor; Vesztergombi, Gyorgy; Zsigmond, Anna Julia; Beni, Noemi; Czellar, Sandor; Karancsi, János; Molnar, Jozsef; Palinkas, Jozsef; Szillasi, Zoltan; Makovec, Alajos; Raics, Peter; Trocsanyi, Zoltan Laszlo; Ujvari, Balazs; Swain, Sanjay Kumar; Beri, Suman Bala; Bhatnagar, Vipin; Gupta, Ruchi; Bhawandeep, Bhawandeep; Kalsi, Amandeep Kaur; Kaur, Manjit; Kumar, Ramandeep; Mittal, Monika; Nishu, Nishu; Singh, Jasbir; Kumar, Ashok; Kumar, Arun; Ahuja, Sudha; Bhardwaj, Ashutosh; Choudhary, Brajesh C; Kumar, Ajay; Malhotra, Shivali; Naimuddin, Md; Ranjan, Kirti; Sharma, Varun; Banerjee, Sunanda; Bhattacharya, Satyaki; Chatterjee, Kalyanmoy; Dutta, Suchandra; Gomber, Bhawna; Jain, Sandhya; Jain, Shilpi; Khurana, Raman; Modak, Atanu; Mukherjee, Swagata; Roy, Debarati; Sarkar, Subir; Sharan, Manoj; Abdulsalam, Abdulla; Dutta, Dipanwita; Kailas, Swaminathan; Kumar, Vineet; Mohanty, Ajit Kumar; Pant, Lalit Mohan; Shukla, Prashant; Topkar, Anita; Aziz, Tariq; Banerjee, Sudeshna; Bhowmik, Sandeep; Chatterjee, Rajdeep Mohan; Dewanjee, Ram Krishna; Dugad, Shashikant; Ganguly, Sanmay; Ghosh, Saranya; Guchait, Monoranjan; Gurtu, Atul; Kole, Gouranga; Kumar, Sanjeev; Maity, Manas; Majumder, Gobinda; Mazumdar, Kajari; Mohanty, Gagan Bihari; Parida, Bibhuti; Sudhakar, Katta; Wickramage, Nadeesha; Bakhshiansohi, Hamed; Behnamian, Hadi; Etesami, Seyed Mohsen; Fahim, Ali; Goldouzian, Reza; Khakzad, Mohsen; Mohammadi Najafabadi, Mojtaba; Naseri, Mohsen; Paktinat Mehdiabadi, Saeid; Rezaei Hosseinabadi, Ferdos; Safarzadeh, Batool; Zeinali, Maryam; Felcini, Marta; Grunewald, Martin; Abbrescia, Marcello; Calabria, Cesare; Chhibra, Simranjit Singh; Colaleo, Anna; Creanza, Donato; De Filippis, Nicola; De Palma, Mauro; Fiore, Luigi; Iaselli, Giuseppe; Maggi, Giorgio; Maggi, Marcello; My, Salvatore; Nuzzo, Salvatore; Pompili, Alexis; Pugliese, Gabriella; Radogna, Raffaella; Selvaggi, Giovanna; Sharma, Archana; Silvestris, Lucia; Venditti, Rosamaria; Verwilligen, Piet; Abbiendi, Giovanni; Benvenuti, Alberto; Bonacorsi, Daniele; Braibant-Giacomelli, Sylvie; Brigliadori, Luca; Campanini, Renato; Capiluppi, Paolo; Castro, Andrea; Cavallo, Francesca Romana; Codispoti, Giuseppe; Cuffiani, Marco; Dallavalle, Gaetano-Marco; Fabbri, Fabrizio; Fanfani, Alessandra; Fasanella, Daniele; Giacomelli, Paolo; Grandi, Claudio; Guiducci, Luigi; Marcellini, Stefano; Masetti, Gianni; Montanari, Alessandro; Navarria, Francesco; Perrotta, Andrea; Primavera, Federica; Rossi, Antonio; Rovelli, Tiziano; Siroli, Gian Piero; Tosi, Nicolò; Travaglini, Riccardo; Albergo, Sebastiano; Cappello, Gigi; Chiorboli, Massimiliano; Costa, Salvatore; Giordano, Ferdinando; Potenza, Renato; Tricomi, Alessia; Tuve, Cristina; Barbagli, Giuseppe; Ciulli, Vitaliano; Civinini, Carlo; D'Alessandro, Raffaello; Focardi, Ettore; Gallo, Elisabetta; Gonzi, Sandro; Gori, Valentina; Lenzi, Piergiulio; Meschini, Marco; Paoletti, Simone; Sguazzoni, Giacomo; Tropiano, Antonio; Benussi, Luigi; Bianco, Stefano; Fabbri, Franco; Piccolo, Davide; Ferretti, Roberta; Ferro, Fabrizio; Lo Vetere, Maurizio; Robutti, Enrico; Tosi, Silvano; Dinardo, Mauro Emanuele; Fiorendi, Sara; Gennai, Simone; Gerosa, Raffaele; Ghezzi, Alessio; Govoni, Pietro; Lucchini, Marco Toliman; Malvezzi, Sandra; Manzoni, Riccardo Andrea; Martelli, Arabella; Marzocchi, Badder; Menasce, Dario; Moroni, Luigi; Paganoni, Marco; Pedrini, Daniele; Ragazzi, Stefano; Redaelli, Nicola; Tabarelli de Fatis, Tommaso; Buontempo, Salvatore; Cavallo, Nicola; Di Guida, Salvatore; Fabozzi, Francesco; Iorio, Alberto Orso Maria; Lista, Luca; Meola, Sabino; Merola, Mario; Paolucci, Pierluigi; Azzi, Patrizia; Bacchetta, Nicola; Biasotto, Massimo; Bisello, Dario; Branca, Antonio; Carlin, Roberto; Checchia, Paolo; Dall'Osso, Martino; Dorigo, Tommaso; Dosselli, Umberto; Fanzago, Federica; Galanti, Mario; Gasparini, Ugo; Giubilato, Piero; Gozzelino, Andrea; Lacaprara, Stefano; Margoni, Martino; Meneguzzo, Anna Teresa; Pazzini, Jacopo; Pozzobon, Nicola; Ronchese, Paolo; Simonetto, Franco; Torassa, Ezio; Tosi, Mia; Ventura, Sandro; Zotto, Pierluigi; Zucchetta, Alberto; Gabusi, Michele; Ratti, Sergio P; Re, Valerio; Riccardi, Cristina; Salvini, Paola; Vitulo, Paolo; Biasini, Maurizio; Bilei, Gian Mario; Ciangottini, Diego; Fanò, Livio; Lariccia, Paolo; Mantovani, Giancarlo; Menichelli, Mauro; Saha, Anirban; Santocchia, Attilio; Spiezia, Aniello; Androsov, Konstantin; Azzurri, Paolo; Bagliesi, Giuseppe; Bernardini, Jacopo; Boccali, Tommaso; Broccolo, Giuseppe; Castaldi, Rino; Ciocci, Maria Agnese; Dell'Orso, Roberto; Donato, Silvio; Fiori, Francesco; Foà, Lorenzo; Giassi, Alessandro; Grippo, Maria Teresa; Ligabue, Franco; Lomtadze, Teimuraz; Martini, Luca; Messineo, Alberto; Moon, Chang-Seong; Palla, Fabrizio; Rizzi, Andrea; Savoy-Navarro, Aurore; Serban, Alin Titus; Spagnolo, Paolo; Squillacioti, Paola; Tenchini, Roberto; Tonelli, Guido; Venturi, Andrea; Verdini, Piero Giorgio; Vernieri, Caterina; Barone, Luciano; Cavallari, Francesca; D'imperio, Giulia; Del Re, Daniele; Diemoz, Marcella; Jorda, Clara; Longo, Egidio; Margaroli, Fabrizio; Meridiani, Paolo; Micheli, Francesco; Nourbakhsh, Shervin; Organtini, Giovanni; Paramatti, Riccardo; Rahatlou, Shahram; Rovelli, Chiara; Santanastasio, Francesco; Soffi, Livia; Traczyk, Piotr; Amapane, Nicola; Arcidiacono, Roberta; Argiro, Stefano; Arneodo, Michele; Bellan, Riccardo; Biino, Cristina; Cartiglia, Nicolo; Casasso, Stefano; Costa, Marco; Degano, Alessandro; Demaria, Natale; Finco, Linda; Mariotti, Chiara; Maselli, Silvia; Migliore, Ernesto; Monaco, Vincenzo; Musich, Marco; Obertino, Maria Margherita; Ortona, Giacomo; Pacher, Luca; Pastrone, Nadia; Pelliccioni, Mario; Pinna Angioni, Gian Luca; Potenza, Alberto; Romero, Alessandra; Ruspa, Marta; Sacchi, Roberto; Solano, Ada; Staiano, Amedeo; Tamponi, Umberto; Belforte, Stefano; Candelise, Vieri; Casarsa, Massimo; Cossutti, Fabio; Della Ricca, Giuseppe; Gobbo, Benigno; La Licata, Chiara; Marone, Matteo; Schizzi, Andrea; Umer, Tomo; Zanetti, Anna; Chang, Sunghyun; Kropivnitskaya, Anna; Nam, Soon-Kwon; Kim, Dong Hee; Kim, Gui Nyun; Kim, Min Suk; Kong, Dae Jung; Lee, Sangeun; Oh, Young Do; Park, Hyangkyu; Sakharov, Alexandre; Son, Dong-Chul; Kim, Tae Jeong; Kim, Jae Yool; Song, Sanghyeon; Choi, Suyong; Gyun, Dooyeon; Hong, Byung-Sik; Jo, Mihee; Kim, Hyunchul; Kim, Yongsun; Lee, Byounghoon; Lee, Kyong Sei; Park, Sung Keun; Roh, Youn; Yoo, Hwi Dong; Choi, Minkyoo; Kim, Ji Hyun; Park, Inkyu; Ryu, Geonmo; Ryu, Min Sang; Choi, Young-Il; Choi, Young Kyu; Goh, Junghwan; Kim, Donghyun; Kwon, Eunhyang; Lee, Jongseok; Yu, Intae; Juodagalvis, Andrius; Komaragiri, Jyothsna Rani; Md Ali, Mohd Adli Bin; Casimiro Linares, Edgar; Castilla-Valdez, Heriberto; De La Cruz-Burelo, Eduard; Heredia-de La Cruz, Ivan; Hernandez-Almada, Alberto; Lopez-Fernandez, Ricardo; Sánchez Hernández, Alberto; Carrillo Moreno, Salvador; Vazquez Valencia, Fabiola; Pedraza, Isabel; Salazar Ibarguen, Humberto Antonio; Morelos Pineda, Antonio; Krofcheck, David; Butler, Philip H; Reucroft, Steve; Ahmad, Ashfaq; Ahmad, Muhammad; Hassan, Qamar; Hoorani, Hafeez R; Khan, Wajid Ali; Khurshid, Taimoor; Shoaib, Muhammad; Bialkowska, Helena; Bluj, Michal; Boimska, Bożena; Frueboes, Tomasz; Górski, Maciej; Kazana, Malgorzata; Nawrocki, Krzysztof; Romanowska-Rybinska, Katarzyna; Szleper, Michal; Zalewski, Piotr; Brona, Grzegorz; Bunkowski, Karol; Cwiok, Mikolaj; Dominik, Wojciech; Doroba, Krzysztof; Kalinowski, Artur; Konecki, Marcin; Krolikowski, Jan; Misiura, Maciej; Olszewski, Michał; Wolszczak, Weronika; Bargassa, Pedrame; Beirão Da Cruz E Silva, Cristóvão; Faccioli, Pietro; Ferreira Parracho, Pedro Guilherme; Gallinaro, Michele; Lloret Iglesias, Lara; Nguyen, Federico; Rodrigues Antunes, Joao; Seixas, Joao; Varela, Joao; Vischia, Pietro; Golutvin, Igor; Gorbunov, Ilya; Kamenev, Alexey; Karjavin, Vladimir; Konoplyanikov, Viktor; Kozlov, Guennady; Lanev, Alexander; Malakhov, Alexander; Matveev, Viktor; Moisenz, Petr; Palichik, Vladimir; Perelygin, Victor; Savina, Maria; Shmatov, Sergey; Shulha, Siarhei; Skatchkov, Nikolai; Smirnov, Vitaly; Zarubin, Anatoli; Golovtsov, Victor; Ivanov, Yury; Kim, Victor; Levchenko, Petr; Murzin, Victor; Oreshkin, Vadim; Smirnov, Igor; Sulimov, Valentin; Uvarov, Lev; Vavilov, Sergey; Vorobyev, Alexey; Vorobyev, Andrey; Andreev, Yuri; Dermenev, Alexander; Gninenko, Sergei; Golubev, Nikolai; Kirsanov, Mikhail; Krasnikov, Nikolai; Pashenkov, Anatoli; Tlisov, Danila; Toropin, Alexander; Epshteyn, Vladimir; Gavrilov, Vladimir; Lychkovskaya, Natalia; Popov, Vladimir; Pozdnyakov, Ivan; Safronov, Grigory; Semenov, Sergey; Spiridonov, Alexander; Stolin, Viatcheslav; Vlasov, Evgueni; Zhokin, Alexander; Andreev, Vladimir; Azarkin, Maksim; Dremin, Igor; Kirakosyan, Martin; Leonidov, Andrey; Mesyats, Gennady; Rusakov, Sergey V; Vinogradov, Alexey; Belyaev, Andrey; Boos, Edouard; Bunichev, Viacheslav; Dubinin, Mikhail; Dudko, Lev; Gribushin, Andrey; Klyukhin, Vyacheslav; Kodolova, Olga; Lokhtin, Igor; Obraztsov, Stepan; Perfilov, Maxim; Petrushanko, Sergey; Savrin, Viktor; Azhgirey, Igor; Bayshev, Igor; Bitioukov, Sergei; Kachanov, Vassili; Kalinin, Alexey; Konstantinov, Dmitri; Krychkine, Victor; Petrov, Vladimir; Ryutin, Roman; Sobol, Andrei; Tourtchanovitch, Leonid; Troshin, Sergey; Tyurin, Nikolay; Uzunian, Andrey; Volkov, Alexey; Adzic, Petar; Ekmedzic, Marko; Milosevic, Jovan; Rekovic, Vladimir; Alcaraz Maestre, Juan; Battilana, Carlo; Calvo, Enrique; Cerrada, Marcos; Chamizo Llatas, Maria; Colino, Nicanor; De La Cruz, Begona; Delgado Peris, Antonio; Domínguez Vázquez, Daniel; Escalante Del Valle, Alberto; Fernandez Bedoya, Cristina; Fernández Ramos, Juan Pablo; Flix, Jose; Fouz, Maria Cruz; Garcia-Abia, Pablo; Gonzalez Lopez, Oscar; Goy Lopez, Silvia; Hernandez, Jose M; Josa, Maria Isabel; Navarro De Martino, Eduardo; Pérez-Calero Yzquierdo, Antonio María; Puerta Pelayo, Jesus; Quintario Olmeda, Adrián; Redondo, Ignacio; Romero, Luciano; Senghi Soares, Mara; Albajar, Carmen; de Trocóniz, Jorge F; Missiroli, Marino; Moran, Dermot; Brun, Hugues; Cuevas, Javier; Fernandez Menendez, Javier; Folgueras, Santiago; Gonzalez Caballero, Isidro; Brochero Cifuentes, Javier Andres; Cabrillo, Iban Jose; Calderon, Alicia; Duarte Campderros, Jordi; Fernandez, Marcos; Gomez, Gervasio; Graziano, Alberto; Lopez Virto, Amparo; Marco, Jesus; Marco, Rafael; Martinez Rivero, Celso; Matorras, Francisco; Munoz Sanchez, Francisca Javiela; Piedra Gomez, Jonatan; Rodrigo, Teresa; Rodríguez-Marrero, Ana Yaiza; Ruiz-Jimeno, Alberto; Scodellaro, Luca; Vila, Ivan; Vilar Cortabitarte, Rocio; Abbaneo, Duccio; Auffray, Etiennette; Auzinger, Georg; Bachtis, Michail; Baillon, Paul; Ball, Austin; Barney, David; Benaglia, Andrea; Bendavid, Joshua; Benhabib, Lamia; Benitez, Jose F; Bernet, Colin; Bloch, Philippe; Bocci, Andrea; Bonato, Alessio; Bondu, Olivier; Botta, Cristina; Breuker, Horst; Camporesi, Tiziano; Cerminara, Gianluca; Colafranceschi, Stefano; D'Alfonso, Mariarosaria; D'Enterria, David; Dabrowski, Anne; David Tinoco Mendes, Andre; De Guio, Federico; De Roeck, Albert; De Visscher, Simon; Di Marco, Emanuele; Dobson, Marc; Dordevic, Milos; Dorney, Brian; Dupont-Sagorin, Niels; Elliott-Peisert, Anna; Eugster, Jürg; Franzoni, Giovanni; Funk, Wolfgang; Gigi, Dominique; Gill, Karl; Giordano, Domenico; Girone, Maria; Glege, Frank; Guida, Roberto; Gundacker, Stefan; Guthoff, Moritz; Hammer, Josef; Hansen, Magnus; Harris, Philip; Hegeman, Jeroen; Innocente, Vincenzo; Janot, Patrick; Kousouris, Konstantinos; Krajczar, Krisztian; Lecoq, Paul; Lourenco, Carlos; Magini, Nicolo; Malgeri, Luca; Mannelli, Marcello; Marrouche, Jad; Masetti, Lorenzo; Meijers, Frans; Mersi, Stefano; Meschi, Emilio; Moortgat, Filip; Morovic, Srecko; Mulders, Martijn; Orsini, Luciano; Pape, Luc; Perez, Emmanuelle; Perrozzi, Luca; Petrilli, Achille; Petrucciani, Giovanni; Pfeiffer, Andreas; Pimiä, Martti; Piparo, Danilo; Plagge, Michael; Racz, Attila; Rolandi, Gigi; Rovere, Marco; Sakulin, Hannes; Schäfer, Christoph; Schwick, Christoph; Sharma, Archana; Siegrist, Patrice; Silva, Pedro; Simon, Michal; Sphicas, Paraskevas; Spiga, Daniele; Steggemann, Jan; Stieger, Benjamin; Stoye, Markus; Takahashi, Yuta; Treille, Daniel; Tsirou, Andromachi; Veres, Gabor Istvan; Wardle, Nicholas; Wöhri, Hermine Katharina; Wollny, Heiner; Zeuner, Wolfram Dietrich; Bertl, Willi; Deiters, Konrad; Erdmann, Wolfram; Horisberger, Roland; Ingram, Quentin; Kaestli, Hans-Christian; Kotlinski, Danek; Langenegger, Urs; Renker, Dieter; Rohe, Tilman; Bachmair, Felix; Bäni, Lukas; Bianchini, Lorenzo; Buchmann, Marco-Andrea; Casal, Bruno; Chanon, Nicolas; Dissertori, Günther; Dittmar, Michael; Donegà, Mauro; Dünser, Marc; Eller, Philipp; Grab, Christoph; Hits, Dmitry; Hoss, Jan; Lustermann, Werner; Mangano, Boris; Marini, Andrea Carlo; Marionneau, Matthieu; Martinez Ruiz del Arbol, Pablo; Masciovecchio, Mario; Meister, Daniel; Mohr, Niklas; Musella, Pasquale; Nägeli, Christoph; Nessi-Tedaldi, Francesca; Pandolfi, Francesco; Pauss, Felicitas; Peruzzi, Marco; Quittnat, Milena; Rebane, Liis; Rossini, Marco; Starodumov, Andrei; Takahashi, Maiko; Theofilatos, Konstantinos; Wallny, Rainer; Weber, Hannsjoerg Artur; Amsler, Claude; Canelli, Maria Florencia; Chiochia, Vincenzo; De Cosa, Annapaola; Hinzmann, Andreas; Hreus, Tomas; Kilminster, Benjamin; Lange, Clemens; Millan Mejias, Barbara; Ngadiuba, Jennifer; Pinna, Deborah; Robmann, Peter; Ronga, Frederic Jean; Taroni, Silvia; Verzetti, Mauro; Yang, Yong; Cardaci, Marco; Chen, Kuan-Hsin; Ferro, Cristina; Kuo, Chia-Ming; Lin, Willis; Lu, Yun-Ju; Volpe, Roberta; Yu, Shin-Shan; Chang, Paoti; Chang, You-Hao; Chang, Yu-Wei; Chao, Yuan; Chen, Kai-Feng; Chen, Po-Hsun; Dietz, Charles; Grundler, Ulysses; Hou, George Wei-Shu; Kao, Kai-Yi; Liu, Yueh-Feng; Lu, Rong-Shyang; Majumder, Devdatta; Petrakou, Eleni; Tzeng, Yeng-Ming; Wilken, Rachel; Asavapibhop, Burin; Singh, Gurpreet; Srimanobhas, Norraphat; Suwonjandee, Narumon; Adiguzel, Aytul; Bakirci, Mustafa Numan; Cerci, Salim; Dozen, Candan; Dumanoglu, Isa; Eskut, Eda; Girgis, Semiray; Gokbulut, Gul; Gurpinar, Emine; Hos, Ilknur; Kangal, Evrim Ersin; Kayis Topaksu, Aysel; Onengut, Gulsen; Ozdemir, Kadri; Ozturk, Sertac; Polatoz, Ayse; Sunar Cerci, Deniz; Tali, Bayram; Topakli, Huseyin; Vergili, Mehmet; Akin, Ilina Vasileva; Bilin, Bugra; Bilmis, Selcuk; Gamsizkan, Halil; Isildak, Bora; Karapinar, Guler; Ocalan, Kadir; Sekmen, Sezen; Surat, Ugur Emrah; Yalvac, Metin; Zeyrek, Mehmet; Albayrak, Elif Asli; Gülmez, Erhan; Kaya, Mithat; Kaya, Ozlem; Yetkin, Taylan; Cankocak, Kerem; Vardarlı, Fuat Ilkehan; Levchuk, Leonid; Sorokin, Pavel; Brooke, James John; Clement, Emyr; Cussans, David; Flacher, Henning; Goldstein, Joel; Grimes, Mark; Heath, Greg P; Heath, Helen F; Jacob, Jeson; Kreczko, Lukasz; Lucas, Chris; Meng, Zhaoxia; Newbold, Dave M; Paramesvaran, Sudarshan; Poll, Anthony; Sakuma, Tai; Senkin, Sergey; Smith, Vincent J; Williams, Thomas; Bell, Ken W; Belyaev, Alexander; Brew, Christopher; Brown, Robert M; Cockerill, David JA; Coughlan, John A; Harder, Kristian; Harper, Sam; Olaiya, Emmanuel; Petyt, David; Shepherd-Themistocleous, Claire; Thea, Alessandro; Tomalin, Ian R; Womersley, William John; Worm, Steven; Baber, Mark; Bainbridge, Robert; Buchmuller, Oliver; Burton, Darren; Colling, David; Cripps, Nicholas; Dauncey, Paul; Davies, Gavin; Della Negra, Michel; Dunne, Patrick; Ferguson, William; Fulcher, Jonathan; Futyan, David; Hall, Geoffrey; Iles, Gregory; Jarvis, Martyn; Karapostoli, Georgia; Kenzie, Matthew; Lane, Rebecca; Lucas, Robyn; Lyons, Louis; Magnan, Anne-Marie; Malik, Sarah; Mathias, Bryn; Nash, Jordan; Nikitenko, Alexander; Pela, Joao; Pesaresi, Mark; Petridis, Konstantinos; Raymond, David Mark; Rogerson, Samuel; Rose, Andrew; Seez, Christopher; Sharp, Peter; Tapper, Alexander; Vazquez Acosta, Monica; Virdee, Tejinder; Zenz, Seth Conrad; Cole, Joanne; Hobson, Peter R; Khan, Akram; Kyberd, Paul; Leggat, Duncan; Leslie, Dawn; Reid, Ivan; Symonds, Philip; Teodorescu, Liliana; Turner, Mark; Dittmann, Jay; Hatakeyama, Kenichi; Kasmi, Azeddine; Liu, Hongxuan; Scarborough, Tara; Charaf, Otman; Cooper, Seth; Henderson, Conor; Rumerio, Paolo; Avetisyan, Aram; Bose, Tulika; Fantasia, Cory; Lawson, Philip; Richardson, Clint; Rohlf, James; St John, Jason; Sulak, Lawrence; Alimena, Juliette; Berry, Edmund; Bhattacharya, Saptaparna; Christopher, Grant; Cutts, David; Demiragli, Zeynep; Dhingra, Nitish; Ferapontov, Alexey; Garabedian, Alex; Heintz, Ulrich; Kukartsev, Gennadiy; Laird, Edward; Landsberg, Greg; Luk, Michael; Narain, Meenakshi; Segala, Michael; Sinthuprasith, Tutanon; Speer, Thomas; Swanson, Joshua; Breedon, Richard; Breto, Guillermo; Calderon De La Barca Sanchez, Manuel; Chauhan, Sushil; Chertok, Maxwell; Conway, John; Conway, Rylan; Cox, Peter Timothy; Erbacher, Robin; Gardner, Michael; Ko, Winston; Lander, Richard; Miceli, Tia; Mulhearn, Michael; Pellett, Dave; Pilot, Justin; Ricci-Tam, Francesca; Searle, Matthew; Shalhout, Shalhout; Smith, John; Squires, Michael; Stolp, Dustin; Tripathi, Mani; Wilbur, Scott; Yohay, Rachel; Cousins, Robert; Everaerts, Pieter; Farrell, Chris; Hauser, Jay; Ignatenko, Mikhail; Rakness, Gregory; Takasugi, Eric; Valuev, Vyacheslav; Weber, Matthias; Burt, Kira; Clare, Robert; Ellison, John Anthony; Gary, J William; Hanson, Gail; Heilman, Jesse; Ivova Rikova, Mirena; Jandir, Pawandeep; Kennedy, Elizabeth; Lacroix, Florent; Long, Owen Rosser; Luthra, Arun; Malberti, Martina; Olmedo Negrete, Manuel; Shrinivas, Amithabh; Sumowidagdo, Suharyo; Wimpenny, Stephen; Branson, James G; Cerati, Giuseppe Benedetto; Cittolin, Sergio; D'Agnolo, Raffaele Tito; Holzner, André; Kelley, Ryan; Klein, Daniel; Letts, James; Macneill, Ian; Olivito, Dominick; Padhi, Sanjay; Palmer, Christopher; Pieri, Marco; Sani, Matteo; Sharma, Vivek; Simon, Sean; Tadel, Matevz; Tu, Yanjun; Vartak, Adish; Welke, Charles; Würthwein, Frank; Yagil, Avraham; Barge, Derek; Bradmiller-Feld, John; Campagnari, Claudio; Danielson, Thomas; Dishaw, Adam; Dutta, Valentina; Flowers, Kristen; Franco Sevilla, Manuel; Geffert, Paul; George, Christopher; Golf, Frank; Gouskos, Loukas; Incandela, Joe; Justus, Christopher; Mccoll, Nickolas; Richman, Jeffrey; Stuart, David; To, Wing; West, Christopher; Yoo, Jaehyeok; Apresyan, Artur; Bornheim, Adolf; Bunn, Julian; Chen, Yi; Duarte, Javier; Mott, Alexander; Newman, Harvey B; Pena, Cristian; Pierini, Maurizio; Spiropulu, Maria; Vlimant, Jean-Roch; Wilkinson, Richard; Xie, Si; Zhu, Ren-Yuan; Azzolini, Virginia; Calamba, Aristotle; Carlson, Benjamin; Ferguson, Thomas; Iiyama, Yutaro; Paulini, Manfred; Russ, James; Vogel, Helmut; Vorobiev, Igor; Cumalat, John Perry; Ford, William T; Gaz, Alessandro; Krohn, Michael; Luiggi Lopez, Eduardo; Nauenberg, Uriel; Smith, James; Stenson, Kevin; Ulmer, Keith; Wagner, Stephen Robert; Alexander, James; Chatterjee, Avishek; Chaves, Jorge; Chu, Jennifer; Dittmer, Susan; Eggert, Nicholas; Mirman, Nathan; Nicolas Kaufman, Gala; Patterson, Juliet Ritchie; Ryd, Anders; Salvati, Emmanuele; Skinnari, Louise; Sun, Werner; Teo, Wee Don; Thom, Julia; Thompson, Joshua; Tucker, Jordan; Weng, Yao; Winstrom, Lucas; Wittich, Peter; Winn, Dave; Abdullin, Salavat; Albrow, Michael; Anderson, Jacob; Apollinari, Giorgio; Bauerdick, Lothar AT; Beretvas, Andrew; Berryhill, Jeffrey; Bhat, Pushpalatha C; Bolla, Gino; Burkett, Kevin; Butler, Joel Nathan; Cheung, Harry; Chlebana, Frank; Cihangir, Selcuk; Elvira, Victor Daniel; Fisk, Ian; Freeman, Jim; Gao, Yanyan; Gottschalk, Erik; Gray, Lindsey; Green, Dan; Grünendahl, Stefan; Gutsche, Oliver; Hanlon, Jim; Hare, Daryl; Harris, Robert M; Hirschauer, James; Hooberman, Benjamin; Jindariani, Sergo; Johnson, Marvin; Joshi, Umesh; Kaadze, Ketino; Klima, Boaz; Kreis, Benjamin; Kwan, Simon; Linacre, Jacob; Lincoln, Don; Lipton, Ron; Liu, Tiehui; Lykken, Joseph; Maeshima, Kaori; Marraffino, John Michael; Martinez Outschoorn, Verena Ingrid; Maruyama, Sho; Mason, David; McBride, Patricia; Merkel, Petra; Mishra, Kalanand; Mrenna, Stephen; Nahn, Steve; Newman-Holmes, Catherine; O'Dell, Vivian; Prokofyev, Oleg; Sexton-Kennedy, Elizabeth; Sharma, Seema; Soha, Aron; Spalding, William J; Spiegel, Leonard; Taylor, Lucas; Tkaczyk, Slawek; Tran, Nhan Viet; Uplegger, Lorenzo; Vaandering, Eric Wayne; Vidal, Richard; Whitbeck, Andrew; Whitmore, Juliana; Yang, Fan; Acosta, Darin; Avery, Paul; Bortignon, Pierluigi; Bourilkov, Dimitri; Carver, Matthew; Curry, David; Das, Souvik; De Gruttola, Michele; Di Giovanni, Gian Piero; Field, Richard D; Fisher, Matthew; Furic, Ivan-Kresimir; Hugon, Justin; Konigsberg, Jacobo; Korytov, Andrey; Kypreos, Theodore; Low, Jia Fu; Matchev, Konstantin; Mei, Hualin; Milenovic, Predrag; Mitselmakher, Guenakh; Muniz, Lana; Rinkevicius, Aurelijus; Shchutska, Lesya; Snowball, Matthew; Sperka, David; Yelton, John; Zakaria, Mohammed; Hewamanage, Samantha; Linn, Stephan; Markowitz, Pete; Martinez, German; Rodriguez, Jorge Luis; Adams, Todd; Askew, Andrew; Bochenek, Joseph; Diamond, Brendan; Haas, Jeff; Hagopian, Sharon; Hagopian, Vasken; Johnson, Kurtis F; Prosper, Harrison; Veeraraghavan, Venkatesh; Weinberg, Marc; Baarmand, Marc M; Hohlmann, Marcus; Kalakhety, Himali; Yumiceva, Francisco; Adams, Mark Raymond; Apanasevich, Leonard; Berry, Douglas; Betts, Russell Richard; Bucinskaite, Inga; Cavanaugh, Richard; Evdokimov, Olga; Gauthier, Lucie; Gerber, Cecilia Elena; Hofman, David Jonathan; Kurt, Pelin; Moon, Dong Ho; O'Brien, Christine; Sandoval Gonzalez, Irving Daniel; Silkworth, Christopher; Turner, Paul; Varelas, Nikos; Bilki, Burak; Clarida, Warren; Dilsiz, Kamuran; Haytmyradov, Maksat; Merlo, Jean-Pierre; Mermerkaya, Hamit; Mestvirishvili, Alexi; Moeller, Anthony; Nachtman, Jane; Ogul, Hasan; Onel, Yasar; Ozok, Ferhat; Penzo, Aldo; Rahmat, Rahmat; Sen, Sercan; Tan, Ping; Tiras, Emrah; Wetzel, James; Yi, Kai; Barnett, Bruce Arnold; Blumenfeld, Barry; Bolognesi, Sara; Fehling, David; Gritsan, Andrei; Maksimovic, Petar; Martin, Christopher; Swartz, Morris; Baringer, Philip; Bean, Alice; Benelli, Gabriele; Bruner, Christopher; Kenny III, Raymond Patrick; Malek, Magdalena; Murray, Michael; Noonan, Daniel; Sanders, Stephen; Sekaric, Jadranka; Stringer, Robert; Wang, Quan; Wood, Jeffrey Scott; Chakaberia, Irakli; Ivanov, Andrew; Khalil, Sadia; Makouski, Mikhail; Maravin, Yurii; Saini, Lovedeep Kaur; Skhirtladze, Nikoloz; Svintradze, Irakli; Gronberg, Jeffrey; Lange, David; Rebassoo, Finn; Wright, Douglas; Baden, Drew; Belloni, Alberto; Calvert, Brian; Eno, Sarah Catherine; Gomez, Jaime; Hadley, Nicholas John; Kellogg, Richard G; Kolberg, Ted; Lu, Ying; Mignerey, Alice; Pedro, Kevin; Skuja, Andris; Tonjes, Marguerite; Tonwar, Suresh C; Apyan, Aram; Barbieri, Richard; Bauer, Gerry; Busza, Wit; Cali, Ivan Amos; Chan, Matthew; Di Matteo, Leonardo; Gomez Ceballos, Guillelmo; Goncharov, Maxim; Gulhan, Doga; Klute, Markus; Lai, Yue Shi; Lee, Yen-Jie; Levin, Andrew; Luckey, Paul David; Ma, Teng; Paus, Christoph; Ralph, Duncan; Roland, Christof; Roland, Gunther; Stephans, George; Stöckli, Fabian; Sumorok, Konstanty; Velicanu, Dragos; Veverka, Jan; Wyslouch, Bolek; Yang, Mingming; Zanetti, Marco; Zhukova, Victoria; Dahmes, Bryan; Gude, Alexander; Kao, Shih-Chuan; Klapoetke, Kevin; Kubota, Yuichi; Mans, Jeremy; Pastika, Nathaniel; Rusack, Roger; Singovsky, Alexander; Tambe, Norbert; Turkewitz, Jared; Acosta, John Gabriel; Oliveros, Sandra; Avdeeva, Ekaterina; Bloom, Kenneth; Bose, Suvadeep; Claes, Daniel R; Dominguez, Aaron; Gonzalez Suarez, Rebeca; Keller, Jason; Knowlton, Dan; Kravchenko, Ilya; Lazo-Flores, Jose; Meier, Frank; Ratnikov, Fedor; Snow, Gregory R; Zvada, Marian; Dolen, James; Godshalk, Andrew; Iashvili, Ia; Kharchilava, Avto; Kumar, Ashish; Rappoccio, Salvatore; Alverson, George; Barberis, Emanuela; Baumgartel, Darin; Chasco, Matthew; Massironi, Andrea; Morse, David Michael; Nash, David; Orimoto, Toyoko; Trocino, Daniele; Wang, Ren-Jie; Wood, Darien; Zhang, Jinzhong; Hahn, Kristan Allan; Kubik, Andrew; Mucia, Nicholas; Odell, Nathaniel; Pollack, Brian; Pozdnyakov, Andrey; Schmitt, Michael Henry; Stoynev, Stoyan; Sung, Kevin; Velasco, Mayda; Won, Steven; Brinkerhoff, Andrew; Chan, Kwok Ming; Drozdetskiy, Alexey; Hildreth, Michael; Jessop, Colin; Karmgard, Daniel John; Kellams, Nathan; Lannon, Kevin; Lynch, Sean; Marinelli, Nancy; Musienko, Yuri; Pearson, Tessa; Planer, Michael; Ruchti, Randy; Smith, Geoffrey; Valls, Nil; Wayne, Mitchell; Wolf, Matthias; Woodard, Anna; Antonelli, Louis; Brinson, Jessica; Bylsma, Ben; Durkin, Lloyd Stanley; Flowers, Sean; Hart, Andrew; Hill, Christopher; Hughes, Richard; Kotov, Khristian; Ling, Ta-Yung; Luo, Wuming; Puigh, Darren; Rodenburg, Marissa; Winer, Brian L; Wolfe, Homer; Wulsin, Howard Wells; Driga, Olga; Elmer, Peter; Hardenbrook, Joshua; Hebda, Philip; Hunt, Adam; Koay, Sue Ann; Lujan, Paul; Marlow, Daniel; Medvedeva, Tatiana; Mooney, Michael; Olsen, James; Piroué, Pierre; Quan, Xiaohang; Saka, Halil; Stickland, David; Tully, Christopher; Werner, Jeremy Scott; Zuranski, Andrzej; Brownson, Eric; Malik, Sudhir; Mendez, Hector; Ramirez Vargas, Juan Eduardo; Barnes, Virgil E; Benedetti, Daniele; Bortoletto, Daniela; De Mattia, Marco; Gutay, Laszlo; Hu, Zhen; Jha, Manoj; Jones, Matthew; Jung, Kurt; Kress, Matthew; Leonardo, Nuno; Lopes Pegna, David; Maroussov, Vassili; Miller, David Harry; Neumeister, Norbert; Radburn-Smith, Benjamin Charles; Shi, Xin; Shipsey, Ian; Silvers, David; Svyatkovskiy, Alexey; Wang, Fuqiang; Xie, Wei; Xu, Lingshan; Zablocki, Jakub; Zheng, Yu; Parashar, Neeti; Stupak, John; Adair, Antony; Akgun, Bora; Ecklund, Karl Matthew; Geurts, Frank JM; Li, Wei; Michlin, Benjamin; Padley, Brian Paul; Redjimi, Radia; Roberts, Jay; Zabel, James; Betchart, Burton; Bodek, Arie; Covarelli, Roberto; de Barbaro, Pawel; Demina, Regina; Eshaq, Yossof; Ferbel, Thomas; Garcia-Bellido, Aran; Goldenzweig, Pablo; Han, Jiyeon; Harel, Amnon; Khukhunaishvili, Aleko; Korjenevski, Sergey; Petrillo, Gianluca; Vishnevskiy, Dmitry; Ciesielski, Robert; Demortier, Luc; Goulianos, Konstantin; Mesropian, Christina; Arora, Sanjay; Barker, Anthony; Chou, John Paul; Contreras-Campana, Christian; Contreras-Campana, Emmanuel; Duggan, Daniel; Ferencek, Dinko; Gershtein, Yuri; Gray, Richard; Halkiadakis, Eva; Hidas, Dean; Kaplan, Steven; Lath, Amitabh; Panwalkar, Shruti; Park, Michael; Patel, Rishi; Salur, Sevil; Schnetzer, Steve; Somalwar, Sunil; Stone, Robert; Thomas, Scott; Thomassen, Peter; Walker, Matthew; Rose, Keith; Spanier, Stefan; York, Andrew; Bouhali, Othmane; Castaneda Hernandez, Alfredo; Eusebi, Ricardo; Flanagan, Will; Gilmore, Jason; Kamon, Teruki; Khotilovich, Vadim; Krutelyov, Vyacheslav; Montalvo, Roy; Osipenkov, Ilya; Pakhotin, Yuriy; Perloff, Alexx; Roe, Jeffrey; Rose, Anthony; Safonov, Alexei; Suarez, Indara; Tatarinov, Aysen; Akchurin, Nural; Cowden, Christopher; Damgov, Jordan; Dragoiu, Cosmin; Dudero, Phillip Russell; Faulkner, James; Kovitanggoon, Kittikul; Kunori, Shuichi; Lee, Sung Won; Libeiro, Terence; Volobouev, Igor; Appelt, Eric; Delannoy, Andrés G; Greene, Senta; Gurrola, Alfredo; Johns, Willard; Maguire, Charles; Mao, Yaxian; Melo, Andrew; Sharma, Monika; Sheldon, Paul; Snook, Benjamin; Tuo, Shengquan; Velkovska, Julia; Arenton, Michael Wayne; Boutle, Sarah; Cox, Bradley; Francis, Brian; Goodell, Joseph; Hirosky, Robert; Ledovskoy, Alexander; Li, Hengne; Lin, Chuanzhe; Neu, Christopher; Wood, John; Clarke, Christopher; Harr, Robert; Karchin, Paul Edmund; Kottachchi Kankanamge Don, Chamath; Lamichhane, Pramod; Sturdy, Jared; Belknap, Donald; Carlsmith, Duncan; Cepeda, Maria; Dasu, Sridhara; Dodd, Laura; Duric, Senka; Friis, Evan; Hall-Wilton, Richard; Herndon, Matthew; Hervé, Alain; Klabbers, Pamela; Lanaro, Armando; Lazaridis, Christos; Levine, Aaron; Loveless, Richard; Mohapatra, Ajit; Ojalvo, Isabel; Perry, Thomas; Pierro, Giuseppe Antonio; Polese, Giovanni; Ross, Ian; Sarangi, Tapas; Savin, Alexander; Smith, Wesley H; Taylor, Devin; Vuosalo, Carl; Woods, Nathaniel
2015-03-18
A search is performed for long-lived particles that decay into final states that include a pair of electrons or a pair of muons. The experimental signature is a distinctive topology consisting of a pair of charge dleptons originating from a displaced secondary vertex. Events corresponding to an integrated luminosity of $19.6\\,(20.5)~\\mathrm{fb}^{-1}$ in the electron (muon) channel were collected with the CMS detector at the CERN LHC in proton-proton collisions at $\\sqrt{s} = 8~\\mathrm{TeV}$. No significant excess is observed above standard model expectations. Upper limits on the product of the cross section and branching fraction of such a signal are presented as a function of the long-lived particle's mean proper decay length. The limits are presented in an approximately model-independent way, allowing them to be applied to a wide class of models yielding the above topology. Over much of the investigated parameter space, the limits obtained are the most stringent to date. In the specific case of a model in w...
Eigenstate Gibbs Ensemble in Integrable Quantum Systems
Nandy, Sourav; Das, Arnab; Dhar, Abhishek
2016-01-01
The Eigenstate Thermalization Hypothesis implies that for a thermodynamically large system in one of its eigenstates, the reduced density matrix describing any finite subsystem is determined solely by a set of {\\it relevant} conserved quantities. In a generic system, only the energy plays that role and hence eigenstates appear locally thermal. Integrable systems, on the other hand, possess an extensive number of such conserved quantities and hence the reduced density matrix requires specification of an infinite number of parameters (Generalized Gibbs Ensemble). However, here we show by unbiased statistical sampling of the individual eigenstates with a given finite energy density, that the local description of an overwhelming majority of these states of even such an integrable system is actually Gibbs-like, i.e. requires only the energy density of the eigenstate. Rare eigenstates that cannot be represented by the Gibbs ensemble can also be sampled efficiently by our method and their local properties are then s...
Energy Technology Data Exchange (ETDEWEB)
Reboiro, M., E-mail: reboiro@fisica.unlp.edu.ar [IFLP, CONICET-Department of Physics, University of La Plata, c.c. 67 1900, La Plata (Argentina); Civitarese, O., E-mail: osvaldo.civitarese@fisica.unlp.edu.ar [IFLP, CONICET-Department of Physics, University of La Plata, c.c. 67 1900, La Plata (Argentina); Ramírez, R. [IFLP, CONICET-Department of Mathematics, University of La Plata (Argentina)
2017-03-15
The degree of coherence in a hybrid system composed of superconducting flux-qubits and an electron ensemble is analysed. Both, the interactions among the electrons and among the superconducting flux-qubits are taken into account. The time evolution of the hybrid system is solved exactly, and discussed in terms of the reduced density matrix of each subsystem. It is seen that the inclusion of a line width, for the electrons and for the superconducting flux-qubits, influences the pattern of spin-squeezing and the coherence of the superconducting flux qubits. - Highlights: • The degree of coherence in a hybrid system, composed of superconducting flux qubits and an electron ensemble, is analysed. • The time evolution of the hybrid system is solved exactly and discussed in terms of the reduced density matrix of each subsystem. • It is shown that the initial state of the system evolves to a stationary squeezed state.
Laser control of molecular excitations in stochastic dissipative media.
Tremblay, Jean Christophe
2011-05-07
In the present work, ideas for controlling photochemical reactions in dissipative environments using shaped laser pulses are presented. New time-local control algorithms for the stochastic Schrödinger equation are introduced and compared to their reduced density matrix analog. The numerical schemes rely on time-dependent targets for guiding the reaction along a preferred path. The methods are tested on the vibrational control of adsorbates at metallic surfaces and on the ultrafast electron dynamics in a strong dissipative medium. The selective excitation of the specific states is achieved with improved yield when using the new algorithms. Both methods exhibit similar convergence behavior and results compare well with those obtained using local optimal control for the reduced density matrix. The favorable scaling of the methods allows to tackle larger systems and to control photochemical reactions in dissipative media of molecules with many more degrees of freedom.
Quantum Decoherence During Inflation from Gravitational Nonlinearities
Nelson, Elliot
2016-01-01
We study the inflationary quantum-to-classical transition for the adiabatic curvature perturbation $\\zeta$ due to quantum decoherence, focusing on the role played by squeezed-limit mode couplings. We evolve the quantum state $\\Psi$ in the Schr\\"odinger picture, for a generic cubic coupling to additional environment degrees of freedom. Focusing on the case of minimal gravitational interactions, we find the evolution of the reduced density matrix for a given long-wavelength fluctuation by tracing out the other (mostly shorterwavelength) modes of $\\zeta$ as an environment. We show that inflation produces phase oscillations in the wave functional $\\Psi[\\zeta(\\mathbf{x})]$, which suppress off-diagonal components of the reduced density matrix, leaving a diagonal mixture of different classical configurations. Gravitational nonlinearities thus provide a minimal mechanism for generating classical stochastic perturbations from inflation. We identify the time when decoherence occurs, which is delayed after horizon cross...
Note on the Harmonic Approximation in the Treatment of Entanglement: N Cold Trapped Ions
Kościk, Przemysław; Maj, Radosław
2014-12-01
We study a one-dimensional system composed of N charged bosons confined in an external harmonic potential. In the limit of a strong interaction between the particles, we apply the harmonic approximation and derive an integral representation for the purity of the one-particle reduced density matrix, enabling an easy determination of the asymptotic entanglement. Results for the dependence of the asymptotic linear entropy on N are provided and discussed in detail for the first time.
Transformation of time dependence to linear algebra
Menšík, Miroslav
2005-10-01
Reduced density matrix and memory function in the Nakajima-Zwanzig equation are expanded in properly chosen basis of special functions. This trick completely transforms time dependence to linear algebra. Then, the master equation for memory function is constructed and expanded in the same basis functions. For the model of a simple harmonic oscillator it is shown that this trick introduces infinite partial summation of the memory function in the system-bath interaction.
Motor effect in electron transport through a molecular junction with torsional vibrations
Pshenichnyuk, Ivan A.; Čížek, Martin
2010-01-01
We propose a model for a molecular junction with internal anharmonic torsional vibrations interacting with an electric current. The Wangsness-Bloch-Redfield master equation approach is used to determine the stationary reduced density matrix of the molecule. The dependence of the current, excitation energy and angular momentum of the junction on the applied voltage is studied. Negative differential conductance is observed in the current-voltage characteristics. It is shown that a model with vi...
Peltier effect in strongly driven quantum wires
Mierzejewski, M.; Crivelli, D.; Prelovsek, P.
2013-01-01
We study a microscopic model of a thermocouple device with two connected correlated quantum wires driven by a constant electric field. In such isolated system we follow the time-- and position--dependence of the entropy density using the concept of the reduced density matrix. At weak driving, the initial changes of the entropy at the junctions can be described by the linear Peltier response. At longer times the quasiequilibrium situation is reached with well defined local temperatures which i...
Dissipative many-electron dynamics of ionizing systems.
Tremblay, Jean Christophe; Klinkusch, Stefan; Klamroth, Tillmann; Saalfrank, Peter
2011-01-28
In this paper, we perform many-electron dynamics using the time-dependent configuration-interaction method in its reduced density matrix formulation (ρ-TDCI). Dissipation is treated implicitly using the Lindblad formalism. To include the effect of ionization on the state-resolved dynamics, we extend a recently introduced heuristic model for ionizing states to the ρ-TDCI method, which leads to a reduced density matrix evolution that is not norm-preserving. We apply the new method to the laser-driven excitation of H(2) in a strongly dissipative environment, for which the state-resolve lifetimes are tuned to a few femtoseconds, typical for dynamics of adsorbate at metallic surfaces. Further testing is made on the laser-induced intramolecular charge transfer in a quinone derivative as a model for a molecular switch. A modified scheme to treat ionizing states is proposed to reduce the computational burden associated with the density matrix propagation, and it is thoroughly tested and compared to the results obtained with the former model. The new approach scales favorably (∼N(2)) with the number of configurations N used to represent the reduced density matrix in the ρ-TDCI method, as compared to a N(3) scaling for the model in its original form.
Jacobs, Verne L.
2017-06-01
This investigation has been devoted to the theoretical description and computer modeling of atomic processes giving rise to radiative emission in energetic electron and ion beam interactions and in laboratory plasmas. We are also interested in the effects of directed electron and ion collisions and of anisotropic electric and magnetic fields. In the kinetic-theory description, we treat excitation, de-excitation, ionization, and recombination in electron and ion encounters with partially ionized atomic systems, including the indirect contributions from processes involving autoionizing resonances. These fundamental collisional and electromagnetic interactions also provide particle and photon transport mechanisms. From the spectral perspective, the analysis of atomic radiative emission can reveal detailed information on the physical properties in the plasma environment, such as non-equilibrium electron and charge-state distributions as well as electric and magnetic field distributions. In this investigation, a reduced-density-matrix formulation is developed for the microscopic description of atomic electromagnetic interactions in the presence of environmental (collisional and radiative) relaxation and decoherence processes. Our central objective is a fundamental microscopic description of atomic electromagnetic processes, in which both bound-state and autoionization-resonance phenomena can be treated in a unified and self-consistent manner. The time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations of the reduced-density-matrix approach are developed in a unified and self-consistent manner. This is necessary for our ultimate goal of a systematic and self-consistent treatment of non-equilibrium (possibly coherent) atomic-state kinetics and high-resolution (possibly overlapping) spectral-line shapes. We thereby propose the introduction of a generalized collisional-radiative atomic-state kinetics model based on a reduced-density-matrix
Zhong, Z Z
2004-01-01
In this paper, we first discuss how to more strictly define the concept of the partial separability of the multipartite qubit density matrixes, further we give a way of reduction from an arbitrary multipartite qubit density matrix through to a bipartite qubit density matrix in one step. We prove that a necessary condition of a N-partite qubit density matrix to be partially separable with respect to a separation is that the corresponding reduced density matrix satisfies the PPT condition. Some examples are given.
Piris, Mario
2016-01-01
The potential energy curves of P2 and P2+ have been calculated using an approximate, albeit strictly N-representable, energy functional of the one-particle reduced density matrix: PNOF5. Quite satisfactory accord is found for the equilibrium bond lengths and dissociation energies for both species. The predicted vertical ionization energy for P2 by means of the extended Koopmans' theorem is 10.57 eV in good agreement with the experimental data. Comparison of the vibrational energies and anharmonicities with their corresponding experimental values supports the quality of the resultant potential energy curves.
Coxeter groups $A_{4}$, $B_{4}$ and $D_{4}$ for two-qubit systems
Indian Academy of Sciences (India)
Ramazan Koç; M Yakup Haciibrahimoğlu; Mehmet Koca
2013-08-01
The Coxeter–Weyl groups $W(A_{4})$, $W(B_{4})$ and $W(D_{4})$ have proven very useful for two-qubit systems in quantum information theory. A simple technique is employed to construct the unitary matrix representations of the groups, based on quaternionic transformation of the usual reflection matrices. The von Neumann entropy of each reduced density matrix is calculated. It is shown that these unitary matrix representations are naturally related to various universal quantum gates and they lead to entangled states. Canonical decomposition of generators in terms of fundamental gate representations is given to construct the quantum circuits.
Ragot, S; Becker, P J; Ragot, Sebastien; Gillet, Jean-Michel; Becker, Pierre J
2001-01-01
In this paper we show that 1-electron properties such as Compton profiles and structure factors of crystals can be asymptotically retrieved through cluster-based calculations, followed by an appropriate partition of the 1-electron reduced density matrix (1RDM). This approach, conceptually simple, is checked with respects to both position and momentum spaces simultaneously for insulators and a covalent crystal. Restricting the calculations to small clusters further enables a fair description of local correlation effects in ionic compounds, which improves both Compton profiles and structure factors vs. their experimentally determined counterparts.
A quantum measure of the multiverse
Vilenkin, Alexander
2014-05-01
It has been recently suggested that probabilities of different events in the multiverse are given by the frequencies at which these events are encountered along the worldline of a geodesic observer (the ``watcher''). Here I discuss an extension of this probability measure to quantum theory. The proposed extension is gauge-invariant, as is the classical version of this measure. Observations of the watcher are described by a reduced density matrix, and the frequencies of events can be found using the decoherent histories formalism of Quantum Mechanics (adapted to open systems). The quantum watcher measure makes predictions in agreement with the standard Born rule of QM.
A quantum measure of the multiverse
Vilenkin, Alexander
2013-01-01
It has been recently suggested that probabilities of different events in the multiverse are given by the frequencies at which these events are encountered along the worldline of a geodesic observer (the "watcher"). Here I discuss an extension of this probability measure to quantum theory. The proposed extension is gauge-invariant, as is the classical version of this measure. Observations of the watcher are described by a reduced density matrix, and the frequencies of events can be found using the decoherent histories formalism of Quantum Mechanics (adapted to open systems). The quantum watcher measure makes predictions in agreement with the standard Born rule of QM.
Cosmological implications of quantum entanglement in the multiverse
Kanno, Sugumi
2015-12-01
We explore the cosmological implications of quantum entanglement between two causally disconnected universes in the multiverse. We first consider two causally separated de Sitter spaces with a state which is initially entangled. We derive the reduced density matrix of our universe and compute the spectrum of vacuum fluctuations. We then consider the same system with an initially non-entangled state. We find that due to quantum interference scale dependent modulations may enter the spectrum for the case of initially non-entangled state. This gives rise to the possibility that the existence of causally disconnected universes may be experimentally tested by analyzing correlators in detail.
Cosmological implications of quantum entanglement in the multiverse
Kanno, Sugumi
2015-01-01
We explore the cosmological implications of quantum entanglement between two causally disconnected universes in the multiverse. We first consider two causally separated de Sitter spaces with a state which is initially entangled. We derive the reduced density matrix of our universe and compute the spectrum of vacuum fluctuations. We then consider the same system with an initially non-entangled state. We find that scale dependent modulations may enter the spectrum for the case of initially non-entangled state due to quantum interference. This gives rise to the possibility that the existence of causally disconnected universes may be experimentally tested by analyzing correlators in detail.
Cosmological implications of quantum entanglement in the multiverse
Energy Technology Data Exchange (ETDEWEB)
Kanno, Sugumi, E-mail: sugumi.kanno@ehu.es [Department of Theoretical Physics and History of Science, University of the Basque Country UPV/EHU, 48080 Bilbao (Spain); IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013 Bilbao (Spain)
2015-12-17
We explore the cosmological implications of quantum entanglement between two causally disconnected universes in the multiverse. We first consider two causally separated de Sitter spaces with a state which is initially entangled. We derive the reduced density matrix of our universe and compute the spectrum of vacuum fluctuations. We then consider the same system with an initially non-entangled state. We find that due to quantum interference scale dependent modulations may enter the spectrum for the case of initially non-entangled state. This gives rise to the possibility that the existence of causally disconnected universes may be experimentally tested by analyzing correlators in detail.
Cosmological implications of quantum entanglement in the multiverse
Directory of Open Access Journals (Sweden)
Sugumi Kanno
2015-12-01
Full Text Available We explore the cosmological implications of quantum entanglement between two causally disconnected universes in the multiverse. We first consider two causally separated de Sitter spaces with a state which is initially entangled. We derive the reduced density matrix of our universe and compute the spectrum of vacuum fluctuations. We then consider the same system with an initially non-entangled state. We find that due to quantum interference scale dependent modulations may enter the spectrum for the case of initially non-entangled state. This gives rise to the possibility that the existence of causally disconnected universes may be experimentally tested by analyzing correlators in detail.
A quantum measure of the multiverse
Energy Technology Data Exchange (ETDEWEB)
Vilenkin, Alexander, E-mail: vilenkin@cosmos.phy.tufts.edu [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155 (United States)
2014-05-01
It has been recently suggested that probabilities of different events in the multiverse are given by the frequencies at which these events are encountered along the worldline of a geodesic observer (the ''watcher''). Here I discuss an extension of this probability measure to quantum theory. The proposed extension is gauge-invariant, as is the classical version of this measure. Observations of the watcher are described by a reduced density matrix, and the frequencies of events can be found using the decoherent histories formalism of Quantum Mechanics (adapted to open systems). The quantum watcher measure makes predictions in agreement with the standard Born rule of QM.
Dymarsky, Anatoly; Liu, Hong
2016-01-01
Motivated by the qualitative picture of Canonical Typicality, we propose a refined formulation of the Eigenstate Thermalization Hypothesis (ETH) for chaotic quantum systems. The new formulation, which we refer to as subsystem ETH, is in terms of the reduced density matrix of subsystems. This strong form of ETH clarifies which set of observables defined within the subsystem will thermalize. We discuss the limits when the size of the subsystem is small or comparable to its complement. Finally, we provide numerical evidence for the proposal in case of one-dimensional Ising spin-chain.
On a Random Matrix Models of Quantum Relaxation
Lebowitz, J L; Pastur, L
2007-01-01
Earlier two of us (J.L. and L.P.) considered a matrix model for a two-level system interacting with a $n\\times n$ reservoir and assuming that the interaction is modelled by a random matrix. We presented there a formula for the reduced density matrix in the limit $n\\to \\infty $ as well as several its properties and asymptotic forms in various regimes. In this paper we give the proofs of the assertions, and present also a new fact about the model.
Entanglement of self interacting scalar fields in an expanding spacetime
Alexander, Helder; Mansfield, Paul; da Paz, I G; Sampaio, Marcos
2016-01-01
We evaluate self-interaction effects on the quantum correlations of field modes of opposite momenta for scalar $\\lambda \\phi^4$ theory in a two-dimensional asymptotically flat Robertson-Walker spacetime. Such correlations are encoded both in the von-Neumann entropy defined through the reduced density matrix in one of the modes and in the covariance expressed in terms of the expectation value of the number operators for each mode in the evolved state. The entanglement between field modes carries information about the underlying spacetime evolution.
Note on Entanglement of an Arbitrary State of Two Qubits
Institute of Scientific and Technical Information of China (English)
WANG An-Min
2000-01-01
It is shown that the norm of the polarization vector of the reduced density matrix can characterize the entangle ment of two qubits and so it is defined as a simple measure of entanglement. It is then extended to the generalized entanglement of polarization vector. It is proved that the entanglement of formation belongs to the generalized entanglement of polarization vector. Under the local general measurement and classical communication how this generalized entanglement of polarization vector changes is proved strictly and so the first and second laws of quantum information processing are verified clearly.
Density matrix theory for reductive electron transfer in DNA
Energy Technology Data Exchange (ETDEWEB)
Kleinekathoefer, Ulrich [Institut fuer Physik, Technische Universitaet Chemnitz, 09107 Chemnitz (Germany)]. E-mail: kleinekathoefer@physik.tu-chemnitz.de; Li Guangqi [Institut fuer Physik, Technische Universitaet Chemnitz, 09107 Chemnitz (Germany); Schreiber, Michael [Institut fuer Physik, Technische Universitaet Chemnitz, 09107 Chemnitz (Germany)
2006-07-15
Reductive electron transfer in DNA is investigated using the reduced density matrix formalism. For reductive electron transfer in DNA an electron donor is attached to the DNA. The photo-excitation of this donor by ultrashort laser pulses is described explicitly in the current investigation, as well as the transfer of the electron from the donor to the acceptor. In addition, the effect of an additional bridge molecule is studied. All these studies are performed using three different quantum master equations: a Markovian one and two non-Markovian ones derived from either a time-local or a time-nonlocal formalism. The deviations caused by these three different approaches are discussed.
Eigenstate Thermalization Hypothesis in Conformal Field Theory
Lashkari, Nima; Liu, Hong
2016-01-01
We investigate the eigenstate thermalization hypothesis (ETH) in d+1 dimensional conformal field theories by studying reduced density matrices in energy eigenstates. We show that if local probes of high energy primary eigenstates satisfy ETH, then any finite energy observable with support on a subsystem of finite size satisfies ETH. In two dimensions, we discover that if ETH holds locally, the finite size reduced density matrix of states created by heavy primary operators is well-approximated by a projection to the Virasoro identity block.
Subsystem's dynamics under random Hamiltonian evolution
Vinayak,
2011-01-01
We study time evolution of a subsystem's density matrix under a unitary evolution, generated by a sufficiently complex, say quantum chaotic, Hamiltonian. We exactly calculate all coherences, purity and fluctuations. The reduced density matrix is described in terms of a noncentral correlated Wishart ensemble. Our description accounts for a transition from an arbitrary initial state towards a random state at large times, enabling us to determine the convergence time after which random states are reached. We identify and describe a number of other interesting features, like a series of collisions between the largest eigenvalue and the bulk, accompanied by a phase transition in its distribution function.
Fine-grained entanglement loss along renormalization group flows
Latorre, J I; Rico, E; Vidal, G
2004-01-01
We explore entanglement loss along renormalization group trajectories as a basic quantum information property underlying their irreversibility. This analysis is carried out for the quantum Ising chain as a transverse magnetic field is changed. We consider the ground-state entanglement between a large block of spins and the rest of the chain. Entanglement loss is seen to follow from a rigid reordering, satisfying the majorization relation, of the eigenvalues of the reduced density matrix for the spin block. More generally, our results indicate that it may be possible to prove the irreversibility along RG trajectories from the properties of the vacuum only, without need to study the whole hamiltonian.
Orbitals from local RDMFT: Are they Kohn-Sham or Natural Orbitals?
Theophilou, Iris; Gidopoulos, Nikitas I; Rubio, Angel; Helbig, Nicole
2015-01-01
Recently, an approximation was introduced in reduced density matrix functional theory (RDMFT), called local-RDMFT, where functionals of the one-body reduced density matrix (1-RDM) are minimized under the additional condition that the optimal orbitals satisfy a single electron Schr\\"odinger equation with a local potential. In the present work, we assess the impact of this additional condition on the optimal orbitals. In particular we compare orbitals obtained by local-RDMFT with those obtained with the full minimization (without the extra condition) by comparing them with the exact NOs and orbitals from a density functional calculation using the local density approximation (LDA). We find that the orbitals from local-RMDFT are very close to LDA orbitals, contrary to those of the full minimization that resemble the exact NOs. Since local RDMFT preserves the good quality of the description of strong static correlation, this finding opens the way to a mixed density/density matrix scheme, where Kohn-Sham orbitals o...
Macroscopic superposition states and decoherence by quantum telegraph noise
Energy Technology Data Exchange (ETDEWEB)
Abel, Benjamin Simon
2008-12-19
In the first part of the present thesis we address the question about the size of superpositions of macroscopically distinct quantum states. We propose a measure for the ''size'' of a Schroedinger cat state, i.e. a quantum superposition of two many-body states with (supposedly) macroscopically distinct properties, by counting how many single-particle operations are needed to map one state onto the other. We apply our measure to a superconducting three-junction flux qubit put into a superposition of clockwise and counterclockwise circulating supercurrent states and find this Schroedinger cat to be surprisingly small. The unavoidable coupling of any quantum system to many environmental degrees of freedom leads to an irreversible loss of information about an initially prepared superposition of quantum states. This phenomenon, commonly referred to as decoherence or dephasing, is the subject of the second part of the thesis. We have studied the time evolution of the reduced density matrix of a two-level system (qubit) subject to quantum telegraph noise which is the major source of decoherence in Josephson charge qubits. We are able to derive an exact expression for the time evolution of the reduced density matrix. (orig.)
Schröder, Markus; Schreiber, Michael; Kleinekathöfer, Ulrich
2007-03-21
Several techniques to solve a hierarchical set of equations of motion for propagating a reduced density matrix coupled to a thermal bath have been developed in recent years. This is either done using the path integral technique as in the original proposal by Tanimura and Kubo [J. Phys. Soc. Jpn. 58, 101 (1998)] or by the use of stochastic fields as done by Yan et al. [Chem. Phys. Lett. 395, 216 (2004)]. Based on the latter ansatz a compact derivation of the hierarchy using a decomposition of the spectral density function is given in the present contribution. The method is applied to calculate the time evolution of the reduced density matrix describing the motion in a harmonic, an anharmonic, and two coupled oscillators where each system is coupled to a thermal bath. Calculations to several orders in the system-bath coupling with two different truncations of the hierarchy are performed. The respective density matrices are used to calculate the time evolution of various system properties and the results are compared and discussed with a special focus on the convergence with respect to the truncation scheme applied.
Dattani, Nikesh S
2012-01-01
This MATLAB program calculates the dynamics of the reduced density matrix of an open quantum system modeled by the Feynman-Vernon model. The user gives the program a vector describing the coordinate of an open quantum system, a hamiltonian matrix describing its energy, and a spectral distribution function and temperature describing the environment's influence on it, in addition to the open quantum system's intial density matrix and a grid of times. With this, the program returns the reduced density matrix of the open quantum system at all (or some) moments specified by that grid of times. This overall calculation can be divided into two stages: the setup of the Feynman integral, and the actual calculation of the Feynman integral for time-propagation of the density matrix. When this program calculates this propagation on a multi-core CPU, it is this propagation that is usually the rate limiting step of the calculation, but when it is calculated on a GPU, the propagation is calculated so quickly that the setup ...
Orbitals from local RDMFT: Are they Kohn-Sham or natural orbitals?
Energy Technology Data Exchange (ETDEWEB)
Theophilou, Iris; Helbig, Nicole [Peter-Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich (Germany); Lathiotakis, Nektarios N. [Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, Vass. Constantinou 48, GR-11635 Athens (Greece); Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle (Saale) (Germany); Gidopoulos, Nikitas I. [Department of Physics, Durham University, South Road, Durham DH1 3LE (United Kingdom); Rubio, Angel [Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg (Germany); Nano-Bio Spectroscopy Group and ETSF Scientific Development Centre, Dpto. Física de Materiales, Universidad del País Vasco, CFM CSIC-UPV/EHU-MPC and DIPC, Av. Tolosa 72, E-20018 San Sebastián (Spain)
2015-08-07
Recently, an approximate theoretical framework was introduced, called local reduced density matrix functional theory (local-RDMFT), where functionals of the one-body reduced density matrix (1-RDM) are minimized under the additional condition that the optimal orbitals satisfy a single electron Schrödinger equation with a local potential. In the present work, we focus on the character of these optimal orbitals. In particular, we compare orbitals obtained by local-RDMFT with those obtained with the full minimization (without the extra condition) by contrasting them against the exact NOs and orbitals from a density functional calculation using the local density approximation (LDA). We find that the orbitals from local-RMDFT are very close to LDA orbitals, contrary to those of the full minimization that resemble the exact NOs. Since local RDMFT preserves the good quality of the description of strong static correlation, this finding opens the way to a mixed density/density matrix scheme, where Kohn-Sham orbitals obtain fractional occupations from a minimization of the occupation numbers using 1-RDM functionals. This will allow for a description of strong correlation at a cost only minimally higher than a density functional calculation.
Eigenstate Gibbs ensemble in integrable quantum systems
Nandy, Sourav; Sen, Arnab; Das, Arnab; Dhar, Abhishek
2016-12-01
The eigenstate thermalization hypothesis conjectures that for a thermodynamically large system in one of its energy eigenstates, the reduced density matrix describing any finite subsystem is determined solely by a set of relevant conserved quantities. In a chaotic quantum system, only the energy is expected to play that role and hence eigenstates appear locally thermal. Integrable systems, on the other hand, possess an extensive number of such conserved quantities and therefore the reduced density matrix requires specification of all the corresponding parameters (generalized Gibbs ensemble). However, here we show by unbiased statistical sampling of the individual eigenstates with a given finite energy density that the local description of an overwhelming majority of these states of even such an integrable system is actually Gibbs-like, i.e., requires only the energy density of the eigenstate. Rare eigenstates that cannot be represented by the Gibbs ensemble can also be sampled efficiently by our method and their local properties are then shown to be described by appropriately truncated generalized Gibbs ensembles. We further show that the presence of these rare eigenstates differentiates the model from the chaotic case and leads to the system being described by a generalized Gibbs ensemble at long time under a unitary dynamics following a sudden quench, even when the initial state is a typical (Gibbs-like) eigenstate of the prequench Hamiltonian.
Yanai, Takeshi; Saitow, Masaaki; Xiong, Xiao-Gen; Chalupský, Jakub; Kurashige, Yuki; Guo, Sheng; Sharma, Sandeep
2017-09-07
We present the development of the multistate multireference second-order perturbation theory (CASPT2) with multi-root references, which are described using the density matrix renormalization group (DMRG) method to handle a large active space. The multistate first-order wave functions are expanded into the internally contracted (IC) basis of the single-state single-reference (SS-SR) scheme, which is shown to be the most feasible variant to use DMRG references. The feasibility of the SS-SR scheme comes from two factors: first, it formally does not require the fourth-order transition reduced density matrix (TRDM); and second, the computational complexity scales linearly with the number of the reference states. The extended multistate (XMS) treatment is further incorporated, giving suited treatment of the zeroth-order Hamiltonian despite the fact that the SS-SR based IC basis is not invariant with respect the XMS rotation. In addition, the state-specific fourth-order reduced density matrix (RDM) is eliminated in an approximate fashion using the cumulant reconstruction formula, as also done in the previous state-specific DMRG-cu(4)-CASPT2 approach. The resultant method, referred to as DMRG-cu(4)-XMS-CASPT2, uses the RDMs and TRDMs of up to third-order provided by the DMRG calculation. The multistate potential energy curves of the photoisomerization of diarylethene derivatives with CAS(26e,24o) are presented to illustrate the applicability of our theoretical approach.
Alon, Ofir E.
2017-07-01
A mixture of two kinds of identical bosons, species 1 with N 1 bosons of mass m 1 and species 2 with N 2 bosons of mass m 2, held in a harmonic potential of frequency ω and interacting by harmonic intra-species and inter-species particle-particle interactions of strengths λ1 , λ2 , and λ12 is discussed. This is an exactly-solvable model of a generic mixture of trapped interacting bosons which allows one to investigate and determine analytically properties of interest. To start, closed form expressions for the frequencies, ground-state energy, and wave-function of the mixture are obtained and briefly analyzed as a function of the masses, numbers of particles, and strengths and signs of interactions. To prove Bose-Einstein condensation of the mixture three steps are needed. First, we integrate the all-particle density matrix, employing a four-parameter matrix-recurrence relations, down to the lowest-order intra-species and inter-species reduced density matrices of the mixture. Second, the coupled Gross-Pitaevskii (mean-field) equations of the mixture are solved analytically. Third, we analyze the mixture’s reduced density matrices in the limit of an infinite number of particles of both species 1 and 2 (when the interaction parameters, i.e. the products of the number of particles times the intra-species and inter-species interaction strengths, are held fixed) and prove that: (i) both species 1 and 2 are 100% condensed; (ii) the inter-species reduced density matrix per particle is separable and given by the product of the intra-species reduced density matrices per particle; and (iii) the mixture’s energy per particle, and reduced density matrices and densities per particle all coincide with the Gross-Pitaevskii quantities. Finally, when the infinite-particle limit is taken with respect to, say, species 1 only (with interaction parameters held fixed) we prove that: (iv) only species 1 is 100% condensed and its reduced density matrix and density per particle, as
The Edge of Jets and Subleading Non-Global Logs
Neill, Duff
2015-01-01
A persistent and fascinating problem at the high energy colliders are jets. Often trying to observe physics underlying the hard interactions at colliders requires experimental cuts in phase space, defining several jet or beam regions. QCD being a gauge theory that readily decays into infra-red modes, correlations between jet regions is almost inevitable, spoiling the predictivity of fixed order QCD calculations. One is faced with the task of calculating the evolution of a reduced density matrix, where successively less energetic (jet) regions are integrated out, to gain control of the calculation. I relate the decay rates governing the flow into the IR to an effective field theory expansion in soft jets, allowing a systematic and resummed calculation of these rates, while further relating them to physically observable features of the QCD cascade. To demonstrate the utility of the soft jet expansion, I present a factorization theorem for a soft subjet collinearly splitting in and out of a parent fat jet. Using...
Hollowood, Timothy J
2013-01-01
We describe an interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description for macro-systems. The interpretation is a modal one, but does not suffer from the range of problems that plague other modal interpretations. The key feature is that quantum states carry an additional property assignment in the form of one the eigenvectors of the reduced density matrix which evolves evolves according to a stochastic process driven by the unmodified Schrodinger equation, but it is usually hidden from the emergent classical description due to the ergodic nature of its dynamics. However, during a quantum measurement, ergodicity is broken by decoherence and definite outcomes occur with probabilities that agree with the Born rule.
Strong parameter renormalization from optimum lattice model orbitals
Brosco, Valentina; Ying, Zu-Jian; Lorenzana, José
2017-01-01
Which is the best single-particle basis to express a Hubbard-like lattice model? A rigorous variational answer to this question leads to equations the solution of which depends in a self-consistent manner on the lattice ground state. Contrary to naive expectations, for arbitrary small interactions, the optimized orbitals differ from the noninteracting ones, leading also to substantial changes in the model parameters as shown analytically and in an explicit numerical solution for a simple double-well one-dimensional case. At strong coupling, we obtain the direct exchange interaction with a very large renormalization with important consequences for the explanation of ferromagnetism with model Hamiltonians. Moreover, in the case of two atoms and two fermions we show that the optimization equations are closely related to reduced density-matrix functional theory, thus establishing an unsuspected correspondence between continuum and lattice approaches.
Density-Matrix Propagation Driven by Semiclassical Correlation
Elliott, Peter
2016-01-01
Methods based on propagation of the one-body reduced density-matrix hold much promise for the simulation of correlated many-electron dynamics far from equilibrium, but difficulties with finding good approximations for the interaction term in its equation of motion have so far impeded their application. These difficulties include the violation of fundamental physical principles such as energy conservation, positivity conditions on the density, or unchanging natural orbital occupation numbers. We review some of the recent efforts to confront these problems, and explore a semiclassical approximation for electron correlation coupled to time-dependent Hartree-Fock propagation. We find that this approach captures changing occupation numbers, and excitations to doubly-excited states, improving over TDHF and adiabatic approximations in density-matrix propagation. However, it does not guarantee $N$-representability of the density-matrix, consequently resulting sometimes in violation of positivity conditions, even thou...
Atomic focusing by quantum fields: Entanglement properties
Energy Technology Data Exchange (ETDEWEB)
Paz, I.G. da [Departamento de Física, Universidade Federal do Piauí, Campus Ministro Petrônio Portela, CEP 64049-550, Teresina, PI (Brazil); Frazão, H.M. [Universidade Federal do Piauí, Campus Profa. Cinobelina Elvas, CEP 64900-000, Bom Jesus, PI (Brazil); Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, Caixa Postal 702, Belo Horizonte, MG 30123-970 (Brazil); Nemes, M.C. [Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, Caixa Postal 702, Belo Horizonte, MG 30123-970 (Brazil); Peixoto de Faria, J.G. [Departamento de Física e Matemática, Centro Federal de Educação Tecnológica de Minas Gerais, Av. Amazonas 7675, Belo Horizonte, MG 30510-000 (Brazil)
2014-04-01
The coherent manipulation of the atomic matter waves is of great interest both in science and technology. In order to study how an atom optic device alters the coherence of an atomic beam, we consider the quantum lens proposed by Averbukh et al. [1] to show the discrete nature of the electromagnetic field. We extend the analysis of this quantum lens to the study of another essentially quantum property present in the focusing process, i.e., the atom–field entanglement, and show how the initial atomic coherence and purity are affected by the entanglement. The dynamics of this process is obtained in closed form. We calculate the beam quality factor and the trace of the square of the reduced density matrix as a function of the average photon number in order to analyze the coherence and purity of the atomic beam during the focusing process.
Entanglement spectrum in cluster dynamical mean-field theory
Udagawa, Masafumi; Motome, Yukitoshi
2015-01-01
We study the entanglement spectrum of the Hubbard model at half filling on a kagome lattice. The entanglement spectrum is defined by the set of eigenvalues of a reduced thermal density matrix, which is naturally obtained in the framework of the dynamical mean-field theory. Adopting the cluster dynamical mean-field theory combined with continuous-time auxiliary-field Monte Carlo method, we calculate the entanglement spectrum for a three-site triangular cluster in the kagome Hubbard model. We find that the results at the three-particle sector well capture the qualitative nature of the system. In particular, the eigenvalue of the reduced density matrix, corresponding to the chiral degrees of freedom, exhibits a characteristic temperature scale Tchiral, below which a metallic state with large quasiparticle mass is stabilized. The entanglement spectra at different particle number sectors also exhibit characteristic changes around Tchiral, implying the development of inter-triangular ferromagnetic correlations in the correlated metallic regime.
Left-right entanglement entropy of boundary states
Energy Technology Data Exchange (ETDEWEB)
Zayas, Leopoldo A. Pando [Michigan Center for Theoretical Physics,Randall Laboratory of Physics, The University of Michigan,Ann Arbor, MI 48109-1120 (United States); Quiroz, Norma [Facultad de Ciencias, Universidad de Colima,Bernal Díaz del Castillo 340, Col. Villas San Sebastián,Colima 28045 (Mexico)
2015-01-21
We study entanglement entropy of boundary states in a free bosonic conformal field theory. A boundary state can be thought of as composed of a particular combination of left and right-moving modes of the two-dimensional conformal field theory. We investigate the reduced density matrix obtained by tracing over the right-moving modes in various boundary states. We consider Dirichlet and Neumann boundary states of a free noncompact as well as a compact boson. The results for the entanglement entropy indicate that the reduced system can be viewed as a thermal CFT gas. Our findings are in agreement and generalize results in quantum mechanics and quantum field theory where coherent states can also be considered. In the compact case we verify that the entanglement entropy expressions are consistent with T-duality.
Effects of curvature and gravity from flat spacetime
Roy, Debraj
2014-01-01
We study some aspects of gravity in relation to flat spacetime. At first, we study an accelerated observer in Minkowski space as a quantum tunnelling problem in Rindler space. Both Bosonic and Fermionic modes are calculated to construct a reduced density matrix of particles tunnelling out across the accelerated Rindler horizon, giving a thermal spectrum characterized by a temperature proportional to the local acceleration - Unruh temperature. So, we calculate both the spectrum and temperature from within the tunnelling framework. In another direction, following Utiyama-Sciama-Kibble, we localise the Poincare group to obtain a Poincare gauge theory (PGT) of gravity. It had been pointed before in the literature, that the Poincare symmetries seemed to be recoverable canonically only on-shell. This would however mean existence of two independent sets of symmetries, each by itself having number of gauge parameters equal to the Poincare group, implying an apparent doubling of symmetries. To resolve this, we first s...
Cosmic decoherence: massive fields
Energy Technology Data Exchange (ETDEWEB)
Liu, Junyu [Department of Physics, California Institute of Technology,Pasadena, California 91125 (United States); School of the Gifted Young, University of Science and Technology of China,Hefei, Anhui 230026 (China); Sou, Chon-Man; Wang, Yi [Department of Physics, The Hong Kong University of Science and Technology,Clear Water Bay, Kowloon, Hong Kong (China)
2016-10-14
We study the decoherence of massive fields during inflation based on the Zurek’s density matrix approach. With the cubic interaction between inflaton and massive fields, the reduced density matrix for the massive fields can be calculated in the Schrödinger picture which is related to the variance of the non-Gaussian exponent in the wave functional. The decoherence rate is computed in the one-loop form from functional integration. For heavy fields with m≳O(H), quantum fluctuations will easily stay in the quantum state and decoherence is unlikely. While for light fields with mass smaller than O(H), quantum fluctuations are easily decohered within 5∼10 e-folds after Hubble crossing. Thus heavy fields can play a key role in studying problems involving inflationary quantum information.
Limitation of computational resource as physical principle
Ozhigov, Y I
2003-01-01
Limitation of computational resources is considered as a universal principle that for simulation is as fundamental as physical laws are. It claims that all experimentally verifiable implications of physical laws can be simulated by the effective classical algorithms. It is demonstrated through a completely deterministic approach proposed for the simulation of biopolymers assembly. A state of molecule during its assembly is described in terms of the reduced density matrix permitting only limited tunneling. An assembly is treated as a sequence of elementary scatterings of simple molecules from the environment on the point of assembly. A decoherence is treated as a forced measurement of quantum state resulted from the shortage of computational resource. All results of measurements are determined by a choice from the limited number of special options of the nonphysical nature which stay unchanged till the completion of assembly; we do not use the random numbers generators. Observations of equal states during the ...
Deriving covariant holographic entanglement
Dong, Xi; Lewkowycz, Aitor; Rangamani, Mukund
2016-11-01
We provide a gravitational argument in favour of the covariant holographic entanglement entropy proposal. In general time-dependent states, the proposal asserts that the entanglement entropy of a region in the boundary field theory is given by a quarter of the area of a bulk extremal surface in Planck units. The main element of our discussion is an implementation of an appropriate Schwinger-Keldysh contour to obtain the reduced density matrix (and its powers) of a given region, as is relevant for the replica construction. We map this contour into the bulk gravitational theory, and argue that the saddle point solutions of these replica geometries lead to a consistent prescription for computing the field theory Rényi entropies. In the limiting case where the replica index is taken to unity, a local analysis suffices to show that these saddles lead to the extremal surfaces of interest. We also comment on various properties of holographic entanglement that follow from this construction.
Deriving covariant holographic entanglement
Dong, Xi; Rangamani, Mukund
2016-01-01
We provide a gravitational argument in favour of the covariant holographic entanglement entropy proposal. In general time-dependent states, the proposal asserts that the entanglement entropy of a region in the boundary field theory is given by a quarter of the area of a bulk extremal surface in Planck units. The main element of our discussion is an implementation of an appropriate Schwinger-Keldysh contour to obtain the reduced density matrix (and its powers) of a given region, as is relevant for the replica construction. We map this contour into the bulk gravitational theory, and argue that the saddle point solutions of these replica geometries lead to a consistent prescription for computing the field theory Renyi entropies. In the limiting case where the replica index is taken to unity, a local analysis suffices to show that these saddles lead to the extremal surfaces of interest. We also comment on various properties of holographic entanglement that follow from this construction.
Electronic coherence dynamics in trans-polyacetylene oligomers
Franco, Ignacio
2011-01-01
Electronic decoherence processes in trans-polyacetylene oligomers are considered by explicitly computing the time dependent molecular polarization from the coupled dynamics of electronic and vibrational degrees of freedom in a mean-field mixed quantum-classical approximation. The oligomers are described by the SSH Hamiltonian and the effect of decoherence is incorporated by propagating an ensemble of quantum-classical trajectories with initial conditions obtained by sampling the Wigner distribution of the nuclear degrees of freedom. The decoherence for superpositions between the ground and excited and between pairs of excited states is considered for chains of different length, and the dynamics is discussed in terms of the nuclear overlap function that appears in the off-diagonal elements of the electronic reduced density matrix. For long oligomers the loss of coherence occurs in tens of femtoseconds. This timescale is determined by the initial decay of the nuclear overlap and by the decay of population into ...
Entanglement of two optically driven quantum dots mediated by phonons in nanomechanical resonator
He, Yong; Jiang, Meiping
2017-01-01
The exciton-phonon coupling between an optically driven quantum dot (QD) and a mechanical resonator can be described by Jaynes-Cummings model under a certain condition, revealing phonon absorption and emission. When two optically driven QDs share a common phonon mode, it shows the phonon-mediated coupling between the QDs. Based on the effective master equation for the reduced density matrix of the two QDs, the temporal evolution of each state and the concurrence (quantum entanglement) between them are studied. The results suggest that the stationary concurrence depends strongly on the resonator temperature. The non-negligible entanglement in the hybrid system is advantaged to develop solid-state quantum information processing.
Chou, C H; Yu, T; Chou, Chung-Hsien; Yu, Ting
2007-01-01
In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment made up of many harmonic oscillators at arbitrary temperature for a general spectral density function. We first show a simple derivation based on the observation that the two harmonic oscillator model can be effectively mapped into that of a single harmonic oscillator in a general environment plus a free harmonic oscillator. Since the exact one harmonic oscillator master equation is known [Hu, Paz and Zhang, Phys. Rev. D \\textbf{45}, 2843 (1992)], the exact master equation with all its coefficients for this two harmonic oscillator model can be easily deduced from the known results of the single harmonic oscillator case. In the second part we give an influence functional treatment of this model and provide explicit expressions for the evolution operator of the reduced density matrix which are useful for the study of decoherence and disentanglement issues. We ...
Stochastic description for open quantum systems
Calzetta, E A; Verdaguer, E; Calzetta, Esteban; Roura, Albert; Verdaguer, Enric
2000-01-01
A linear open quantum system consisting of a harmonic oscillator coupled linearly to an infinite set of independent harmonic oscillators is considered; these oscillators have a general spectral density function and are initially in thermal equilibrium. Using the influence functional formalism a formal Langevin equation can be introduced to describe the system's fully quantum properties even beyond the semiclassical regime. It is shown that the reduced Wigner function for the system is exactly the formal distribution function resulting from averaging both over the initial conditions and the stochastic source of the formal Langevin equation. The master equation for the reduced density matrix is then obtained in the same way a Fokker-Planck equation can always be derived from a Langevin equation characterizing a stochastic process. We also show that the quantum correlation functions for the system can be deduced within the stochastic description provided by the Langevin equation. It is emphasized that when the s...
Entanglement hamiltonians in two-dimensional conformal field theory
Cardy, John
2016-01-01
We enumerate the cases in 2d conformal field theory where the logarithm of the reduced density matrix (the entanglement or modular hamiltonian) may be written as an integral over the energy-momentum tensor times a local weight. These include known examples and new ones corresponding to the time-dependent scenarios of a global and local quench. In these latter cases the entanglement hamiltonian depends on the momentum density as well as the energy density. In all cases the entanglement spectrum is that of the appropriate boundary CFT. We emphasize the role of boundary conditions at the entangling surface and the appearance of boundary entropies as universal O(1) terms in the entanglement entropy.
Entanglement entropy in particle decay
Lello, Louis; Holman, Richard
2013-01-01
The decay of a parent particle into two or more daughter particles results in an entangled quantum state, as a consequence of conservation laws in the decay process. We use the Wigner-Weisskopf formalism to construct an approximation to this state that evolves in time in a {\\em manifestly unitary} way. We then construct the entanglement entropy for one of the daughter particles by use of the reduced density matrix obtained by tracing out the unobserved states and follow its time evolution. We find that it grows over a time scale determined by the lifetime of the parent particle to a maximum, which when the width of the parent particle is narrow, describes the phase space distribution of maximally entangled Bell-like states.
Irreducible many-body correlations in topologically ordered systems
Liu, Yang; Zeng, Bei; Zhou, D. L.
2016-02-01
Topologically ordered systems exhibit large-scale correlation in their ground states, which may be characterized by quantities such as topological entanglement entropy. We propose that the concept of irreducible many-body correlation (IMC), the correlation that cannot be implied by all local correlations, may also be used as a signature of topological order. In a topologically ordered system, we demonstrate that for a part of the system with holes, the reduced density matrix exhibits IMCs which become reducible when the holes are removed. The appearance of these IMCs then represents a key feature of topological phase. We analyze the many-body correlation structures in the ground state of the toric code model in external magnetic fields, and show that the topological phase transition is signaled by the IMCs.
Two-band model as a quantum data bus for quantum state transfer
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
We study the dynamics of an electron spin state transfer along a half-filled two-band model(TBM).It is shown that this solvable and realistic medium has an energy gap between the ground and first-excited states in the half-filled case.By connecting two qubits to two sites of the TBM,the system can accomplish a high-fidelity and long-distance quantum state transfer(QST).Moreover,numerical simulations have been performed for a finite system.The results show that the numerical and analytical results of the effective coupling strength agree well with each other.Furthermore,the investigation shows that the reduced density matrix also has high fidelity beyond the range of perturbation.
Transfer and reconstruction of the density matrix in off-axis electron holography.
Röder, Falk; Lubk, Axel
2014-11-01
The reduced density matrix completely describes the quantum state of an electron scattered by an object in transmission electron microscopy. However, the detection process restricts access to the diagonal elements only. The off-diagonal elements, determining the coherence of the scattered electron, may be obtained from electron holography. In order to extract the influence of the object from the off-diagonals, however, a rigorous consideration of the electron microscope influences like aberrations of the objective lens and the Möllenstedt biprism in the presence of partial coherence is required. Here, we derive a holographic transfer theory based on the generalization of the transmission cross-coefficient including all known holographic phenomena. We furthermore apply a particular simplification of the theory to the experimental analysis of aloof beam electrons scattered by plane silicon surfaces.
Selective subsurface absorption of hydrogen in palladium using laser distillation.
Tremblay, Jean Christophe; Saalfrank, Peter
2009-08-28
A theoretical model for the selective subsurface absorption of atomic hydrogen in a Pd(111) surface by infrared (IR) laser pulses is presented. The dynamics of the adsorbate is studied within the reduced density matrix approach. Energy and phase relaxation of the hydrogen atom are treated using the semigroup formalism. The vibrational excitation leading to subsurface absorption is performed using rationally designed pulses as well as IR laser pulses optimized on-the-fly. It is shown that dissipation can be used as a tool to transfer population to an otherwise inaccessible state via a mechanism known as "laser distillation." We demonstrate that when the reaction path is generalized from a reduced one-dimensional to full three-dimensional treatment of the system, the laser control strategy can prove very different.
Black hole entropy divergence and the uncertainty principle
Brustein, Ram
2011-01-01
Black hole entropy has been shown by 't Hooft to diverge at the horizon. The region near the horizon is in a thermal state, so entropy is linear to energy which consequently also diverges. We find a similar divergence for the energy of the reduced density matrix of relativistic and non-relativistic field theories, extending previous results in quantum mechanics. This divergence is due to an infinitely sharp boundary, and it stems from the position/momentum uncertainty relation in the same way that the momentum fluctuations of a precisely localized quantum particle diverge. We show that when the boundary is smoothed the divergence is tamed. We argue that the divergence of black hole entropy can also be interpreted as a consequence of position/momentum uncertainty, and that 't Hooft's brick wall tames the divergence in the same way, by smoothing the boundary.
Inspecting non-perturbative contributions to the Entanglement Entropy via wavefunctions
Bhattacharyya, Arpan; Lau, P H C; Liu, Si-Nong
2016-01-01
In this paper, we would like to systematically explore the implications of non-perturbative effects on entanglement in a many body system. Instead of pursuing the usual path-integral method in a singular space, we attempt to study the wavefunctions in detail. We begin with a toy model of multiple particles whose interaction potential admits multiple minima. We study the entanglement of the true ground state after taking the tunnelling effects into account and find some simple patterns. Notably, in the case of multiple particle interactions, entanglement entropy generically decreases with increasing number of minima. The knowledge of the subsystem actually increases as the number of minima increases. The reduced density matrix can also be seen to have close connections with graph spectra. In a more careful study of the two-well tunnelling system, we also extract the exponentially suppressed tail contribution, the analogues of instantons. To understand the effects of multiple minima in a field theory, it inspir...
Non-Canonical Statistics of a Spin-Boson Model: Theory and Exact Monte-Carlo Simulations
Lee, Chee Kong; Gong, Jiangbin
2012-01-01
Equilibrium canonical distribution in statistical mechanics assumes weak system-bath coupling (SBC). In real physical situations this assumption can be invalid and equilibrium quantum statistics of the system may be non-canonical. By exploiting both polaron transformation and perturbation theory in a spin-boson model, an analytical treatment is advocated to study non-canonical statistics of a two-level system at arbitrary temperature and for arbitrary SBC strength, yielding theoretical results in agreement with exact Monte-Carlo simulations. In particular, the eigen-representation of system's reduced density matrix is used to quantify non-canonical statistics as well as the quantumness of the open system. For example, it is found that irrespective of SBC strength, non-canonical statistics enhances as temperature decreases but vanishes at high temperature.
Bultinck, Patrick; Clarisse, Dorien; Ayers, Paul W; Carbo-Dorca, Ramon
2011-04-07
The Fukui matrix is introduced as the derivative of the one-electron reduced density matrix with respect to a change in the number of electrons under constant external potential. The Fukui matrix extends the Fukui function concept: the diagonal of the Fukui matrix is the Fukui function. Diagonalizing the Fukui matrix gives a set of eigenvectors, the Fukui orbitals, and accompanying eigenvalues. At the level of theory used, there is always one dominant eigenvector, with an eigenvalue equal to 1. The remaining eigenvalues are either zero or come in pairs with eigenvalues of the same magnitude but opposite sign. Analysis of the frontier molecular orbital coefficient in the eigenvector with eigenvalue 1 gives information on the quality of the frontier molecular orbital picture. The occurrence of negative Fukui functions can be easily interpreted in terms of the nodal character of the dominant eigenvector versus the characteristics of the remaining eigenvectors and eigenvalues.
Renyi Correlations and Phase Transitions in the Transverse-Field Ising model
Singh, Rajiv; Devakul, Trithep
2015-03-01
We calculate T = 0 spin-spin correlation functions with respect to a probability distribution given by an integer power (n) of the reduced density matrix ρcirc;A, when a transverse-field Ising model (TFIM) system is bipartitioned by a planar interface. Using series expansion methods these calculations are done in the thermodynamic limit for arbitrary positive integer n, with n = 1 giving us the bulk correlations. We study the TFIM system on isotropic and anisotropic simple-cubic lattices. We examine the evidence for whether the critical point of the transition deviates from the bulk critical point as a function of n and whether the critical behavior lies in the 2 D or 4 D Ising universality classes as would be expected from a surface transition at finite temperature and a T = 0 bulk transition, respectively. Work supported in part by NSF Grant Number DMR-1306048.
Wigner rotations, Bell states, and Lorentz invariance of entanglement and von Neumann entropy
Soo, C; Soo, Chopin; Lin, Cyrus C. Y.
2003-01-01
We compute, for massive particles, the explicit Wigner rotations of one-particle states for arbitrary Lorentz transformations; and the explicit Hermitian generators of the infinite-dimensional unitary representation. For a pair of spin 1/2 particles, Einstein-Podolsky-Rosen-Bell entangled states and their behaviour under the Lorentz group are analysed in the context of quantum field theory. Group theoretical considerations suggest a convenient definition of the Bell states which is slightly different from the conventional assignment. The behaviour of Bell states under arbitrary Lorentz transformations can then be described succinctly. Reduced density matrices applicable to identical particles are defined through Yang's prescription. The von Neumann entropy of each of the reduced density matrix is Lorentz invariant; and its relevance as a measure of entanglement is discussed, and illustrated with an explicit example. A regularization of the entropy in terms of generalized zeta functions is also suggested.
Quantum entanglement between electronic and vibrational degrees of freedom in molecules
McKemmish, Laura K; Hush, Noel S; Reimers, Jeffrey R
2011-01-01
We consider the quantum entanglement of the electronic and vibrational degrees of freedom in molecules with a tendency towards double welled potentials using model coupled harmonic diabatic potential-energy surfaces. The von Neumann entropy of the reduced density matrix is used to quantify the electron-vibration entanglement for the lowest two vibronic wavefunctions in such a bipartite system. Significant entanglement is found only in the region in which the ground vibronic state contains a density profile that is bimodal (i.e., contains two separate local minima). However, in this region two distinct types of entanglement are found: (1) entanglement that arises purely from the degeneracy of energy levels in the two potential wells and which is destroyed by slight asymmetry, and (2) entanglement that involves strongly interacting states in each well that is relatively insensitive to asymmetry. These two distinct regions are termed fragile degeneracy-induced entanglement and persistent entanglement, respective...
DMRG-CASPT2 study of the longitudinal static second hyperpolarizability of all-trans polyenes
Wouters, Sebastian; Van Neck, Dimitri
2016-01-01
We have implemented internally contracted complete active space second order perturbation theory (CASPT2) with the density matrix renormalization group (DMRG) as active space solver [Y. Kurashige and T. Yanai, J. Chem. Phys. 135, 094104 (2011)]. Internally contracted CASPT2 requires to contract the generalized Fock matrix with the 4-particle reduced density matrix (4-RDM) of the reference wavefunction. The required 4-RDM elements can be obtained from 3-particle reduced density matrices (3-RDM) of different wavefunctions, formed by symmetry-conserving single-particle excitations op top of the reference wavefunction. In our spin-adapted DMRG code chemps2 [https://github.com/sebwouters/chemps2], we decompose these excited wavefunctions as spin-adapted matrix product states, and calculate their 3-RDM in order to obtain the required contraction of the generalized Fock matrix with the 4-RDM of the reference wavefunction. In this work, we study the longitudinal static second hyperpolarizability of all-trans polyenes...
Classical and quantum dissipation in non homogeneous environments
Illuminati, F; Sodano, P
1994-01-01
We generalize the oscillator model of a particle interacting with a thermal reservoir by introducing arbitrary nonlinear couplings in the particle coordinates.The equilibrium positions of the heat bath oscillators are promoted to space-time functions, which are shown to represent a modulation of the internal noise by the external forces. The model thus provides a description of classical and quantum dissipation in non homogeneous environments. In the classical case we derive a generalized Langevin equation with nonlinear multiplicative noise and a position-dependent fluctuation- dissipation theorem associated to non homogeneous dissipative forces. When time-modulation of the noise is present, a new force term is predicted besides the dissipative and random ones. The model is quantized to obtain the non homogenous influence functional and master equation for the reduced density matrix of the Brownian particle. The quantum evolution equations reproduce the correct Langevin dynamics in the semiclassical limit. T...
Linear Scaling Real Time TDDFT in the CONQUEST Code
O'Rourke, Conn
2014-01-01
The real time formulation of Time Dependent Density Functional Theory (RT-TDDFT) is implemented in the linear scaling density functional theory code CONQEST. Proceeding through the propagation of the density matrix, as opposed to the Kohn-Sham orbitals, it is possible to reduced the computational workload. Imposing a cut-off on the density matrix the effort can be made to scale linearly with the size of the system under study. Propagation of the reduced density matrix in this manner provides direct access to the optical response of very large systems, which would be otherwise impractical to obtain using the standard formulations of TDDFT. We discuss our implementation and present several benchmark tests illustrating the validity of the method, and the factors affecting its accuracy. Finally we illustrate the effect of density matrix truncation on the optical response, and illustrate that computational load scales linearly with the system size.
Decoherence of mesoscopic states of cavity fields
Fonseca-Romero, K M; De Faria, J G P; Salgueiro, A N; De Toledo di Piza, A F R
1998-01-01
We show that two-atom correlation measurements of the type involved in a recent experimental study of the evolution of a mesoscopic superposition state prepared in a definite mode of a high-Q cavity can be used to determine the eigenvalues of the reduced density matrix of the field, provided the assumed dynamical conditions are actually fulfilled to experimental accuracy. These conditions involve i) a purely dispersive coupling of the field to the Rydberg atoms used to manipulate and to monitor the cavity field, and ii) the effective absence of correlations in the ground state of the system consisting of the cavity coupled to the ``reservoir'' which accounts for the decoherence and damping processes. A microscopic calculation at zero temperature is performed and compared to master equation results.
Ma, Chen-Te
2015-01-01
Entanglement is a physical phenomenon that each state cannot be described individually. Entanglement entropy gives quantitative understanding to the entanglement. We use decomposition of the Hilbert space to discuss properties of the entanglement. Therefore, partial trace operator becomes important to define the reduced density matrix from different centers, which commutes with all elements in the Hilbert space, corresponding to different entanglement choices or different observations on entangling surface. Entanglement entropy is expected to satisfy the strong subadditivity. We discuss decomposition of the Hilbert space for the strong subadditivity and other related inequalities. The entanglement entropy with centers can be computed from the Hamitonian formulations systematically, provided that we know wavefunctional. In the Hamitonian formulation, it is easier to obtain symmetry structure. We consider massless $p$-form theory as an example. The massless $p$-form theory in ($2p+2)$-dimensions has global symm...
Hewson, Alex C; Bauer, Johannes
2010-03-24
We show that information on the probability density of local fluctuations can be obtained from a numerical renormalization group calculation of a reduced density matrix. We apply this approach to the Anderson-Holstein impurity model to calculate the ground state probability density ρ(x) for the displacement x of the local oscillator. From this density we can deduce an effective local potential for the oscillator and compare its form with that obtained from a semiclassical approximation as a function of the coupling strength. The method is extended to the infinite dimensional Holstein-Hubbard model using dynamical mean field theory. We use this approach to compare the probability densities for the displacement of the local oscillator in the normal, antiferromagnetic and charge ordered phases.
Buyens, Boye; Montangero, Simone; Haegeman, Jutho; Verstraete, Frank; Van Acoleyen, Karel
2017-05-01
It has been established that matrix product states can be used to compute the ground state and single-particle excitations and their properties of lattice gauge theories at the continuum limit. However, by construction, in this formalism the Hilbert space of the gauge fields is truncated to a finite number of irreducible representations of the gauge group. We investigate quantitatively the influence of the truncation of the infinite number of representations in the Schwinger model, one-flavor QED2 , with a uniform electric background field. We compute the two-site reduced density matrix of the ground state and the weight of each of the representations. We find that this weight decays exponentially with the quadratic Casimir invariant of the representation which justifies the approach of truncating the Hilbert space of the gauge fields. Finally, we compute the single-particle spectrum of the model as a function of the electric background field.
Extending the applicability of Redfield theories into highly non-Markovian regimes
Montoya-Castillo, Andrés; Reichman, David R
2015-01-01
We present a new, computationally inexpensive method for the calculation of reduced density matrix dynamics for systems with a potentially large number of subsystem degrees of freedom coupled to a generic bath. The approach consists of propagation of weak-coupling Redfield-like equations for the high frequency bath degrees of freedom only, while the low frequency bath modes are dynamically arrested but statistically sampled. We examine the improvements afforded by this approximation by comparing with exact results for the spin-boson model over a wide range of parameter space. The results from the method are found to dramatically improve Redfield dynamics in highly non--Markovian regimes, at a similar computational cost. Relaxation of the mode-freezing approximation via classical (Ehrenfest) evolution of the low frequency modes results in a dynamical hybrid method. We find that this Redfield-based dynamical hybrid approach, which is computationally more expensive than bare Redfield dynamics, yields only a marg...
Entanglement entropy for the n-sphere
Casini, H
2010-01-01
We calculate the entanglement entropy for a sphere and a massless scalar field in any dimensions. The reduced density matrix is expressed in terms of the infinitesimal generator of conformal transformations keeping the sphere fixed. The problem is mapped to the one of a thermal gas in a hyperbolic space and solved by the heat kernel approach. The coefficient of the logarithmic term in the entropy for 2 and 4 spacetime dimensions are in accordance with previous numerical and analytical results. In particular, the four dimensional result, together with the one reported by Solodukhin, gives support to the Ryu-Takayanagi holographic anzats. We also find there is no logarithmic contribution to the entropy for odd space time dimensions.
Entanglement dynamics via semiclassical propagators in systems of two spins
Ribeiro, A D
2012-01-01
We analyze the dynamical generation of entanglement in systems of two interacting spins initially prepared in a product of spin coherent states. For arbitrary time-independent Hamiltonians, we derive a semiclassical expression for the purity of the reduced density matrix as function of time. The final formula, subsidiary to the linear entropy, shows that the short-time dynamics of entanglement depends exclusively on the stability of trajectories governed by the underlying classical Hamiltonian. Also, this semiclassical measure is shown to reproduce the general properties of its quantum counterpart and give the expected result in the large spin limit. The accuracy of the semiclassical formula is further illustrated in a problem of phase exchange for two particles of spin $j$.
He, Lewei; Wang, Wen-Ge
2014-02-01
We study the problem of the basis of an open quantum system, under a quantum chaotic environment, which is preferred in view of its stationary reduced density matrix (RDM), that is, the basis in which the stationary RDM is diagonal. It is shown that, under an initial condition composed of sufficiently many energy eigenstates of the total system, such a basis is given by the eigenbasis of a renormalized self-Hamiltonian of the system, in the limit of large Hilbert space of the environment. Here, the renormalized self-Hamiltonian is given by the unperturbed self-Hamiltonian plus a certain average of the interaction Hamiltonian over the environmental degrees of freedom. Numerical simulations performed in two models, both with the kicked rotor as the environment, give results consistent with the above analytical predictions.
Nonequilibrium density-matrix description of steady-state quantum transport.
Dhar, Abhishek; Saito, Keiji; Hänggi, Peter
2012-01-01
With this work we investigate the stationary nonequilibrium density matrix of current carrying nonequilibrium steady states of in-between quantum systems that are connected to reservoirs. We describe the analytical procedure to obtain the explicit result for the reduced density matrix of quantum transport when the system, the connecting reservoirs, and the system-reservoir interactions are described by quadratic Hamiltonians. Our procedure is detailed for both electronic transport described by the tight-binding Hamiltonian and for phonon transport described by harmonic Hamiltonians. For the special case of weak system-reservoir couplings, a more detailed description of the steady-state density matrix is obtained. Several paradigm transport setups for interelectrode electron transport and low-dimensional phonon heat flux are elucidated.
Extended hierarchy equation of motion for the spin-boson model.
Tang, Zhoufei; Ouyang, Xiaolong; Gong, Zhihao; Wang, Haobin; Wu, Jianlan
2015-12-14
An extended hierarchy equation of motion (HEOM) is proposed and applied to study the dynamics of the spin-boson model. In this approach, a complete set of orthonormal functions are used to expand an arbitrary bath correlation function. As a result, a complete dynamic basis set is constructed by including the system reduced density matrix and auxiliary fields composed of these expansion functions, where the extended HEOM is derived for the time derivative of each element. The reliability of the extended HEOM is demonstrated by comparison with the stochastic Hamiltonian approach under room-temperature classical ohmic and sub-ohmic noises and the multilayer multiconfiguration time-dependent Hartree theory under zero-temperature quantum ohmic noise. Upon increasing the order in the hierarchical expansion, the result obtained from the extended HOEM systematically converges to the numerically exact answer.
Decay Process of Quantum Open System at Finite Temperatures
Institute of Scientific and Technical Information of China (English)
肖骁; 高一波
2012-01-01
Starting from the formal solution to the Heisenberg equation, we revisit an universal model for a quantum open system with a harmonic oscillator linearly coupled to a boson bath. The analysis of the decay process for a Fock state and a coherent state demonstrate that this method is very useful in dealing with the problems in decay process of the open system. For finite temperatures, the calculations of the reduced density matrix and the mean excitation number for the open system show that an initiaJ coherent state will evolve into a temperature-dependant coherent state after tracing over the bath variables. Also in short-time limit, a temperature-dependant effective Hamiltonian for the open system characterizes the decay process of the open system.
Multilayer-MCTDH approach to the energy transfer dynamics in the LH2 antenna complex
Shibl, Mohamed F.; Schulze, Jan; Al-Marri, Mohammed J.; Kühn, Oliver
2017-09-01
The multilayer multiconfiguration time-dependent Hartree method is used to study the coupled exciton-vibrational dynamics in a high-dimensional nonameric model of the LH2 antenna complex of purple bacteria. The exciton-vibrational coupling is parametrized within the Huang-Rhys model according to phonon and intramolecular vibrational modes derived from an experimental bacteriochlorophyll spectral density. In contrast to reduced density matrix approaches, the Schrödinger equation is solved explicitly, giving access to the full wave function. This facilitates an unbiased analysis in terms of the coupled dynamics of excitonic and vibrational degrees of freedom. For the present system, we identify spectator modes for the B800 to B800 transfer and we find a non-additive effect of phonon and intramolecular vibrational modes on the B800 to B850 exciton transfer.
Decay dynamics in a strongly driven atom-molecule coupled system
Rakshit, Arpita; Deb, Bimalendu
2013-01-01
Within the framework of master equation, we study decay dynamics of an atom-molecule system strongly coupled by two photoassociation lasers. Summing over the infinite number of electromagnetic vacuum modes that are coupled to the laser-dressed atom-molecule system, we obtain an integro-differential master equation for the the system's reduced density matrix. The equation is numerically solved to describe system dynamics in the presence of decay. In particular, we discuss correlated spontaneous emission from a pair of electronically excited diatomic ro-vibrational states due to their laser induced coupling to the ground continuum of atomic scattering states. This allows us to calculate time-dependence of emitted radiation intensity. It exhibits quantum beats due to coherent dynamics. The phase difference between the two driving fields is found to significantly affect the decay dynamics and the beats. Our results demonstrate the possibility to control decay from the molecular excited states and the decoherence ...
Spectral properties of reduced fermionic density operators and parity superselection rule
Amosov, Grigori G.; Filippov, Sergey N.
2017-01-01
We consider pure fermionic states with a varying number of quasiparticles and analyze two types of reduced density operators: one is obtained via tracing out modes, the other is obtained via tracing out particles. We demonstrate that spectra of mode-reduced states are not identical in general and fully characterize pure states with equispectral mode-reduced states. Such states are related via local unitary operations with states satisfying the parity superselection rule. Thus, valid purifications for fermionic density operators are found. To get particle-reduced operators for a general system, we introduce the operation \\varPhi (\\varrho ) = sum _i a_i \\varrho a_i^{dag }. We conjecture that spectra of \\varPhi ^p(\\varrho ) and conventional p-particle reduced density matrix \\varrho _p coincide. Non-trivial generalized Pauli constraints are derived for states satisfying the parity superselection rule.
Theory of quantum Loschmidt echoes
Prosen, T; Znidaric, M; Prosen, Tomaz; Seligman, Thomas H.; Znidaric, Marko
2003-01-01
In this paper we review our recent work on the theoretical approach to quantum Loschmidt echoes, i.e. various properties of the so called echo dynamics -- the composition of forward and backward time evolutions generated by two slightly different Hamiltonians, such as the state autocorrelation function (fidelity) and the purity of a reduced density matrix traced over a subsystem (purity fidelity). Our main theoretical result is a linear response formalism, expressing the fidelity and purity fidelity in terms of integrated time autocorrelation function of the generator of the perturbation. Surprisingly, this relation predicts that the decay of fidelity is the slower the faster the decay of correlations. In particular for a static (time-independent) perturbation, and for non-ergodic and non-mixing dynamics where asymptotic decay of correlations is absent, a qualitatively different and faster decay of fidelity is predicted on a time scale 1/delta as opposed to mixing dynamics where the fidelity is found to decay...
Universal Features of Left-Right Entanglement Entropy.
Das, Diptarka; Datta, Shouvik
2015-09-25
We show the presence of universal features in the entanglement entropy of regularized boundary states for (1+1)D conformal field theories on a circle when the reduced density matrix is obtained by tracing over right- or left-moving modes. We derive a general formula for the left-right entanglement entropy in terms of the central charge and the modular S matrix of the theory. When the state is chosen to be an Ishibashi state, this measure of entanglement is shown to precisely reproduce the spatial entanglement entropy of a (2+1)D topological quantum field theory. We explicitly evaluate the left-right entanglement entropies for the Ising model, the tricritical Ising model and the su[over ^](2)_{k} Wess-Zumino-Witten model as examples.
Full counting statistics of information content and particle number
Utsumi, Yasuhiro
2017-08-01
We consider a bipartite quantum conductor and discuss the joint probability distribution of a particle number in a subsystem and the self-information associated with the reduced density matrix of the subsystem. By extending the multicontour Keldysh Green-function technique, we calculate the Rényi entropy of a positive integer order M subjected to the particle number constraint, from which we derive the joint probability distribution. For energy-independent transmission, we derive the time dependence of the accessible entanglement entropy, or the conditional entropy. We analyze the joint probability distribution for energy-dependent transmission probability at the steady state under the coherent resonant tunneling and the incoherent sequential tunneling conditions. We also discuss the probability distribution of the efficiency, which measures the information content transferred by a single electron.
Cosmic Decoherence: Massive Fields
Liu, Junyu; Wang, Yi
2016-01-01
We study the decoherence of massive fields during inflation based on the Zurek's density matrix approach. With the cubic interaction between inflaton and massive fields, the reduced density matrix for the massive fields can be calculated in the Schr\\"odinger picture which is related to the variance of the non-Gaussian exponent in the wave functional. The decoherence rate is computed in the one-loop form from functional integration. For heavy fields with $m\\gtrsim \\mathcal{O}(H)$, quantum fluctuations will easily stay in the quantum state and decoherence is unlikely. While for light fields with mass smaller than $\\mathcal{O}(H)$, quantum fluctuations are easily decohered within $5\\sim10$ e-folds after Hubble crossing. Thus heavy fields can play a key role in studying problems involving inflationary quantum information.
Bath-induced correlations in an infinite-dimensional Hilbert space
Nizama, Marco; Cáceres, Manuel O.
2017-09-01
Quantum correlations between two free spinless dissipative distinguishable particles (interacting with a thermal bath) are studied analytically using the quantum master equation and tools of quantum information. Bath-induced coherence and correlations in an infinite-dimensional Hilbert space are shown. We show that for temperature T> 0 the time-evolution of the reduced density matrix cannot be written as the direct product of two independent particles. We have found a time-scale that characterizes the time when the bath-induced coherence is maximum before being wiped out by dissipation (purity, relative entropy, spatial dispersion, and mirror correlations are studied). The Wigner function associated to the Wannier lattice (where the dissipative quantum walks move) is studied as an indirect measure of the induced correlations among particles. We have supported the quantum character of the correlations by analyzing the geometric quantum discord.
Peltier effect in strongly driven quantum wires
Mierzejewski, M.; Crivelli, D.; Prelovšek, P.
2014-08-01
We study a microscopic model of a thermocouple device with two connected correlated quantum wires driven by a constant electric field. In such a closed system we follow the time and position dependence of the entropy density using the concept of the reduced density matrix. At weak driving, the initial changes of the entropy at the junctions can be described by the linear Peltier response. At longer times the quasiequilibrium situation is reached with well defined local temperatures which increase due to an overall Joule heating. On the other hand, a strong electric field induces a nontrivial nonlinear thermoelectric response, e.g., the Bloch oscillations of the energy current. Moreover, we show for the doped Mott insulators that strong driving can reverse the Peltier effect.
Dynamics and thermodynamics of linear quantum open systems.
Martinez, Esteban A; Paz, Juan Pablo
2013-03-29
We analyze the evolution of the quantum state of networks of quantum oscillators coupled with arbitrary external environments. We show that the reduced density matrix of the network always obeys a local master equation with a simple analytical solution. We use this to study the emergence of thermodynamical laws in the long time regime demonstrating two main results: First, we show that it is impossible to build a quantum absorption refrigerator using linear networks (thus, nonlinearity is an essential resource for such refrigerators recently studied by Levy and Kosloff [Phys. Rev. Lett. 108, 070604 (2012)] and Levy et al. [Phys. Rev. B 85, 061126 (2012)]). Then, we show that the third law imposes constraints on the low frequency behavior of the environmental spectral densities.
Quantum entanglement in topological phases on a torus
Luo, Zhu-Xi; Hu, Yu-Ting; Wu, Yong-Shi
2016-08-01
In this paper, we study the effect of nontrivial spatial topology on quantum entanglement by examining the degenerate ground states of a topologically ordered system on a torus. Using the string-net (fixed-point) wave function, we propose a general formula of the reduced density matrix when the system is partitioned into two cylinders. The cylindrical topology of the subsystems makes a significant difference in regard to entanglement: a global quantum number for the many-body states comes into play, together with a decomposition matrix M which describes how topological charges of the ground states decompose into boundary degrees of freedom. We obtain a general formula for entanglement entropy and generalize the concept of minimally entangled states to minimally entangled sectors. Concrete examples are demonstrated with data from both finite groups and modular tensor categories (i.e., Fibonacci, Ising, etc.), supported by numerical verification.
Lu, Min; Rao, Wen-Jia; Narayanan, Rajesh; Wan, Xin; Zhang, Guang-Ming
2016-12-01
Quantum entanglement under an extensive bipartition can reveal the critical boundary theory of a topological phase in a parameter space. In this study we demonstrate that the infinite-randomness fixed point for spin-1/2 degrees of freedom can emerge from an extensive random bipartition of the spin-1 Affleck-Kennedy-Lieb-Tasaki chain. The nested entanglement entropy of the ground state of the reduced density matrix exhibits a logarithmic scaling with an effective central charge c ˜=0.72 ±0.02 ≈ln2 . We further discuss, in the language of bulk quantum entanglement, how to understand all phase boundaries and the surrounding Griffiths phases for the antiferromagnetic Heisenberg spin-1 chain with quenched disorder and dimerization.
Spectral properties of dissipative chaotic quantum maps.
Braun, Daniel
1999-09-01
I examine spectral properties of a dissipative chaotic quantum map with the help of a recently discovered semiclassical trace formula. I show that in the presence of a small amount of dissipation the traces of any finite power of the propagator of the reduced density matrix, and traces of its classical counterpart, the Frobenius-Perron operator, are identical in the limit of variant Planck's over 2pi -->0. Numerically I find that even for finite variant Planck's over 2pi the agreement can be very good. This holds in particular if the classical phase space contains a strange attractor, as long as one stays clear of bifurcations. Traces of the quantum propagator for iterations of the map agree well with the corresponding traces of the Frobenius-Perron operator if the classical dynamics is dominated by a strong point attractor. (c) 1999 American Institute of Physics.
Left-Right Entanglement Entropy of Boundary States
Zayas, Leopoldo A Pando
2014-01-01
We study entanglement entropy of boundary states in a free bosonic conformal field theory. A boundary state can be thought of as composed of a particular combination of left and right-moving modes of the two-dimensional conformal field theory. We investigate the reduced density matrix obtained by tracing over the right-moving modes in various boundary states. We consider Dirichlet and Neumann boundary states of a free noncompact as well as a compact boson. The results for the entanglement entropy indicate that the reduced system can be viewed as a thermal gas of photons. Our findings are in agreement and generalize results in quantum mechanics and quantum field theory where coherent states can also be considered. In the compact case we verify that the entanglement entropy expressions are consistent with T-duality.
Leathers, Andrew S.; Micha, David A.; Kilin, Dmitri S.
2009-10-01
The interaction of an excited adsorbate with a medium undergoing electronic and vibrational transitions leads to fast dissipation due to electronic energy relaxation and slow (or delayed) dissipation from vibrational energy relaxation. A theoretical and computational treatment of these phenomena has been done in terms of a reduced density matrix satisfying a generalized Liouville-von Neumann equation, with instantaneous dissipation constructed from state-to-state transition rates, and delayed dissipation given by a memory term derived from the time-correlation function (TCF) of atomic displacements in the medium. Two representative applications are presented here, where electronic excitation may enhance vibrational relaxation of an adsorbate. They involve femtosecond excitation of (a) a CO molecule adsorbed on the Cu(001) metal surface and (b) a metal cluster on a semiconductor surface, Ag3Si(111):H, both electronically excited by visible light and undergoing electron transfer and dissipative dynamics by electronic and vibrational relaxations. Models have been parametrized in both cases from electronic structure calculations and known TCFs for the medium, which are slowly decaying in case (a) and fast decaying in case (b). This requires different numerical procedures in the solution of the integrodifferential equations for the reduced density matrix, which have been solved with an extension of the Runge-Kutta algorithm. Results for the populations of vibronic states versus time show that they oscillate due to vibrational coupling through dissipative interaction with the substrate and show quantum coherence. The total population of electronic states is, however, little affected by vibrational motions. Vibrational relaxation is important only at very long times to establish thermal equilibrium.
Goldstein, Sheldon; Lebowitz, Joel L.; Mastrodonato, Christian; Tumulka, Roderich; Zanghì, Nino
2016-03-01
A quantum system (with Hilbert space {H}1) entangled with its environment (with Hilbert space {H}2) is usually not attributed to a wave function but only to a reduced density matrix {ρ1}. Nevertheless, there is a precise way of attributing to it a random wave function {ψ1}, called its conditional wave function, whose probability distribution {μ1} depends on the entangled wave function {ψ in H1 ⊗ H2} in the Hilbert space of system and environment together. It also depends on a choice of orthonormal basis of H2 but in relevant cases, as we show, not very much. We prove several universality (or typicality) results about {μ1}, e.g., that if the environment is sufficiently large then for every orthonormal basis of H2, most entangled states {ψ} with given reduced density matrix {ρ1} are such that {μ1} is close to one of the so-called GAP (Gaussian adjusted projected) measures, {GAP(ρ1)}. We also show that, for most entangled states {ψ} from a microcanonical subspace (spanned by the eigenvectors of the Hamiltonian with energies in a narrow interval {[E, E+ δ E]}) and most orthonormal bases of H2, {μ1} is close to {GAP({tr}2 ρ_{mc})} with {ρ_{mc}} the normalized projection to the microcanonical subspace. In particular, if the coupling between the system and the environment is weak, then {μ1} is close to {GAP(ρ_β)} with {ρ_β} the canonical density matrix on H1 at inverse temperature {β=β(E)}. This provides the mathematical justification of our claim in Goldstein et al. (J Stat Phys 125: 1193-1221, 2006) that GAP measures describe the thermal equilibrium distribution of the wave function.
IDN2 and its paralogs form a complex required for RNA-directed DNA methylation.
Directory of Open Access Journals (Sweden)
Cui-Jun Zhang
Full Text Available IDN2/RDM12 has been previously identified as a component of the RNA-directed DNA methylation (RdDM machinery in Arabidopsis thaliana, but how it functions in RdDM remains unknown. By affinity purification of IDN2, we co-purified two IDN2 paralogs IDP1 and IDP2 (IDN2 PARALOG 1 and 2. The coiled-coil domain between the XS and XH domains of IDN2 is essential for IDN2 homodimerization, whereas the IDN2 C-terminal XH domain but not the coiled-coil domain is required for IDN2 interaction with IDP1 and IDP2. By introducing the wild-type IDN2 sequence and its mutated derivatives into the idn2 mutant for complementation testing, we demonstrated that the previously uncharacterized IDN2 XH domain is required for the IDN2-IDP1/IDP2 complex formation as well as for IDN2 function. IDP1 is required for de novo DNA methylation, siRNA accumulation, and transcriptional gene silencing, whereas IDP2 has partially overlapping roles with IDP1. Unlike IDN2, IDP1 and IDP2 are incapable of binding double-stranded RNA, suggesting that the roles of IDP1 and IDP2 are different from those of IDN2 in the IDN2-IDP1/IDP2 complex and that IDP1 and IDP2 are essential for the functioning of the complex in RdDM.
Tulipano, P. Karina; Millar, William S.; Imielinska, Celina; Liu, Xin; Rosiene, Joel; D'Ambrosio, Anthony L.
2006-03-01
Magnetic resonance (MR) imaging is an imaging modality that is used in the management and diagnosis of acute stroke. Common MR imaging techniques such as diffusion weighted imaging (DWI) and apparent diffusion coefficient maps (ADC) are used routinely in the diagnosis of acute infarcts. However, advances in radiology information systems and imaging protocols have led to an overload of image information that can be difficult to manage and time consuming. Automated techniques to assist in the identification of acute ischemic stroke can prove beneficial to 1) the physician by providing a mechanism for early detection and 2) the patient by providing effective stroke therapy at an early stage. We have processed DW images and ADC maps using a novel automated Relative Difference Map (RDM) method that was tailored to the identification and delineation of the stroke region. Results indicate that the technique can delineate regions of acute infarctions on DW images and ADC maps. A formal evaluation of the RDM algorithm was performed by comparing accuracy measurements between 1) expert generated ground truths with the RDM delineated DWI infarcts and 2) RDM delineated DWI infarcts with RDM delineated ADC infarcts. The accuracy measurements indicate that the RDM delineated DWI infarcts are comparable to the expert generated ground truths. The true positive volume fraction value (TPVF), between RDM delineated DWI and ADC infarcts, is nonzero for all cases with an acute infarct while the value for non-acute cases remains zero.
Pernal, Katarzyna
2012-05-14
Time-dependent density functional theory (TD-DFT) in the adiabatic formulation exhibits known failures when applied to predicting excitation energies. One of them is the lack of the doubly excited configurations. On the other hand, the time-dependent theory based on a one-electron reduced density matrix functional (time-dependent density matrix functional theory, TD-DMFT) has proven accurate in determining single and double excitations of H(2) molecule if the exact functional is employed in the adiabatic approximation. We propose a new approach for computing excited state energies that relies on functionals of electron density and one-electron reduced density matrix, where the latter is applied in the long-range region of electron-electron interactions. A similar approach has been recently successfully employed in predicting ground state potential energy curves of diatomic molecules even in the dissociation limit, where static correlation effects are dominating. In the paper, a time-dependent functional theory based on the range-separation of electronic interaction operator is rigorously formulated. To turn the approach into a practical scheme the adiabatic approximation is proposed for the short- and long-range components of the coupling matrix present in the linear response equations. In the end, the problem of finding excitation energies is turned into an eigenproblem for a symmetric matrix. Assignment of obtained excitations is discussed and it is shown how to identify double excitations from the analysis of approximate transition density matrix elements. The proposed method used with the short-range local density approximation (srLDA) and the long-range Buijse-Baerends density matrix functional (lrBB) is applied to H(2) molecule (at equilibrium geometry and in the dissociation limit) and to Be atom. The method accounts for double excitations in the investigated systems but, unfortunately, the accuracy of some of them is poor. The quality of the other
Energy Technology Data Exchange (ETDEWEB)
Uranga-Piña, L. [Facultad de Física, Universidad de la Habana, San Lázaro y L, Vedado, 10400 Havana (Cuba); Institute for Chemistry and Biochemistry, Freie Universität Berlin, Takustr. 3, D-14195 Berlin (Germany); Tremblay, J. C., E-mail: jean.c.tremblay@gmail.com [Institute for Chemistry and Biochemistry, Freie Universität Berlin, Takustr. 3, D-14195 Berlin (Germany)
2014-08-21
We investigate the effect of inter-mode coupling on the vibrational relaxation dynamics of molecules in weak dissipative environments. The simulations are performed within the reduced density matrix formalism in the Markovian regime, assuming a Lindblad form for the system-bath interaction. The prototypical two-dimensional model system representing two CO molecules approaching a Cu(100) surface is adapted from an ab initio potential, while the diatom-diatom vibrational coupling strength is systematically varied. In the weak system-bath coupling limit and at low temperatures, only first order non-adiabatic uni-modal coupling terms contribute to surface-mediated vibrational relaxation. Since dissipative dynamics is non-unitary, the choice of representation will affect the evolution of the reduced density matrix. Two alternative representations for computing the relaxation rates and the associated operators are thus compared: the fully coupled spectral basis, and a factorizable ansatz. The former is well-established and serves as a benchmark for the solution of Liouville-von Neumann equation. In the latter, a contracted grid basis of potential-optimized discrete variable representation is tailored to incorporate most of the inter-mode coupling, while the Lindblad operators are represented as tensor products of one-dimensional operators, for consistency. This procedure results in a marked reduction of the grid size and in a much more advantageous scaling of the computational cost with respect to the increase of the dimensionality of the system. The factorizable method is found to provide an accurate description of the dissipative quantum dynamics of the model system, specifically of the time evolution of the state populations and of the probability density distribution of the molecular wave packet. The influence of intra-molecular vibrational energy redistribution appears to be properly taken into account by the new model on the whole range of coupling strengths. It
Dattani, Nikesh S.
2013-12-01
This MATLAB program calculates the dynamics of the reduced density matrix of an open quantum system modeled either by the Feynman-Vernon model or the Caldeira-Leggett model. The user gives the program a Hamiltonian matrix that describes the open quantum system as if it were in isolation, a matrix of the same size that describes how that system couples to its environment, and a spectral distribution function and temperature describing the environment’s influence on it, in addition to the open quantum system’s initial density matrix and a grid of times. With this, the program returns the reduced density matrix of the open quantum system at all moments specified by that grid of times (or just the last moment specified by the grid of times if the user makes this choice). This overall calculation can be divided into two stages: the setup of the Feynman integral, and the actual calculation of the Feynman integral for time propagation of the density matrix. When this program calculates this propagation on a multi-core CPU, it is this propagation that is usually the rate-limiting step of the calculation, but when it is calculated on a GPU, the propagation is calculated so quickly that the setup of the Feynman integral can actually become the rate-limiting step. The overhead of transferring information from the CPU to the GPU and back seems to have a negligible effect on the overall runtime of the program. When the required information cannot fit on the GPU, the user can choose to run the entire program on a CPU. Catalogue identifier: AEPX_v1_0. Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEPX_v1_0.html. Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland. Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html. No. of lines in distributed program, including test data, etc.: 703. No. of bytes in distributed program, including test data, etc.: 11026. Distribution format: tar.gz. Programming
Uranga-Piña, L; Tremblay, J C
2014-08-21
We investigate the effect of inter-mode coupling on the vibrational relaxation dynamics of molecules in weak dissipative environments. The simulations are performed within the reduced density matrix formalism in the Markovian regime, assuming a Lindblad form for the system-bath interaction. The prototypical two-dimensional model system representing two CO molecules approaching a Cu(100) surface is adapted from an ab initio potential, while the diatom-diatom vibrational coupling strength is systematically varied. In the weak system-bath coupling limit and at low temperatures, only first order non-adiabatic uni-modal coupling terms contribute to surface-mediated vibrational relaxation. Since dissipative dynamics is non-unitary, the choice of representation will affect the evolution of the reduced density matrix. Two alternative representations for computing the relaxation rates and the associated operators are thus compared: the fully coupled spectral basis, and a factorizable ansatz. The former is well-established and serves as a benchmark for the solution of Liouville-von Neumann equation. In the latter, a contracted grid basis of potential-optimized discrete variable representation is tailored to incorporate most of the inter-mode coupling, while the Lindblad operators are represented as tensor products of one-dimensional operators, for consistency. This procedure results in a marked reduction of the grid size and in a much more advantageous scaling of the computational cost with respect to the increase of the dimensionality of the system. The factorizable method is found to provide an accurate description of the dissipative quantum dynamics of the model system, specifically of the time evolution of the state populations and of the probability density distribution of the molecular wave packet. The influence of intra-molecular vibrational energy redistribution appears to be properly taken into account by the new model on the whole range of coupling strengths. It
Theoretical Study of Plasmonic Lasing in Junctions with many Molecules
Zhang, Yuan; May, Volkhard
2016-01-01
We calculate the quantum state of the plasmon field excited by an ensemble of molecular emitters, which are driven by exchange of electrons with metallic nano-particle electrodes. Assuming identical emitters that are coupled collectively to the plasmon mode but are otherwise subject to independent relaxation channels, we show that symmetry constraints on the total system density matrix imply a drastic reduction in the numerical complexity. For $N_{\\text{m}}$ three-level molecules we may thus represent the density matrix by a number of terms scaling as $(N_{\\rm m}+8)!/(8!N_{\\rm m}!)$ instead of $9^{N_{\\text{m}}}$, and this allows exact simulations of up to $N_{\\text{m}}=10$ molecules. Our simulations demonstrate that many emitters compensate strong plasmon damping and lead to the population of high plasmon number states and a narrowed linewidth of the plasmon field. For large $N_{\\text{m}}$, our exact results are reproduced by an approximate approach based on the plasmon reduced density matrix. With this appro...
The classical correlation limits the ability of the measurement-induced average coherence
Zhang, Jun; Yang, Si-ren; Zhang, Yang; Yu, Chang-shui
2017-01-01
Coherence is the most fundamental quantum feature in quantum mechanics. For a bipartite quantum state, if a measurement is performed on one party, the other party, based on the measurement outcomes, will collapse to a corresponding state with some probability and hence gain the average coherence. It is shown that the average coherence is not less than the coherence of its reduced density matrix. In particular, it is very surprising that the extra average coherence (and the maximal extra average coherence with all the possible measurements taken into account) is upper bounded by the classical correlation of the bipartite state instead of the quantum correlation. We also find the sufficient and necessary condition for the null maximal extra average coherence. Some examples demonstrate the relation and, moreover, show that quantum correlation is neither sufficient nor necessary for the nonzero extra average coherence within a given measurement. In addition, the similar conclusions are drawn for both the basis-dependent and the basis-free coherence measure. PMID:28374756
Chu, Iek-Heng; Cheng, Hai-Ping
2013-01-01
We have studied the energetics, electronic structure, optical excitation, and electron relaxation of dinitromethane molecules (CH$_{2}$N$_{2}$O$_{4}$) adsorbed on semiconducting carbon nanotubes (CNTs) of chiral index (n,0) (n=7, 10, 13, 16, 19). Using first-principles density functional theory (DFT) with generalized gradient approximations and van der Waals corrections, we have calculated adsorption energies of dinitropentylpyrene, in which the dinitromethane is linked to the pyrene via an aliphatic chain, on a CNT. A 75.26 kJ/mol binding energy has been found, which explains why such aliphatic chain-pyrene units can be and have been used in experiments to bind functional molecules to CNTs. The calculated electronic structures show that the dinitromethane introduces a localized state inside the band gap of CNT systems of n=10, 13, 16 and 19; such a state can trap an electron when the CNT is photoexcited. We have therefore investigated the dynamics of intra-band relaxations using the reduced density matrix fo...
Quantum Diffusion on a Dynamically Disordered and Harmonically Driven Lattice with Static Bias:
Singh, Navinder; Kumar, N.
We revisit the problem of quantum diffusion of a particle moving on a lattice with dynamical disorder. Decoherence, essential for the diffusive motion, is introduced via a set of Lindblad operators, known to guarantee per se the positivity, Hermiticity and the trace-class nature of the reduced density matrix, are derived and solved analytically for several transport quantities of interest. For the special Hermitian choice of the Lindblad operators projected onto the lattice sites, we recover several known results, obtained by others, e.g. through the stochastic Liouville equation using phenomenological damping terms for the off-diagonal density-matrix elements. An interesting result that we obtained is for the case of a 1D lattice with static potential bias and a time-harmonic modulation (ac drive) of its transition-matrix element, where the diffusion coefficient shows an oscillatory behavior as function of the drive amplitude and frequency — clearly, a Wannier-Stark ladder signature. The question of dissipation is also briefly discussed.
Approximate but accurate quantum dynamics from the Mori formalism: I. Nonequilibrium dynamics
Montoya-Castillo, Andrés; Reichman, David R.
2016-05-01
We present a formalism that explicitly unifies the commonly used Nakajima-Zwanzig approach for reduced density matrix dynamics with the more versatile Mori theory in the context of nonequilibrium dynamics. Employing a Dyson-type expansion to circumvent the difficulty of projected dynamics, we obtain a self-consistent equation for the memory kernel which requires only knowledge of normally evolved auxiliary kernels. To illustrate the properties of the current approach, we focus on the spin-boson model and limit our attention to the use of a simple and inexpensive quasi-classical dynamics, given by the Ehrenfest method, for the calculation of the auxiliary kernels. For the first time, we provide a detailed analysis of the dependence of the properties of the memory kernels obtained via different projection operators, namely, the thermal (Redfield-type) and population based (NIBA-type) projection operators. We further elucidate the conditions that lead to short-lived memory kernels and the regions of parameter space to which this program is best suited. Via a thorough analysis of the different closures available for the auxiliary kernels and the convergence properties of the self-consistently extracted memory kernel, we identify the mechanisms whereby the current approach leads to a significant improvement over the direct usage of standard semi- and quasi-classical dynamics.
Boudjada, Nazim; Segal, Dvira
2014-11-26
We study in a unified manner the dissipative dynamics and the transfer of heat in the two-bath spin-boson model. We use the Bloch-Redfield (BR) formalism, valid in the very weak system-bath coupling limit, the noninteracting-blip approximation (NIBA), applicable in the nonadiabatic limit, and iterative, numerically exact path integral tools. These methodologies were originally developed for the description of the dissipative dynamics of a quantum system, and here they are applied to explore the problem of quantum energy transport in a nonequilibrium setting. Specifically, we study the weak-to-intermediate system-bath coupling regime at high temperatures kBT/ħ > ε, with ε as the characteristic frequency of the two-state system. The BR formalism and NIBA can lead to close results for the dynamics of the reduced density matrix (RDM) in a certain range of parameters. However, relatively small deviations in the RDM dynamics propagate into significant qualitative discrepancies in the transport behavior. Similarly, beyond the strict nonadiabatic limit NIBA's prediction for the heat current is qualitatively incorrect: It fails to capture the turnover behavior of the current with tunneling energy and temperature. Thus, techniques that proved meaningful for describing the RDM dynamics, to some extent even beyond their rigorous range of validity, should be used with great caution in heat transfer calculations, because qualitative-serious failures develop once parameters are mildly stretched beyond the techniques' working assumptions.
The Role of the Environment in Molecular Systems
Kilin, D S
2000-01-01
The work is devoted to the investigation of the influence of a heat bath on the physical processes in a quantum system. We use the density matrix theory as one of the most powerfool tool for investigation of quantum relaxation. In the beginning of the work (chapter 2) we mention and recall the most important steps of derivation of the equation of motion for the reduced density matrix (master equation) for an arbitrary quantum system in diabatic representation interacting with the environment modeled by a set of independent harmonic oscillators. Chapter 3 deals with the question of the border between classical and quantum effects and reports on a study of the environmental influence on the time evolution of a coherent state or the superposition of two coherent states of a harmonic oscillator as a simple system displaying the peculiarities of the transition from quantum to classical regime. Chapters 4 and 5 concern the electron transfer (ET) problem, namely the mathematical description of the ET in molecular zi...
Thermality and excited state Rényi entropy in two-dimensional CFT
Lin, Feng-Li; Wang, Huajia; Zhang, Jia-ju
2016-11-01
We evaluate one-interval Rényi entropy and entanglement entropy for the excited states of two-dimensional conformal field theory (CFT) on a cylinder, and examine their differences from the ones for the thermal state. We assume the interval to be short so that we can use operator product expansion (OPE) of twist operators to calculate Rényi entropy in terms of sum of one-point functions of OPE blocks. We find that the entanglement entropy for highly excited state and thermal state behave the same way after appropriate identification of the conformal weight of the state with the temperature. However, there exists no such universal identification for the Rényi entropy in the short-interval expansion. Therefore, the highly excited state does not look thermal when comparing its Rényi entropy to the thermal state one. As the Rényi entropy captures the higher moments of the reduced density matrix but the entanglement entropy only the average, our results imply that the emergence of thermality depends on how refined we look into the entanglement structure of the underlying pure excited state.
Comparison of two models for bridge-assisted charge transfer
Schreiber, M; Kleinekathöfer, U
1999-01-01
Based on the reduced density matrix method, we compare two different approaches to calculate the dynamics of the electron transfer in systems with donor, bridge, and acceptor. In the first approach a vibrational substructure is taken into account for each electronic state and the corresponding states are displaced along a common reaction coordinate. In the second approach it is assumed that vibrational relaxation is much faster than the electron transfer and therefore the states are modeled by electronic levels only. In both approaches the system is coupled to a bath of harmonic oscillators but the way of relaxation is quite different. The theory is applied to the electron transfer in ${\\rm H_2P}-{\\rm ZnP}-{\\rm Q}$ with free-base porphyrin (${\\rm H_2P}$) being the donor, zinc porphyrin (${\\rm ZnP}$) being the bridge and quinone (${\\rm Q}$) the acceptor. The parameters are chosen as similar as possible for both approaches and the quality of the agreement is discussed.
Basilevsky, M. V.; Odinokov, A. V.; Titov, S. V.; Mitina, E. A.
2013-12-01
The algorithm for a theoretical calculation of transfer reaction rates for light quantum particles (i.e., the electron and H-atom transfers) in non-polar solid matrices is formulated and justified. The mechanism postulated involves a local mode (an either intra- or inter-molecular one) serving as a mediator which accomplishes the energy exchange between the reacting high-frequency quantum mode and the phonon modes belonging to the environment. This approach uses as a background the Fermi golden rule beyond the usually applied spin-boson approximation. The dynamical treatment rests on the one-dimensional version of the standard quantum relaxation equation for the reduced density matrix, which describes the frequency fluctuation spectrum for the local mode under consideration. The temperature dependence of a reaction rate is controlled by the dimensionless parameter ξ0 = ℏω0/kBT where ω0 is the frequency of the local mode and T is the temperature. The realization of the computational scheme is different for the high/intermediate (ξ0 Dokl. Akad. Nauk SSSR, Ser. Fiz. Khim. 124, 213 (1959); J. Ulstrup, Charge Transfer in Condensed Media (Springer, Berlin, 1979); M. Bixon and J. Jortner, Adv. Chem. Phys. 106, 35 (1999)] underlying it is discussed and illustrated by the results of computations for practically important target systems.
Chakrabarti, R.; Yogesh, V.
2016-04-01
We study the evolution of the hybrid entangled states in a bipartite (ultra) strongly coupled qubit-oscillator system. Using the generalized rotating wave approximation the reduced density matrices of the qubit and the oscillator are obtained. The reduced density matrix of the oscillator yields the phase space quasi probability distributions such as the diagonal P-representation, the Wigner W-distribution and the Husimi Q-function. In the strong coupling regime the Q-function evolves to uniformly separated macroscopically distinct Gaussian peaks representing ‘kitten’ states at certain specified times that depend on multiple time scales present in the interacting system. The ultrastrong coupling strength of the interaction triggers appearance of a large number of modes that quickly develop a randomization of their phase relationships. A stochastic averaging of the dynamical quantities sets in, and leads to the decoherence of the system. The delocalization in the phase space of the oscillator is studied by using the Wehrl entropy. The negativity of the W-distribution reflects the departure of the oscillator from the classical states, and allows us to study the underlying differences between various information-theoretic measures such as the Wehrl entropy and the Wigner entropy. Other features of nonclassicality such as the existence of the squeezed states and appearance of negative values of the Mandel parameter are realized during the course of evolution of the bipartite system. In the parametric regime studied here these properties do not survive in the time-averaged limit.
Uniformly accelerated observer in a thermal bath
Kolekar, Sanved
2013-01-01
We investigate the quantum field aspects in flat spacetime for an uniformly accelerated observer moving in a thermal bath. In particular, we obtain an exact closed expression of the reduced density matrix for an uniformly accelerated observer with acceleration $a = 2\\pi T$ when the state of the quantum field is a thermal bath at temperature $T^\\prime$. We find that the density matrix has a simple form with an effective partition function $Z$ being a product, $Z = Z_T Z_{T^\\prime}$, of two thermal partition functions corresponding to temperatures $T$ and $T^\\prime$ and hence is not thermal, even when $T = T^\\prime$. We show that, even though the partition function has a product structure, the two thermal baths are, in fact, interacting systems; although in the high frequency limit $\\omega_k \\gg T$ and $\\omega_k \\gg T^\\prime$, the interactions are found to become sub-dominant. We further demonstrate that the resulting spectrum of the Rindler particles can be interpreted in terms of spontaneous and stimulated em...
Arian Zad, Hamid
2016-12-01
We analytically investigate Multiple Quantum (MQ) NMR dynamics in a mixed-three-spin (1/2,1,1/2) system with XXX Heisenberg model at the front of an external homogeneous magnetic field B. A single-ion anisotropy property ζ is considered for the spin-1. The intensities dependence of MQ NMR coherences on their orders (zeroth and second orders) for two pairs of spins (1,1/2) and (1/2,1/2) of the favorite tripartite system are obtained. It is also investigated dynamics of the pairwise quantum entanglement for the bipartite (sub)systems (1,1/2) and (1/2,1/2) permanently coupled by, respectively, coupling constants J}1 and J}2, by means of concurrence and fidelity. Then, some straightforward comparisons are done between these quantities and the intensities of MQ NMR coherences and ultimately some interesting results are reported. We also show that the time evolution of MQ coherences based on the reduced density matrix of the pair spins (1,1/2) is closely connected with the dynamics of the pairwise entanglement. Finally, we prove that one can introduce MQ coherence of the zeroth order corresponds to the pair spins (1,1/2) as an entanglement witness at some special time intervals.
Coarse Grained Quantum Dynamics
Agon, Cesar; Kasko, Skyler; Lawrence, Albion
2014-01-01
We consider coarse graining a quantum system divided between short distance and long distance degrees of freedom, which are coupled by the Hamiltonian. Observations using purely long distance observables can be described by the reduced density matrix that arises from tracing out the short-distance observables. The dynamics of this density matrix is that of an open quantum system, and is nonlocal in time, on the order of some short time scale. We describe these dynamics in a model system with a simple hierarchy of energy gaps $\\Delta E_{UV} > \\Delta E_{IR}$, in which the coupling between high-and low-energy degrees of freedom is treated to second order in perturbation theory. We then describe the equations of motion under suitable time averaging, reflecting the limited time resolution of actual experiments, and find an expansion of the master equation in powers of $\\Delta E_{IR}/\\Delta E_{UV}$, in which the failure of the system to be Hamiltonian or even Markovian appears at higher orders in this ratio. We com...
Singh, Navinder
2011-01-01
A direct numerical algorithm for solving the time-nonlocal non-Markovian master equation in the second Born approximation is introduced and the range of utility of this approximation, and of the Markov approximation, is analyzed for the traditional dimer system that models excitation energy transfer in photosynthesis. Specifically, the coupled integro-differential equations for the reduced density matrix are solved by an efficient auxiliary function method in both the energy and site representations. In addition to giving exact results to this order, the approach allows us to computationally assess the range of the reorganization energy and decay rates of the phonon auto-correlation function for which the Markovian Redfield theory and the second order approximation is valid. For example, the use of Redfield theory for $\\lambda> 10 \\textrm{cm}^{-1}$ in systems like Fenna-Mathews-Olson (FMO) type systems is shown to be in error. In addition, analytic inequalities are obtained for the regime of validity of the M...
Decoherence, entanglement decay, and equilibration produced by chaotic environments.
Lemos, Gabriela Barreto; Toscano, Fabricio
2011-07-01
We investigate decoherence in quantum systems coupled via dephasing-type interactions to an arbitrary environment with chaotic underlying classical dynamics. The coherences of the reduced state of the central system written in the preferential energy eigenbasis are quantum Loschmidt echoes, which in the strong coupling regime are characterized at long time scales by fluctuations around a constant mean value. We show that due to the chaotic dynamics of the environment, the mean value and the width of the Loschmidt-echo fluctuations are inversely proportional to the quantity we define as the effective Hilbert-space dimension of the environment, which in general is smaller than the dimension of the entire available Hilbert space. Nevertheless, in the semiclassical regime this effective Hilbert-space dimension is in general large, in which case even a chaotic environment with few degrees of freedom produces decoherence without revivals. Moreover we show that in this regime the environment leads the central system to equilibrate to the time average of its reduced density matrix, which corresponds to a diagonal state in the preferential energy eigenbasis. For the case of two uncoupled, initially entangled central systems that interact with identical local quantum environments with chaotic underlying classical dynamics, we show that in the semiclassical limit the equilibration state is arbitrarily close to a separable state. We confirm our results with numerical simulations in which the environment is modeled by the quantum kicked rotor in the chaotic regime.
Dynamics of Collective Decoherence and Thermalization
Merkli, M; Sigal, I M
2008-01-01
We analyze the dynamics of N interacting spins (quantum register) collectively coupled to a thermal environment. Each spin experiences the same environment interaction, consisting of an energy conserving and an energy exchange part. We find the decay rates of the reduced density matrix elements in the energy basis. We show that if the spins do not interact among each other, then the fastest decay rates of off-diagonal matrix elements induced by the energy conserving interaction is of order N^2, while that one induced by the energy exchange interaction is of the order N only. Moreover, the diagonal matrix elements approach their limiting values at a rate independent of N. For a general spin system the decay rates depend in a rather complicated (but explicit) way on the size N and the interaction between the spins. Our method is based on a dynamical quantum resonance theory valid for small, fixed values of the couplings. We do not make Markov-, Born- or weak coupling (van Hove) approximations.
Dynamics of collective decoherence and thermalization
Merkli, M.; Berman, G. P.; Sigal, I. M.
2008-12-01
We analyze the dynamics of N interacting spins (quantum register) collectively coupled to a thermal environment. Each spin experiences the same environment interaction, consisting of an energy conserving and an energy exchange part. We find the decay rates of the reduced density matrix elements in the energy basis. We show that if the spins do not interact among each other, then the fastest decay rates of off-diagonal matrix elements induced by the energy conserving interaction is of order N2 , while that one induced by the energy exchange interaction is of the order N only. Moreover, the diagonal matrix elements approach their limiting values at a rate independent of N. For a general spin system the decay rates depend in a rather complicated (but explicit) way on the size N and the interaction between the spins. Our method is based on a dynamical quantum resonance theory valid for small, fixed values of the couplings. We do not make Markov-, Born- or weak coupling (van Hove) approximations.
Natural occupation numbers: when do they vanish?
Giesbertz, K J H; van Leeuwen, R
2013-09-14
The non-vanishing of the natural orbital (NO) occupation numbers of the one-particle density matrix of many-body systems has important consequences for the existence of a density matrix-potential mapping for nonlocal potentials in reduced density matrix functional theory and for the validity of the extended Koopmans' theorem. On the basis of Weyl's theorem we give a connection between the differentiability properties of the ground state wavefunction and the rate at which the natural occupations approach zero when ordered as a descending series. We show, in particular, that the presence of a Coulomb cusp in the wavefunction leads, in general, to a power law decay of the natural occupations, whereas infinitely differentiable wavefunctions typically have natural occupations that decay exponentially. We analyze for a number of explicit examples of two-particle systems that in case the wavefunction is non-analytic at its spatial diagonal (for instance, due to the presence of a Coulomb cusp) the natural orbital occupations are non-vanishing. We further derive a more general criterium for the non-vanishing of NO occupations for two-particle wavefunctions with a certain separability structure. On the basis of this criterium we show that for a two-particle system of harmonically confined electrons with a Coulombic interaction (the so-called Hookium) the natural orbital occupations never vanish.
Approximate but Accurate Quantum Dynamics from the Mori Formalism: I. Nonequilibrium Dynamics
Montoya-Castillo, Andrés
2016-01-01
We present a formalism that explicitly unifies the commonly used Nakajima-Zwanzig approach for reduced density matrix dynamics with the more versatile Mori theory in the context of nonequilibrium dynamics. Employing a Dyson-type expansion to circumvent the difficulty of projected dynamics, we obtain a self-consistent equation for the memory kernel which requires only knowledge of normally evolved auxiliary kernels. To illustrate the properties of the current approach, we focus on the spin-boson model and limit our attention to the use of a simple and inexpensive quasi-classical dynamics, given by the Ehrenfest method, for the calculation of the auxiliary kernels. For the first time, we provide a detailed analysis of the dependence of the properties of the memory kernels obtained via different projection operators, namely the thermal (Redfield-type) and population based (NIBA-type) projection operators. We further elucidate the conditions that lead to short-lived memory kernels and the regions of parameter spa...
Thingna, Juzar; Zhou, Hangbo; Wang, Jian-Sheng
2014-11-21
We present a general theory to calculate the steady-state heat and electronic currents for nonlinear systems using a perturbative expansion in the system-bath coupling. We explicitly demonstrate that using the truncated Dyson-series leads to divergences in the steady-state limit, thus making it impossible to be used for actual applications. In order to resolve the divergences, we propose a unique choice of initial condition for the reduced density matrix, which removes the divergences at each order. Our approach not only allows us to use the truncated Dyson-series, with a reasonable choice of initial condition, but also gives the expected result that the steady-state solutions should be independent of initial preparations. Using our improved Dyson series we evaluate the heat and electronic currents up to fourth-order in system-bath coupling, a considerable improvement over the standard quantum master equation techniques. We then numerically corroborate our theory for archetypal settings of linear systems using the exact nonequilibrium Green's function approach. Finally, to demonstrate the advantage of our approach, we deal with the nonlinear spin-boson model to evaluate heat current up to fourth-order and find signatures of cotunnelling process.
Negativity spectrum of one-dimensional conformal field theories
Ruggiero, Paola; Calabrese, Pasquale
2016-01-01
The partial transpose $\\rho_A^{T_2}$ of the reduced density matrix $\\rho_A$ is the key object to quantify the entanglement in mixed states, in particular through the presence of negative eigenvalues in its spectrum. Here we derive analytically the distribution of the eigenvalues of $\\rho_A^{T_2}$, that we dub negativity spectrum, in the ground sate of gapless one-dimensional systems described by a Conformal Field Theory (CFT), focusing on the case of two adjacent intervals. We show that the negativity spectrum is universal and depends only on the central charge of the CFT, similarly to the entanglement spectrum. The precise form of the negativity spectrum depends on whether the two intervals are in a pure or mixed state, and in both cases, a dependence on the sign of the eigenvalues is found. This dependence is weak for bulk eigenvalues, whereas it is strong at the spectrum edges. We also investigate the scaling of the smallest (negative) and largest (positive) eigenvalues of $\\rho_A^{T_2}$. We check our resu...
Entanglement and Nonlocality in Infinite 1D Systems
Wang, Zizhu; Singh, Sukhwinder; Navascués, Miguel
2017-06-01
We consider the problem of detecting entanglement and nonlocality in one-dimensional (1D) infinite, translation-invariant (TI) systems when just near-neighbor information is available. This issue is deeper than one might think a priori, since, as we show, there exist instances of local separable states (classical boxes) which admit only entangled (nonclassical) TI extensions. We provide a simple characterization of the set of local states of multiseparable TI spin chains and construct a family of linear witnesses which can detect entanglement in infinite TI states from the nearest-neighbor reduced density matrix. Similarly, we prove that the set of classical TI boxes forms a polytope and devise a general procedure to generate all Bell inequalities which characterize it. Using an algorithm based on matrix product states, we show how some of them can be violated by distant parties conducting identical measurements on an infinite TI quantum state. All our results can be easily adapted to detect entanglement and nonlocality in large (finite, not TI) 1D condensed matter systems.
Tsuchimoto, Masashi; Tanimura, Yoshitaka
2015-08-11
A system with many energy states coupled to a harmonic oscillator bath is considered. To study quantum non-Markovian system-bath dynamics numerically rigorously and nonperturbatively, we developed a computer code for the reduced hierarchy equations of motion (HEOM) for a graphics processor unit (GPU) that can treat the system as large as 4096 energy states. The code employs a Padé spectrum decomposition (PSD) for a construction of HEOM and the exponential integrators. Dynamics of a quantum spin glass system are studied by calculating the free induction decay signal for the cases of 3 × 2 to 3 × 4 triangular lattices with antiferromagnetic interactions. We found that spins relax faster at lower temperature due to transitions through a quantum coherent state, as represented by the off-diagonal elements of the reduced density matrix, while it has been known that the spins relax slower due to suppression of thermal activation in a classical case. The decay of the spins are qualitatively similar regardless of the lattice sizes. The pathway of spin relaxation is analyzed under a sudden temperature drop condition. The Compute Unified Device Architecture (CUDA) based source code used in the present calculations is provided as Supporting Information .
Quantum de Finetti theorems and mean-field theory from quantum phase space representations
Trimborn, F.; Werner, R. F.; Witthaut, D.
2016-04-01
We introduce the number-conserving quantum phase space description as a versatile tool to address fundamental aspects of quantum many-body systems. Using phase space methods we prove two alternative versions of the quantum de Finetti theorem for finite-dimensional bosonic quantum systems, which states that a reduced density matrix of a many-body quantum state can be approximated by a convex combination of product states where the error is proportional to the inverse particle number. This theorem provides a formal justification for the mean-field description of many-body quantum systems, as it shows that quantum correlations can be neglected for the calculation of few-body observables when the particle number is large. Furthermore we discuss methods to derive the exact evolution equations for quantum phase space distribution functions as well as upper and lower bounds for the ground state energy. As an important example, we consider the Bose-Hubbard model and show that the mean-field dynamics is given by a classical phase space flow equivalent to the discrete Gross-Pitaevskii equation.
Ab initio study of metal-insulator transition in VO2
Zheng, Huihuo; Wagner, Lucas K.
2013-03-01
The structure distortion accompanied metal-insulator transition (MIT) of vanadium dioxide (VO2) at 340K has been a matter of ongoing controversy for near four decades. It is still unclear whether the nature of this transition is due to a Peierls instability, a Mott-Hubbard transition, or other physics. Most density functional theory based methods fail to describe the nature of the electronic state in this system, further complicating theoretical description of VO2. We will report on progress in applying the first principles diffusion quantum Monte Carlo method to the electronic structure of VO2 in the metallic and insulator phases. By examining the energetic properties, one particle reduced density matrix, as well as other static correlations in the two phases of the system, we will comment on which of the two common descriptions is a closer representation of the physical reality of VO2. This work was supported by the Strategic Research Initiatives project at Illinois(HZ) and NSF DMR 12-06242 (LKW).
Energy Technology Data Exchange (ETDEWEB)
Thingna, Juzar [Institute of Physics, University of Augsburg, Universitätsstrasse 1 D-86135 Augsburg (Germany); Nanosystems Initiative Munich, Schellingrstrasse 4, D-80799 München (Germany); Zhou, Hangbo [Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore 117551 (Singapore); NUS Graduate School for Integrative Sciences and Engineering, National University of Singapore, Singapore 117456 (Singapore); Wang, Jian-Sheng, E-mail: phywjs@nus.edu.sg [Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore 117551 (Singapore)
2014-11-21
We present a general theory to calculate the steady-state heat and electronic currents for nonlinear systems using a perturbative expansion in the system-bath coupling. We explicitly demonstrate that using the truncated Dyson-series leads to divergences in the steady-state limit, thus making it impossible to be used for actual applications. In order to resolve the divergences, we propose a unique choice of initial condition for the reduced density matrix, which removes the divergences at each order. Our approach not only allows us to use the truncated Dyson-series, with a reasonable choice of initial condition, but also gives the expected result that the steady-state solutions should be independent of initial preparations. Using our improved Dyson series we evaluate the heat and electronic currents up to fourth-order in system-bath coupling, a considerable improvement over the standard quantum master equation techniques. We then numerically corroborate our theory for archetypal settings of linear systems using the exact nonequilibrium Green's function approach. Finally, to demonstrate the advantage of our approach, we deal with the nonlinear spin-boson model to evaluate heat current up to fourth-order and find signatures of cotunnelling process.
Increasing Radical Character of Large [n]cyclacenes Unveiled by Wave Function Theory.
Battaglia, Stefano; Faginas-Lago, Noelia; Andrae, Dirk; Evangelisti, Stefano; Leininger, Thierry
2017-05-18
We have investigated the radicality and the vertical singlet-triplet energy gap of [n]cyclacenes (cyclic polyacenes) as a function of the system size for n even, from 6 to 22. The calculations are performed using the complete active space self-consistent field method and second-order n-electron valence perturbation theory. We present a systematic way for the selection of the active space in order to have a balanced description of the wave function as the size of the system increases. Moreover, we provide didactic insight into the failure of an approach based on a minimal active space. We find that the ground state is an open-shell singlet and its multireference character increases progressively with n. The singlet-triplet gap decreases as a function of the system size and approaches a finite positive value for the limit n → ∞. Finally, an analysis based on the one-particle reduced density matrix suggests a polyradical character for the largest cyclacenes.
Statistical mechanics of Floquet systems: the pervasive problem of near degeneracies.
Hone, Daniel W; Ketzmerick, Roland; Kohn, Walter
2009-05-01
Although the statistical mechanics of periodically driven ("Floquet") systems in contact with a heat bath has some formal analogy with the traditional statistical mechanics of undriven systems, closer examination reveals radical differences. In Floquet systems all quasienergies epsilon_{j} can be placed in a finite frequency interval 0statistical mechanics. We show that, for weak but finite coupling between system and heat bath, the accuracy of a calculation within the truncated space spanned by the N lowest energy eigenstates of the undriven system is limited, as N increases indefinitely, only by the usual Born-Markov approximation, which neglects bath memory effects. As we seek higher accuracy by increasing N , we inevitably encounter quasienergy differences smaller than the system-bath coupling. We therefore derive here the equations for the steady-state reduced density matrix without restriction on the size of quasienergy splittings. In general, this matrix is no longer diagonal in the Floquet states. We analyze, in particular, the behavior near a weakly avoided crossing, where near degeneracies of quasienergies appear. In spite of the Floquet state pathologies, the explicit form of our results for the density matrix gives a consistent prescription for the statistical mechanics of periodically driven systems in the limit as N approaches infinity.
Nonrelativistic quantum mechanics with consideration of influence of fundamental environment
Energy Technology Data Exchange (ETDEWEB)
Gevorkyan, A. S., E-mail: g_ashot@sci.am [NAS of Armenia, Institute for Informatics and Automation Problems (Armenia)
2013-08-15
Spontaneous transitions between bound states of an atomic system, the 'Lamb Shift' of energy levels and many other phenomena in real nonrelativistic quantum systems are connected with the influence of the quantum vacuum fluctuations (fundamental environment (FE)), which are impossible to consider in the framework of standard quantum-mechanical approaches. The joint system quantum system (QS) and FE is described in the framework of the stochastic differential equation (SDE) of Langevin-Schroedinger type and is defined on the extended space Double-Struck-Capital-R {sup 3} Circled-Times {Xi}{sup n}, where Double-Struck-Capital-R {sup 3} and {Xi}{sup n} are the Euclidean and functional spaces, respectively. The method of stochastic density matrix is developed and the von Neumann equation for reduced density matrix of QS with FE is generalized. The entropy of QS entangled with FE is defined and investigated. It is proved that the interaction of QS with the environment leads to emerging structures of various topologies which present new quantum-field properties of QS. It is shown that when the physical system (irrelatively to its being micro ormacro) breaks up into two fragments by means of FE, there arises between these fragments a nonpotential interaction which does not disappear at large distances.
Nonrelativistic quantum mechanics with consideration of influence of fundamental environment
Gevorkyan, A. S.
2013-08-01
Spontaneous transitions between bound states of an atomic system, the "Lamb Shift" of energy levels and many other phenomena in real nonrelativistic quantum systems are connected with the influence of the quantum vacuum fluctuations ( fundamental environment (FE)), which are impossible to consider in the framework of standard quantum-mechanical approaches. The joint system quantum system (QS) and FE is described in the framework of the stochastic differential equation (SDE) of Langevin-Schrödinger type and is defined on the extended space ℝ3⊗Ξ n , where ℝ3 and Ξ n are the Euclidean and functional spaces, respectively. The method of stochastic density matrix is developed and the von Neumann equation for reduced density matrix of QS with FE is generalized. The entropy of QS entangled with FE is defined and investigated. It is proved that the interaction of QS with the environment leads to emerging structures of various topologies which present new quantum-field properties of QS. It is shown that when the physical system (irrelatively to its being micro ormacro) breaks up into two fragments by means of FE, there arises between these fragments a nonpotential interaction which does not disappear at large distances.
Thermalization and revivals after a quantum quench in conformal field theory.
Cardy, John
2014-06-06
We consider a quantum quench in a finite system of length L described by a 1+1-dimensional conformal field theory (CFT), of central charge c, from a state with finite energy density corresponding to an inverse temperature β≪L. For times t such that ℓ/2
Entanglement negativity in quantum field theory.
Calabrese, Pasquale; Cardy, John; Tonni, Erik
2012-09-28
We develop a systematic method to extract the negativity in the ground state of a 1+1 dimensional relativistic quantum field theory, using a path integral formalism to construct the partial transpose ρ(A)(T(2) of the reduced density matrix of a subsystem [formula: see text], and introducing a replica approach to obtain its trace norm which gives the logarithmic negativity E=ln//ρ(A)(T(2))//. This is shown to reproduce standard results for a pure state. We then apply this method to conformal field theories, deriving the result E~(c/4)ln[ℓ(1)ℓ(2)/(ℓ(1)+ℓ(2))] for the case of two adjacent intervals of lengths ℓ(1), ℓ(2) in an infinite system, where c is the central charge. For two disjoint intervals it depends only on the harmonic ratio of the four end points and so is manifestly scale invariant. We check our findings against exact numerical results in the harmonic chain.
Energy Technology Data Exchange (ETDEWEB)
Vazhappilly, Tijo [Departments of Chemistry and of Physics, Quantum Theory Project, University of Florida, Gainesville, Florida 32611 (United States); Theoretical Chemistry Section, Bhabha Atomic Research Centre, Mumbai 400 085 (India); Hembree, Robert H.; Micha, David A., E-mail: micha@qtp.ufl.edu [Departments of Chemistry and of Physics, Quantum Theory Project, University of Florida, Gainesville, Florida 32611 (United States)
2016-01-14
A new general computational procedure is presented to obtain photoconductivities starting from atomic structures, combining ab initio electronic energy band states with populations from density matrix theory, and implemented for a specific set of materials based on Si crystalline slabs and their nanostructured surfaces without and with adsorbed Ag clusters. The procedure accounts for charge mobility in semiconductors in photoexcited states, and specifically electron and hole photomobilities at Si(111) surfaces with and without adsorbed Ag clusters using ab initio energy bands and orbitals generated from a generalized gradient functional, however with excited energy levels modified to provide correct bandgaps. Photoexcited state populations for each band and carrier type were generated using steady state solution of a reduced density matrix which includes dissipative medium effects. The present calculations provide photoexcited electronic populations and photoinduced mobilities resulting from applied electric fields and obtained from the change of driven electron energies with their electronic momentum. Extensive results for Si slabs with 8 layers, without and with adsorbed Ag clusters, show that the metal adsorbates lead to substantial increases in the photomobility and photoconductivity of electrons and holes.
The Critical Point Entanglement and Chaos in the Dicke Model
Directory of Open Access Journals (Sweden)
Lina Bao
2015-07-01
Full Text Available Ground state properties and level statistics of the Dicke model for a finite number of atoms are investigated based on a progressive diagonalization scheme (PDS. Particle number statistics, the entanglement measure and the Shannon information entropy at the resonance point in cases with a finite number of atoms as functions of the coupling parameter are calculated. It is shown that the entanglement measure defined in terms of the normalized von Neumann entropy of the reduced density matrix of the atoms reaches its maximum value at the critical point of the quantum phase transition where the system is most chaotic. Noticeable change in the Shannon information entropy near or at the critical point of the quantum phase transition is also observed. In addition, the quantum phase transition may be observed not only in the ground state mean photon number and the ground state atomic inversion as shown previously, but also in fluctuations of these two quantities in the ground state, especially in the atomic inversion fluctuation.
Quantum entanglement in condensed matter systems
Energy Technology Data Exchange (ETDEWEB)
Laflorencie, Nicolas, E-mail: laflo@irsamc.ups-tlse.fr
2016-08-03
This review focuses on the field of quantum entanglement applied to condensed matter physics systems with strong correlations, a domain which has rapidly grown over the last decade. By tracing out part of the degrees of freedom of correlated quantum systems, useful and non-trivial information can be obtained through the study of the reduced density matrix, whose eigenvalue spectrum (the entanglement spectrum) and the associated Rényi entropies are now well recognized to contain key features. In particular, the celebrated area law for the entanglement entropy of ground-states will be discussed from the perspective of its subleading corrections which encode universal details of various quantum states of matter, e.g. symmetry breaking states or topological order. Going beyond entropies, the study of the low-lying part of the entanglement spectrum also allows to diagnose topological properties or give a direct access to the excitation spectrum of the edges, and may also raise significant questions about the underlying entanglement Hamiltonian. All these powerful tools can be further applied to shed some light on disordered quantum systems where impurity/disorder can conspire with quantum fluctuations to induce non-trivial effects. Disordered quantum spin systems, the Kondo effect, or the many-body localization problem, which have all been successfully (re)visited through the prism of quantum entanglement, will be discussed in detail. Finally, the issue of experimental access to entanglement measurement will be addressed, together with its most recent developments.
Performance of the density matrix functional theory in the quantum theory of atoms in molecules.
García-Revilla, Marco; Francisco, E; Costales, A; Martín Pendás, A
2012-02-02
The generalization to arbitrary molecular geometries of the energetic partitioning provided by the atomic virial theorem of the quantum theory of atoms in molecules (QTAIM) leads to an exact and chemically intuitive energy partitioning scheme, the interacting quantum atoms (IQA) approach, that depends on the availability of second-order reduced density matrices (2-RDMs). This work explores the performance of this approach in particular and of the QTAIM in general with approximate 2-RDMs obtained from the density matrix functional theory (DMFT), which rests on the natural expansion (natural orbitals and their corresponding occupation numbers) of the first-order reduced density matrix (1-RDM). A number of these functionals have been implemented in the promolden code and used to perform QTAIM and IQA analyses on several representative molecules and model chemical reactions. Total energies, covalent intra- and interbasin exchange-correlation interactions, as well as localization and delocalization indices have been determined with these functionals from 1-RDMs obtained at different levels of theory. Results are compared to the values computed from the exact 2-RDMs, whenever possible.
Joint product numerical range and geometry of reduced density matrices
Chen, Jianxin; Guo, Cheng; Ji, Zhengfeng; Poon, Yiu-Tung; Yu, Nengkun; Zeng, Bei; Zhou, Jie
2017-02-01
The reduced density matrices of a many-body quantum system form a convex set, whose three-dimensional projection Θ is convex in R3. The boundary ∂Θ of Θ may exhibit nontrivial geometry, in particular ruled surfaces. Two physical mechanisms are known for the origins of ruled surfaces: symmetry breaking and gapless. In this work, we study the emergence of ruled surfaces for systems with local Hamiltonians in infinite spatial dimension, where the reduced density matrices are known to be separable as a consequence of the quantum de Finetti's theorem. This allows us to identify the reduced density matrix geometry with joint product numerical range Π of the Hamiltonian interaction terms. We focus on the case where the interaction terms have certain structures, such that a ruled surface emerges naturally when taking a convex hull of Π. We show that, a ruled surface on ∂Θ sitting in Π has a gapless origin, otherwise it has a symmetry breaking origin. As an example, we demonstrate that a famous ruled surface, known as the oloid, is a possible shape of Θ, with two boundary pieces of symmetry breaking origin separated by two gapless lines.
Generalization of the Kohn-Sham system enabling representing arbitary one electron density matrices
van Dam, Hubertus J J
2015-01-01
Density functional theory is currently the most widely applied method in electronic structure theory. The Kohn-Sham method, based on a fictitious system of non-interacting particles, is the work horse of the theory. The particular form of the Kohn-Sham wavefunction admits only idem-potent one electron density matrices whereas wavefunctions of correlated electrons in post-Hartree-Fock methods invariably have fractional occupation numbers. Here we show that by generalizing the orbital concept, and introducing a suitable dot-product as well as a probability density a non-interacting system can be chosen that can represent the one-electron density matrix of any system, even one with fractional occupation numbers. This fictitious system ensures that the exact electron density is accessible within density functional theory. It can also serve as the basis for reduced density matrix functional theory. Moreover, to aid the analysis of the results the orbitals may be assigned energies from a mean-field Hamiltonian. Thi...
Chen, Xin; Cao, Jianshu; Silbey, Robert J
2013-06-14
The recent experimental discoveries about excitation energy transfer (EET) in light harvesting antenna (LHA) attract a lot of interest. As an open non-equilibrium quantum system, the EET demands more rigorous theoretical framework to understand the interaction between system and environment and therein the evolution of reduced density matrix. A phonon is often used to model the fluctuating environment and convolutes the reduced quantum system temporarily. In this paper, we propose a novel way to construct complex-valued Gaussian processes to describe thermal quantum phonon bath exactly by converting the convolution of influence functional into the time correlation of complex Gaussian random field. Based on the construction, we propose a rigorous and efficient computational method, the covariance decomposition and conditional propagation scheme, to simulate the temporarily entangled reduced system. The new method allows us to study the non-Markovian effect without perturbation under the influence of different spectral densities of the linear system-phonon coupling coefficients. Its application in the study of EET in the Fenna-Matthews-Olson model Hamiltonian under four different spectral densities is discussed. Since the scaling of our algorithm is linear due to its Monte Carlo nature, the future application of the method for large LHA systems is attractive. In addition, this method can be used to study the effect of correlated initial condition on the reduced dynamics in the future.
Weiss, Emily A; Katz, Gil; Goldsmith, Randall H; Wasielewski, Michael R; Ratner, Mark A; Kosloff, Ronnie; Nitzan, Abraham
2006-02-21
We simulate the effects of two types of dephasing processes, a nonlocal dephasing of system eigenstates and a dephasing of semilocal eigenstates, on the rate and mechanism of electron transfer (eT) through a series of donor-bridge-acceptor systems, D-B(N)-A, where N is the number of identical bridge units. Our analytical and numerical results show that pure dephasing, defined as the perturbation of system eigenstates through the system-bath interaction, does not disrupt coherent eT because it induces no localization; electron transfer may proceed through superexchange in a system undergoing only pure dephasing. A more physically reasonable description may be obtained via a system-bath interaction that reflects the perturbation of more local electronic structure by local nuclear distortions and dipole interactions. The degree of locality of this interaction is guided by the structure of the system Hamiltonian and by the nature of the measurement performed on the system (i.e., the nature of the environment). We compare our result from this "semilocal" model with an even more local phenomenological dephasing model. We calculate electron transfer rate by obtaining nonequilibrium steady-state solutions for the elements of a reduced density matrix; a semigroup formalism is used to write down the dissipative part of the equation of motion.
Barth, A. M.; Vagov, A.; Axt, V. M.
2016-09-01
We present a numerical path-integral iteration scheme for the low-dimensional reduced density matrix of a time-dependent quantum dissipative system. Our approach simultaneously accounts for the combined action of a microscopically modeled pure-dephasing-type coupling to a continuum of harmonic oscillators representing, e.g., phonons, and further environmental interactions inducing non-Hamiltonian dynamics in the inner system represented, e.g., by Lindblad-type dissipation or relaxation. Our formulation of the path-integral method allows for a numerically exact treatment of the coupling to the oscillator modes and moreover is general enough to provide a natural way to include Markovian processes that are sufficiently described by rate equations. We apply this new formalism to a model of a single semiconductor quantum dot which includes the coupling to longitudinal acoustic phonons for two cases: (a) external laser excitation taking into account a phenomenological radiative decay of the excited dot state and (b) a coupling of the quantum dot to a single mode of an optical cavity taking into account cavity photon losses.
Quantum entanglement in condensed matter systems
Laflorencie, Nicolas
2016-08-01
This review focuses on the field of quantum entanglement applied to condensed matter physics systems with strong correlations, a domain which has rapidly grown over the last decade. By tracing out part of the degrees of freedom of correlated quantum systems, useful and non-trivial information can be obtained through the study of the reduced density matrix, whose eigenvalue spectrum (the entanglement spectrum) and the associated Rényi entropies are now well recognized to contain key features. In particular, the celebrated area law for the entanglement entropy of ground-states will be discussed from the perspective of its subleading corrections which encode universal details of various quantum states of matter, e.g. symmetry breaking states or topological order. Going beyond entropies, the study of the low-lying part of the entanglement spectrum also allows to diagnose topological properties or give a direct access to the excitation spectrum of the edges, and may also raise significant questions about the underlying entanglement Hamiltonian. All these powerful tools can be further applied to shed some light on disordered quantum systems where impurity/disorder can conspire with quantum fluctuations to induce non-trivial effects. Disordered quantum spin systems, the Kondo effect, or the many-body localization problem, which have all been successfully (re)visited through the prism of quantum entanglement, will be discussed in detail. Finally, the issue of experimental access to entanglement measurement will be addressed, together with its most recent developments.
Yan, YiJing
2014-02-07
This work establishes a strongly correlated system-and-bath dynamics theory, the many-dissipaton density operators formalism. It puts forward a quasi-particle picture for environmental influences. This picture unifies the physical descriptions and algebraic treatments on three distinct classes of quantum environments, electron bath, phonon bath, and two-level spin or exciton bath, as their participating in quantum dissipation processes. Dynamical variables for theoretical description are no longer just the reduced density matrix for system, but remarkably also those for quasi-particles of bath. The present theoretical formalism offers efficient and accurate means for the study of steady-state (nonequilibrium and equilibrium) and real-time dynamical properties of both systems and hybridizing environments. It further provides universal evaluations, exact in principle, on various correlation functions, including even those of environmental degrees of freedom in coupling with systems. Induced environmental dynamics could be reflected directly in experimentally measurable quantities, such as Fano resonances and quantum transport current shot noise statistics.
Quantum dissipation in unbounded systems.
Maddox, Jeremy B; Bittner, Eric R
2002-02-01
In recent years trajectory based methodologies have become increasingly popular for evaluating the time evolution of quantum systems. A revival of the de Broglie--Bohm interpretation of quantum mechanics has spawned several such techniques for examining quantum dynamics from a hydrodynamic perspective. Using techniques similar to those found in computational fluid dynamics one can construct the wave function of a quantum system at any time from the trajectories of a discrete ensemble of hydrodynamic fluid elements (Bohm particles) which evolve according to nonclassical equations of motion. Until very recently these schemes have been limited to conservative systems. In this paper, we present our methodology for including the effects of a thermal environment into the hydrodynamic formulation of quantum dynamics. We derive hydrodynamic equations of motion from the Caldeira-Leggett master equation for the reduced density matrix and give a brief overview of our computational scheme that incorporates an adaptive Lagrangian mesh. Our applications focus upon the dissipative dynamics of open unbounded quantum systems. Using both the Wigner phase space representation and the linear entropy, we probe the breakdown of the Markov approximation of the bath dynamics at low temperatures. We suggest a criteria for rationalizing the validity of the Markov approximation in open unbound systems and discuss decoherence, energy relaxation, and quantum/classical correspondence in the context of the Bohmian paths.
Entangled spins and ghost-spins
Jatkar, Dileep P
2016-01-01
We study patterns of quantum entanglement in systems of spins and ghost-spins regarding them as simple quantum mechanical toy models for theories containing negative norm states. We define a single ghost-spin as in arXiv:1602.06505 [hep-th] as a 2-state spin variable with an indefinite inner product in the state space. We find that whenever the spin sector is disentangled from the ghost-spin sector (both of which could be entangled within themselves), the reduced density matrix obtained by tracing over all the ghost-spins gives rise to positive entanglement entropy for positive norm states, while negative norm states have an entanglement entropy with a negative real part and a constant imaginary part. However when the spins are entangled with the ghost-spins, there are new entanglement patterns in general. For systems where the number of ghost-spins is even, it is possible to find subsectors of the Hilbert space where positive norm states always lead to positive entanglement entropy after tracing over the gho...
Dissipative dynamics of superconducting hybrid qubit systems
Energy Technology Data Exchange (ETDEWEB)
Montes, Enrique; Calero, Jesus M; Reina, John H, E-mail: enriquem@univalle.edu.c, E-mail: j.reina-estupinan@physics.ox.ac.u [Departamento de Fisica, Universidad del Valle, A.A. 25360, Cali (Colombia)
2009-05-01
We perform a theoretical study of composed superconducting qubit systems for the case of a coupled qubit configuration based on a hybrid qubit circuit made of both charge and phase qubits, which are coupled via a sigma{sub x} x sigma{sub z} interaction. We compute the system's eigen-energies in terms of the qubit transition frequencies and the strength of the inter-qubit coupling, and describe the sensitivity of the energy crossing/anti-crossing features to such coupling. We compute the hybrid system's dissipative dynamics for the cases of i) collective and ii) independent decoherence, whereby the system interacts with one common and two different baths of harmonic oscillators, respectively. The calculations have been performed within the Bloch-Redfield formalism and we report the solutions for the populations and the coherences of the system's reduced density matrix. The dephasing and relaxation rates are explicitly calculated as a function of the heat bath temperature.
Quantum entanglement between electronic and vibrational degrees of freedom in molecules.
McKemmish, Laura K; McKenzie, Ross H; Hush, Noel S; Reimers, Jeffrey R
2011-12-28
We consider the quantum entanglement of the electronic and vibrational degrees of freedom in molecules with tendencies towards double welled potentials. In these bipartite systems, the von Neumann entropy of the reduced density matrix is used to quantify the electron-vibration entanglement for the lowest two vibronic wavefunctions obtained from a model Hamiltonian based on coupled harmonic diabatic potential-energy surfaces. Significant entanglement is found only in the region in which the ground vibronic state contains a density profile that is bimodal (i.e., contains two separate local maxima). However, in this region two distinct types of density and entanglement profiles are found: one type arises purely from the degeneracy of energy levels in the two potential wells and is destroyed by slight asymmetry, while the other arises through strong interactions between the diabatic levels of each well and is relatively insensitive to asymmetry. These two distinct types are termed fragile degeneracy-induced entanglement and persistent entanglement, respectively. Six classic molecular systems describable by two diabatic states are considered: ammonia, benzene, BNB, pyridine excited triplet states, the Creutz-Taube ion, and the radical cation of the "special pair" of chlorophylls involved in photosynthesis. These chemically diverse systems are all treated using the same general formalism and the nature of the entanglement that they embody is elucidated.
Photonic Bell states creation around rotating black holes
Racorean, Ovidiu
2016-01-01
We argue that spinning black holes are capable to implement complex quantum information processes encoded in X-ray photons emitted by the accretion disk. Recently, numerical simulations showed that X-ray photons emitted by accretion disk acquire rotation of polarization angle and orbital angular momentum due to strong gravitational field in the vicinity of the rotating black holes. Based on these two degrees of freedom we construct a bipartite two-level quantum system of the photons emitted by the accretion disk. To characterize the quantum states of this system we consider linear entropy for the reduced density matrix of polarization with the intention to exploit its direct relation with the photons degree of polarization. Since the X-ray radiation has a minimum degree of polarization located at the transition region of the accretion disk, the linear entropy is higher for the photons emitted on this region inferring a higher degree of entanglement for the composite system. We emphasize that for an extreme ro...
Tzeng, Yu-Chin; Dai, Li; Chung, Ming-Chiang; Amico, Luigi; Kwek, Leong-Chuan
2016-05-24
We study the entanglement structure and the topological edge states of the ground state of the spin-1/2 XXZ model with bond alternation. We employ parity-density matrix renormalization group with periodic boundary conditions. The finite-size scaling of Rényi entropies S2 and S∞ are used to construct the phase diagram of the system. The phase diagram displays three possible phases: Haldane type (an example of symmetry protected topological ordered phases), Classical Dimer and Néel phases, the latter bounded by two continuous quantum phase transitions. The entanglement and non-locality in the ground state are studied and quantified by the entanglement convertibility. We found that, at small spatial scales, the ground state is not convertible within the topological Haldane dimer phase. The phenomenology we observe can be described in terms of correlations between edge states. We found that the entanglement spectrum also exhibits a distinctive response in the topological phase: the effective rank of the reduced density matrix displays a specifically large "susceptibility" in the topological phase. These findings support the idea that although the topological order in the ground state cannot be detected by local inspection, the ground state response at local scale can tell the topological phases apart from the non-topological phases.
Jacobs, Verne
2016-05-01
Semi-classical and quantum-field descriptions for the interaction of light with matter are systematically discussed. Applications of interest include resonant pump-probe optical phenomena, such as electromagnetically induced transparency. In the quantum-mechanical description of matter systems, we introduce a general reduced-density-matrix framework. Time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations are developed in a unified and self-consistent manner, using a Liouville-space operator representation. In the semi-classical description, the electromagnetic field is described as a classical field satisfying the Maxwell equations. Compact Liouville-space operator expressions are derived for the linear and the general (n'th order) non-linear electromagnetic-response tensors describing moving many-electron systems. The tetradic matrix elements of the Liouville-space self-energy operators are evaluated for environmental collisional and radiative interactions. The quantized-field approach is essential for a fully self-consistent quantum-mechanical description. Work supported by the Office of Naval Research through the Basic Research Program at The Naval Research Laboratory.
DMRG-CASPT2 study of the longitudinal static second hyperpolarizability of all-trans polyenes
Wouters, Sebastian; Van Speybroeck, Veronique; Van Neck, Dimitri
2016-08-01
We have implemented internally contracted complete active space second order perturbation theory (CASPT2) with the density matrix renormalization group (DMRG) as active space solver [Y. Kurashige and T. Yanai, J. Chem. Phys. 135, 094104 (2011)]. Internally contracted CASPT2 requires to contract the generalized Fock matrix with the 4-particle reduced density matrix (4-RDM) of the reference wavefunction. The required 4-RDM elements can be obtained from 3-particle reduced density matrices (3-RDM) of different wavefunctions, formed by symmetry-conserving single-particle excitations op top of the reference wavefunction. In our spin-adapted DMRG code chemps2 https://github.com/sebwouters/chemps2, we decompose these excited wavefunctions as spin-adapted matrix product states and calculate their 3-RDM in order to obtain the required contraction of the generalized Fock matrix with the 4-RDM of the reference wavefunction. In this work, we study the longitudinal static second hyperpolarizability of all-trans polyenes C2nH2n+2 [n = 4-12] in the cc-pVDZ basis set. DMRG-SCF and DMRG-CASPT2 yield substantially lower values and scaling with system size compared to RHF and MP2, respectively.
Approximate but accurate quantum dynamics from the Mori formalism: I. Nonequilibrium dynamics.
Montoya-Castillo, Andrés; Reichman, David R
2016-05-14
We present a formalism that explicitly unifies the commonly used Nakajima-Zwanzig approach for reduced density matrix dynamics with the more versatile Mori theory in the context of nonequilibrium dynamics. Employing a Dyson-type expansion to circumvent the difficulty of projected dynamics, we obtain a self-consistent equation for the memory kernel which requires only knowledge of normally evolved auxiliary kernels. To illustrate the properties of the current approach, we focus on the spin-boson model and limit our attention to the use of a simple and inexpensive quasi-classical dynamics, given by the Ehrenfest method, for the calculation of the auxiliary kernels. For the first time, we provide a detailed analysis of the dependence of the properties of the memory kernels obtained via different projection operators, namely, the thermal (Redfield-type) and population based (NIBA-type) projection operators. We further elucidate the conditions that lead to short-lived memory kernels and the regions of parameter space to which this program is best suited. Via a thorough analysis of the different closures available for the auxiliary kernels and the convergence properties of the self-consistently extracted memory kernel, we identify the mechanisms whereby the current approach leads to a significant improvement over the direct usage of standard semi- and quasi-classical dynamics.
Rukhlenko, Ivan D; Fedorov, Anatoly V; Baymuratov, Anvar S; Premaratne, Malin
2011-08-01
We develop a low-temperature theory of quasi-elastic secondary emission from a semiconductor quantum dot, the electronic subsystem of which is resonant with the confined longitudinal-optical (LO) phonon modes. Our theory employs a generalized model for renormalization of the quantum dot's energy spectrum, which is induced by the polar electron-phonon interaction. The model takes into account the degeneration of electronic states and allows for several LO-phonon modes to be involved in the vibrational resonance. We give solutions to three fundamental problems of energy-spectrum renormalization--arising if one, two, or three LO-phonon modes resonantly couple a pair of electronic states--and discuss the most general problem of this kind that admits an analytical solution. With these results, we solve the generalized master equation for the reduced density matrix, in order to derive an expression for the differential cross section of secondary emission from a single quantum dot. The obtained expression is then analyzed to establish the basics of optical spectroscopy for measuring fundamental parameters of the quantum dot's polaron-like states.
Kidon, Lyran; Wilner, Eli Y; Rabani, Eran
2015-12-21
The generalized quantum master equation provides a powerful tool to describe the dynamics in quantum impurity models driven away from equilibrium. Two complementary approaches, one based on Nakajima-Zwanzig-Mori time-convolution (TC) and the other on the Tokuyama-Mori time-convolutionless (TCL) formulations provide a starting point to describe the time-evolution of the reduced density matrix. A key in both approaches is to obtain the so called "memory kernel" or "generator," going beyond second or fourth order perturbation techniques. While numerically converged techniques are available for the TC memory kernel, the canonical approach to obtain the TCL generator is based on inverting a super-operator in the full Hilbert space, which is difficult to perform and thus, nearly all applications of the TCL approach rely on a perturbative scheme of some sort. Here, the TCL generator is expressed using a reduced system propagator which can be obtained from system observables alone and requires the calculation of super-operators and their inverse in the reduced Hilbert space rather than the full one. This makes the formulation amenable to quantum impurity solvers or to diagrammatic techniques, such as the nonequilibrium Green's function. We implement the TCL approach for the resonant level model driven away from equilibrium and compare the time scales for the decay of the generator with that of the memory kernel in the TC approach. Furthermore, the effects of temperature, source-drain bias, and gate potential on the TCL/TC generators are discussed.
Thermality and excited state R\\'enyi entropy in two-dimensional CFT
Lin, Feng-Li; Zhang, Jia-ju
2016-01-01
We evaluate one-interval R\\'enyi entropy and entanglement entropy for the excited states of two-dimensional conformal field theory (CFT) on a cylinder, and examine their differences from the ones for the thermal state. We assume the interval to be short so that we can use operator product expansion (OPE) of twist operators to calculate R\\'enyi entropy in terms of sum of one-point functions of OPE blocks. We find that the entanglement entropy for highly excited state and thermal state behave the same way after appropriate identification of the conformal weight of the state with the temperature. However, there exists no such universal identification for the R\\'enyi entropy in the short-interval expansion. Therefore, the highly excited state does not look thermal when comparing its R\\'enyi entropy to the thermal state one. As the R\\'enyi entropy captures the higher moments of the reduced density matrix but the entanglement entropy only the average, our results imply that the emergence of thermality depends on ho...
Quantum correlations and coherence in spin-1 Heisenberg chains
Malvezzi, A. L.; Karpat, G.; ćakmak, B.; Fanchini, F. F.; Debarba, T.; Vianna, R. O.
2016-05-01
We explore quantum and classical correlations along with coherence in the ground states of spin-1 Heisenberg chains, namely the one-dimensional XXZ model and the one-dimensional bilinear biquadratic model, with the techniques of density matrix renormalization group theory. Exploiting the tools of quantum information theory, that is, by studying quantum discord, quantum mutual information, and three recently introduced coherence measures in the reduced density matrix of two nearest neighbor spins in the bulk, we investigate the quantum phase transitions and special symmetry points in these models. We point out the relative strengths and weaknesses of correlation and coherence measures as figures of merit to witness the quantum phase transitions and symmetry points in the considered spin-1 Heisenberg chains. In particular, we demonstrate that, as none of the studied measures can detect the infinite-order Kosterlitz-Thouless transition in the XXZ model, they appear to be able to signal the existence of the same type of transition in the biliear biquadratic model. However, we argue that what is actually detected by the measures here is the SU(3) symmetry point of the model rather than the infinite-order quantum phase transition. Moreover, we show in the XXZ model that examining even single site coherence can be sufficient to spotlight the second-order phase transition and the SU(2) symmetry point.
Entanglement, decoherence and thermal relaxation in exactly solvable models
Lychkovskiy, Oleg
2011-01-01
Exactly solvable models provide an opportunity to study different aspects of reduced quantum dynamics in detail. We consider the reduced dynamics of a single spin in finite XX and XY spin 1/2 chains. First we introduce a general expression describing the evolution of the reduced density matrix. This expression proves to be tractable when the combined closed system (i.e. open system plus environment) is integrable. Then we focus on comparing decoherence and thermalization timescales in the XX chain. We find that for a single spin these timescales are comparable, in contrast to what should be expected for a macroscopic body. This indicates that the process of quantum relaxation of a system with few accessible states can not be separated in two distinct stages - decoherence and thermalization. Finally, we turn to finite-size effects in the time evolution of a single spin in the XY chain. We observe three consecutive stages of the evolution: regular evolution, partial revivals, irregular (apparently chaotic) evol...
London, Jack W; Balestrucci, Luanne; Chatterjee, Devjani; Zhan, Tingting
2013-01-01
Background Many cancer interventional clinical trials are not completed because the required number of eligible patients are not enrolled. Objective To assess the value of using a research data mart (RDM) during the design of cancer clinical trials as a predictor of potential patient accrual, so that less trials fail to meet enrollment requirements. Materials and methods The eligibility criteria for 90 interventional cancer trials were translated into i2b2 RDM queries and cohort sizes obtained for the 2 years prior to the trial initiation. These RDM cohort numbers were compared to the trial accrual requirements, generating predictions of accrual success. These predictions were then compared to the actual accrual performance to evaluate the ability of this methodology to predict the trials’ likelihood of enrolling sufficient patients. Results Our methodology predicted successful accrual (specificity) with 0.969 (=31/32 trials) accuracy (95% CI 0.908 to 1) and predicted failed accrual (sensitivity) with 0.397 (=23/58 trials) accuracy (95% CI 0.271 to 0.522). The positive predictive value, or precision rate, is 0.958 (=23/24) (95% CI 0.878 to 1). Discussion A prediction of ‘failed accrual’ by this methodology is very reliable, whereas a prediction of accrual success is less so, as causes of accrual failure other than an insufficient eligible patient pool are not considered. Conclusions The application of this methodology to cancer clinical design would significantly improve cancer clinical research by reducing the costly efforts expended initiating trials that predictably will fail to meet accrual requirements. PMID:23851466
Generalized isotropic Lipkin-Meshkov-Glick models: ground state entanglement and quantum entropies
Carrasco, José A.; Finkel, Federico; González-López, Artemio; Rodríguez, Miguel A.; Tempesta, Piergiulio
2016-03-01
We introduce a new class of generalized isotropic Lipkin-Meshkov-Glick models with \\text{su}(m+1) spin and long-range non-constant interactions, whose non-degenerate ground state is a Dicke state of \\text{su}(m+1) type. We evaluate in closed form the reduced density matrix of a block of L spins when the whole system is in its ground state, and study the corresponding von Neumann and Rényi entanglement entropies in the thermodynamic limit. We show that both of these entropies scale as alog L when L tends to infinity, where the coefficient a is equal to (m - k)/2 in the ground state phase with k vanishing \\text{su}(m+1) magnon densities. In particular, our results show that none of these generalized Lipkin-Meshkov-Glick models are critical, since when L\\to ∞ their Rényi entropy R q becomes independent of the parameter q. We have also computed the Tsallis entanglement entropy of the ground state of these generalized \\text{su}(m+1) Lipkin-Meshkov-Glick models, finding that it can be made extensive by an appropriate choice of its parameter only when m-k≥slant 3 . Finally, in the \\text{su}(3) case we construct in detail the phase diagram of the ground state in parameter space, showing that it is determined in a simple way by the weights of the fundamental representation of \\text{su}(3) . This is also true in the \\text{su}(m+1) case; for instance, we prove that the region for which all the magnon densities are non-vanishing is an (m + 1)-simplex in {{{R}}m} whose vertices are the weights of the fundamental representation of \\text{su}(m+1) .
Random pure states: Quantifying bipartite entanglement beyond the linear statistics.
Vivo, Pierpaolo; Pato, Mauricio P; Oshanin, Gleb
2016-05-01
We analyze the properties of entangled random pure states of a quantum system partitioned into two smaller subsystems of dimensions N and M. Framing the problem in terms of random matrices with a fixed-trace constraint, we establish, for arbitrary N≤M, a general relation between the n-point densities and the cross moments of the eigenvalues of the reduced density matrix, i.e., the so-called Schmidt eigenvalues, and the analogous functionals of the eigenvalues of the Wishart-Laguerre ensemble of the random matrix theory. This allows us to derive explicit expressions for two-level densities, and also an exact expression for the variance of von Neumann entropy at finite N,M. Then, we focus on the moments E{K^{a}} of the Schmidt number K, the reciprocal of the purity. This is a random variable supported on [1,N], which quantifies the number of degrees of freedom effectively contributing to the entanglement. We derive a wealth of analytical results for E{K^{a}} for N=2 and 3 and arbitrary M, and also for square N=M systems by spotting for the latter a connection with the probability P(x_{min}^{GUE}≥sqrt[2N]ξ) that the smallest eigenvalue x_{min}^{GUE} of an N×N matrix belonging to the Gaussian unitary ensemble is larger than sqrt[2N]ξ. As a by-product, we present an exact asymptotic expansion for P(x_{min}^{GUE}≥sqrt[2N]ξ) for finite N as ξ→∞. Our results are corroborated by numerical simulations whenever possible, with excellent agreement.
Cui, Ping
) systems, and its closely related solvation mode transformation of system-bath coupling Hamiltonian in general. The exact QDT of DBO systems is also used to clarify the validity of conventional QDT formulations that involve Markovian approximation. In Chapter 3, we develop three nonequivalent but all complete second-order QDT (CS-QDT) formulations. Two of them are of the conventional prescriptions in terms of time-local dissipation and memory kernel, respectively. The third one is called the correlated driving-dissipation equations of motion (CODDE). This novel CS-QDT combines the merits of the former two for its advantages in both the application and numerical implementation aspects. Also highlighted is the importance of correlated driving-dissipation effects on the dynamics of the reduced system. In Chapter 4, we construct an exact QDT formalism via the calculus on path integrals. The new theory aims at the efficient evaluation of non-Markovian dissipation beyond the weak system-bath interaction regime in the presence of time-dependent external field. By adopting exponential-like expansions for bath correlation function, hierarchical equations of motion formalism and continued fraction Liouville-space Green's function formalism are established. The latter will soon be used together with the Dyson equation technique for an efficient evaluation of non-perturbative reduced density matrix dynamics. The interplay between system-bath interaction strength, non-Markovian property, and the required level of hierarchy is also studied with the aid of simple spin-boson systems, together with the three proposed schemes to truncate the infinite hierarchy. In Chapter 5, we develop a nonperturbative theory of electron transfer (ET) in Debye solvents. The resulting exact and analytical rate expression is constructed on the basis of the aforementioned continued fraction Liouville-space Green's function formalism, together with the Dyson equation technique. Not only does it recover the
Chou, Chung-Hsien; Yu, Ting; Hu, B L
2008-01-01
In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment at arbitrary temperature made up of many harmonic oscillators with a general spectral density function. We first show a simple derivation based on the observation that the two harmonic oscillator model can be effectively mapped into that of a single harmonic oscillator in a general environment plus a free harmonic oscillator. Since the exact one harmonic oscillator master equation is available [B. L. Hu, J. P. Paz, and Y. Zhang, Phys. Rev. D 45, 2843 (1992)], the exact master equation with all its coefficients for this two harmonic oscillator model can be easily deduced from the known results of the single harmonic oscillator case. In the second part we give an influence functional treatment of this model and provide explicit expressions for the evolutionary operator of the reduced density matrix which are useful for the study of decoherence and disentanglement issues. We show three applications of this master equation: on the decoherence and disentanglement of two harmonic oscillators due to their interaction with a common environment under Markovian approximation, and a derivation of the uncertainty principle at finite temperature for a composite object, modeled by two interacting harmonic oscillators. The exact master equation for two, and its generalization to N, harmonic oscillators interacting with a general environment are expected to be useful for the analysis of quantum coherence, entanglement, fluctuations, and dissipation of mesoscopic objects toward the construction of a theoretical framework for macroscopic quantum phenomena.
Density matrix treatment of non-adiabatic photoinduced electron transfer at a semiconductor surface.
Micha, David A
2012-12-14
Photoinduced electron transfer at a nanostructured surface leads to localized transitions and involves three different types of non-adiabatic couplings: vertical electronic transitions induced by light absorption emission, coupling of electronic states by the momentum of atomic motions, and their coupling due to interactions with electronic density fluctuations and vibrational motions in the substrate. These phenomena are described in a unified way by a reduced density matrix (RDM) satisfying an equation of motion that contains dissipative rates. The RDM treatment is used here to distinguish non-adiabatic phenomena that are localized from those due to interaction with a medium. The fast decay of localized state populations due to electronic density fluctuations in the medium has been treated within the Lindblad formulation of rates. The formulation is developed introducing vibronic states constructed from electron orbitals available from density functional calculations, and from vibrational states describing local atomic displacements. Related ab initio molecular dynamics calculations have provided diabatic momentum couplings between excited electronic states. This has been done in detail for an indirect photoexcitation mechanism of the surface Ag(3)Si(111):H, which leads to long lasting electronic charge separation. The resulting coupled density matrix equations are solved numerically to obtain the population of the final charge-separated state as it changes over time, for several values of the diabatic momentum coupling. New insight and unexpected results are presented here which can be understood in terms of photoinduced non-adiabatic transitions involving many vibronic states. It is found that the population of long lasting charge separation states is larger for smaller momentum coupling, and that their population grows faster for smaller coupling.
Energy Technology Data Exchange (ETDEWEB)
Kidon, Lyran [School of Chemistry, The Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978 (Israel); The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978 (Israel); Wilner, Eli Y. [School of Physics and Astronomy, The Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978 (Israel); Rabani, Eran [The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978 (Israel); Department of Chemistry, University of California and Lawrence Berkeley National Laboratory, Berkeley California 94720-1460 (United States)
2015-12-21
The generalized quantum master equation provides a powerful tool to describe the dynamics in quantum impurity models driven away from equilibrium. Two complementary approaches, one based on Nakajima–Zwanzig–Mori time-convolution (TC) and the other on the Tokuyama–Mori time-convolutionless (TCL) formulations provide a starting point to describe the time-evolution of the reduced density matrix. A key in both approaches is to obtain the so called “memory kernel” or “generator,” going beyond second or fourth order perturbation techniques. While numerically converged techniques are available for the TC memory kernel, the canonical approach to obtain the TCL generator is based on inverting a super-operator in the full Hilbert space, which is difficult to perform and thus, nearly all applications of the TCL approach rely on a perturbative scheme of some sort. Here, the TCL generator is expressed using a reduced system propagator which can be obtained from system observables alone and requires the calculation of super-operators and their inverse in the reduced Hilbert space rather than the full one. This makes the formulation amenable to quantum impurity solvers or to diagrammatic techniques, such as the nonequilibrium Green’s function. We implement the TCL approach for the resonant level model driven away from equilibrium and compare the time scales for the decay of the generator with that of the memory kernel in the TC approach. Furthermore, the effects of temperature, source-drain bias, and gate potential on the TCL/TC generators are discussed.
Decision theory and information propagation in quantum physics
Forrester, Alan
In recent papers, Zurek [(2005). Probabilities from entanglement, Born's rule p k =| ψ k | 2 from entanglement. Physical Review A, 71, 052105] has objected to the decision-theoretic approach of Deutsch [(1999) Quantum theory of probability and decisions. Proceedings of the Royal Society of London A, 455, 3129-3137] and Wallace [(2003). Everettian rationality: defending Deutsch's approach to probability in the Everett interpretation. Studies in History and Philosophy of Modern Physics, 34, 415-438] to deriving the Born rule for quantum probabilities on the grounds that it courts circularity. Deutsch and Wallace assume that the many worlds theory is true and that decoherence gives rise to a preferred basis. However, decoherence arguments use the reduced density matrix, which relies upon the partial trace and hence upon the Born rule for its validity. Using the Heisenberg picture and quantum Darwinism-the notion that classical information is quantum information that can proliferate in the environment pioneered in Ollivier et al. [(2004). Objective properties from subjective quantum states: Environment as a witness. Physical Review Letters, 93, 220401 and (2005). Environment as a witness: Selective proliferation of information and emergence of objectivity in a quantum universe. Physical Review A, 72, 042113]-I show that measurement interactions between two systems only create correlations between a specific set of commuting observables of system 1 and a specific set of commuting observables of system 2. This argument picks out a unique basis in which information flows in the correlations between those sets of commuting observables. I then derive the Born rule for both pure and mixed states and answer some other criticisms of the decision theoretic approach to quantum probability.
Navrotskaya, Irina; Soudackov, Alexander V; Hammes-Schiffer, Sharon
2008-06-28
An extension of the Anderson-Newns-Schmickler model for electrochemical proton-coupled electron transfer (PCET) is presented. This model describes reactions in which electron transfer between a solute complex in solution and an electrode is coupled to proton transfer within the solute complex. The model Hamiltonian is derived in a basis of electron-proton vibronic states defined within a double adiabatic approximation for the electrons, transferring proton, and bath modes. The interaction term responsible for electronic transitions between the solute complex and the electrode depends on the proton donor-acceptor vibrational mode within the solute complex. This model Hamiltonian is used to derive the anodic and cathodic rate constants for nonadiabatic electrochemical PCET. The derivation is based on the master equations for the reduced density matrix of the electron-proton subsystem, which includes the electrons of the solute complex and the electrode, as well as the transferring proton. The rate constant expressions differ from analogous expressions for electrochemical electron transfer because of the summation over electron-proton vibronic states and the dependence of the couplings on the proton donor-acceptor vibrational motion. These differences lead to additional contributions to the total reorganization energy, an additional exponential temperature-dependent prefactor, and a temperature-dependent term in the effective activation energy that has different signs for the anodic and cathodic processes. This model can be generalized to describe both nonadiabatic and adiabatic electrochemical PCET reactions and provides the framework for the inclusion of additional effects, such as the breaking and forming of other chemical bonds.
A heuristic model of damped quantum rotation effects in nuclear magnetic resonance spectra.
Szymański, S
2011-01-28
The damped quantum rotation (DQR) theory describes temperature effects in NMR spectra of hindered molecular rotators composed of identical atoms arranged in regular N-gons. In the standard approach, the relevant coherent dynamics are described quantum mechanically and the stochastic, thermally activated motions classically. The DQR theory is consistent. In place of random jumps over one, two, etc., maxima of the hindering potential, here one has damping processes of certain long-lived coherences between spin-space correlated eigenstates of the rotator. The damping-rate constants outnumber the classical jump-rate constants. The jump picture is recovered when the former cluster appropriately around only as many values as the number of the latter. The DQR theory was confirmed experimentally for hindered methyl groups in solids and even in liquids above 170 K. In this paper it is shown that for three-, four-, and sixfold rotators, the Liouville space equations of NMR line shapes, derived previously with the use of the quantum mechanical reduced density matrix approach, can be be given a heuristic justification. It is based on an equation of motion for the effective spin density matrix, where the relevant spin hamiltonian contains randomly fluctuating terms. The occurrence of the latter can be rationalized in terms of fluctuations of the tunneling splittings between the torsional sublevels of the rotator, including momentary liftings of the Kramers degeneracies. The question whether such degeneracy liftings are physical or virtual is discussed. The random terms in the effective hamiltonian can be Monte Carlo modeled as piecewise constant in time, which affords the stochastic equation of motion to be solved numerically in the Hilbert spin space. For sixfold rotators, this way of calculating the spectra can be useful in the instances where the Liouville space formalism of the original DQR theory is numerically unstable.
Theory of Quantum Loschmidt Echoes
Prosen, T.; Seligman, T. H.; Žnidarič, M.
In this paper we review our recent work on the theoretical approach to quantum Loschmidt echoes, i.e., various properties of the so-called echo dynamics -- the composition of forward and backward time evolutions generated by two slightly different Hamiltonians, such as the state autocorrelation function (fidelity) and the purity of a reduced density matrix traced over a subsystem (purity fidelity). Our main theoretical result is a linear response formalism, expressing the fidelity and purity fidelity in terms of integrated time autocorrelation function of the generator of the perturbation. Surprisingly, this relation predicts that the decay of fidelity is the slower the faster the decay of correlations. In particular for a static (time-independent) perturbation, and for non-ergodic and non-mixing dynamics where asymptotic decay of correlations is absent, a qualitatively different and faster decay of fidelity is predicted on a time scale ∝ 1/δ as opposed to mixing dynamics where the fidelity is found to decay exponentially on a time-scale ∝ 1/δ2, where δ is a strength of perturbation. A detailed discussion of a semi-classical regime of small effective values of Planck constant hbar is given where classical correlation functions can be used to predict quantum fidelity decay. Note that the correct and intuitively expected classical stability behavior is recovered in the classical limit hbarto 0, as the two limits δto 0 and hbarto 0 do not commute. The theoretical results are demonstrated numerically for two models, the quantized kicked top and the multi-level Jaynes Cummings model. Our method can for example be applied to the stability analysis of quantum computation and quantum information processing.
Energy Technology Data Exchange (ETDEWEB)
Cotton, Stephen J.; Igumenshchev, Kirill; Miller, William H., E-mail: millerwh@berkeley.edu [Department of Chemistry and Kenneth S. Pitzer Center for Theoretical Chemistry, University of California, and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)
2014-08-28
It has recently been shown [S. J. Cotton and W. H. Miller, J. Chem. Phys. 139, 234112 (2013)] that a symmetrical windowing quasi-classical (SQC) approach [S. J. Cotton and W. H. Miller, J. Phys. Chem. A 117, 7190 (2013)] applied to the Meyer-Miller model [H.-D. Meyer and W. H. Miller, J. Chem. Phys. 70, 3214 (1979)] for the electronic degrees of freedom in electronically non-adiabatic dynamics is capable of quantitatively reproducing quantum mechanical results for a variety of test applications, including cases where “quantum” coherence effects are significant. Here we apply this same SQC methodology, within a flux-side correlation function framework, to calculate thermal rate constants corresponding to several proposed models of electron transfer processes [P. Huo, T. F. Miller III, and D. F. Coker, J. Chem. Phys. 139, 151103 (2013); A. R. Menzeleev, N. Ananth, and T. F. Miller III, J. Chem. Phys. 135, 074106 (2011)]. Good quantitative agreement with Marcus Theory is obtained over several orders of magnitude variation in non-adiabatic coupling. Moreover, the “inverted regime” in thermal rate constants (with increasing bias) known from Marcus Theory is also reproduced with good accuracy by this very simple classical approach. The SQC treatment is also applied to a recent model of photoinduced proton coupled electron transfer [C. Venkataraman, A. V. Soudackov, and S. Hammes-Schiffer, J. Chem. Phys. 131, 154502 (2009)] and population decay of the photoexcited donor state is found to be in reasonable agreement with results calculated via reduced density matrix theory.
Random pure states: Quantifying bipartite entanglement beyond the linear statistics
Vivo, Pierpaolo; Pato, Mauricio P.; Oshanin, Gleb
2016-05-01
We analyze the properties of entangled random pure states of a quantum system partitioned into two smaller subsystems of dimensions N and M . Framing the problem in terms of random matrices with a fixed-trace constraint, we establish, for arbitrary N ≤M , a general relation between the n -point densities and the cross moments of the eigenvalues of the reduced density matrix, i.e., the so-called Schmidt eigenvalues, and the analogous functionals of the eigenvalues of the Wishart-Laguerre ensemble of the random matrix theory. This allows us to derive explicit expressions for two-level densities, and also an exact expression for the variance of von Neumann entropy at finite N ,M . Then, we focus on the moments E {Ka} of the Schmidt number K , the reciprocal of the purity. This is a random variable supported on [1 ,N ] , which quantifies the number of degrees of freedom effectively contributing to the entanglement. We derive a wealth of analytical results for E {Ka} for N =2 and 3 and arbitrary M , and also for square N =M systems by spotting for the latter a connection with the probability P (xminGUE≥√{2 N }ξ ) that the smallest eigenvalue xminGUE of an N ×N matrix belonging to the Gaussian unitary ensemble is larger than √{2 N }ξ . As a by-product, we present an exact asymptotic expansion for P (xminGUE≥√{2 N }ξ ) for finite N as ξ →∞ . Our results are corroborated by numerical simulations whenever possible, with excellent agreement.
Characterization of a qubit in presence of dissipation and external driving
Energy Technology Data Exchange (ETDEWEB)
Nesi, F.
2007-07-15
In this PhD thesis we have been concerned with dissipative and decoherence processes which take place specifically for quantum systems in a dissipative bistable potential. This potential describes a Hamiltonian system whose spectrum is composed by a ladder of levels, grouped as doublets under the potential barrier and being almost equally spaced above it. The system interacts with a thermal environment, which in this work has been chosen to be composed by an ensemble of harmonic oscillators. The dynamical quantity we looked at is the so-called reduced density matrix (RDM), obtained by tracing out the full density matrix the environmental degrees of freedom. The Feynman-Vernon real-time path-integral technique is illustrated, where the matrix elements for the RDM are exactly evaluated. Depending on which regime of parameters we are interested in, i.e. temperature and coupling strength with the reservoir, a few or several energy levels contribute to the dynamics. In particular, a two-level system is analyzed. This corresponds to the regime where only the lowest doublet is energetically accessible. The environment enters the dynamics via the bath-correlation function, expressed as an integral over the so-called bath spectral density, which fully characterizes the bath spectrum. Then a wide class of spectral densities is considered. In particular, the case of Ohmic and super-Ohmic spectral densities is discussed and analytical results for the kernels governing the dynamics of the population difference are obtained. Our theory, called Weakly-Interacting Blip Approximation is developed by using the real-time path-integral technique. Finally, we discussed the more general case of an M-level system coupled with an Ohmic environment. This situation describes the case of a bistable potential where the temperature is high enough that higher-lying energy levels are being populated and the system cannot be reduced to a simple TLS. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Roura, Albert [Los Alamos National Laboratory; Fleming, C H [UNIV OF MARYLAND; Hu, B L [UNIV OF MARYLAND
2008-01-01
We revisit the model of a system made up of a Brownian quantum oscillator linearly coupled to an environment made up of many quantum oscillators at finite temperature. We show that the HPZ master equation for the reduced density matrix derived earlier [B.L. Hu, J.P. Paz, Y. Zhang, Phys. Rev. D 45, 2843 (1992)] has incorrectly specified coefficients for the case of nonlocal dissipation. We rederive the QBM master equation, correctly specifying all coefficients, and determine the position uncertainty to be free of excessive cutoff sensitivity. Our coefficients and solutions are reduced entirely to contour integration for analytic spectra at arbitrary temperature, coupling strength, and cut-off. As an illustration we calculate the master equation coefficients and solve the master equation for ohmic coupling (with finite cutoff) and example supra-ohmic and sub-ohmic spectral densities. We determine the effect of an external force on the quantum oscillator and also show that our representation of the master equation and solutions naturally extends to a system of multiple oscillators bilinearly coupled to themselves and the bath in arbitrary fashion. This produces a formula for investigating the standard quantum limit which is central to addressing many theoretical issues in macroscopic quantum phenomena and experimental concerns related to low temperature precision measurements. We find that in a dissipative environment, all initial states settle down to a Gaussian density matrix whose covariance is determined by the thermal reservoir and whose mean is determined by the external force. We specify the thermal covariance for the spectral densities we explore.
Non equilibrium dynamics of mixing, oscillations, and equilibration: A model study
Energy Technology Data Exchange (ETDEWEB)
Ho, Chiu Man; Boyanovsky, D.; Ho, C. M.
2006-12-22
The non-equilibrium dynamics of mixing, oscillations and equilibration is studied in a field theory of flavored neutral mesons that effectively models two flavors of mixed neutrinos, in interaction with other mesons that represent a thermal bath of hadrons or quarks and charged leptons. This model describes the general features of neutrino mixing and relaxation via charged currents in a medium. The reduced density matrix and the non-equilibrium effective action that describes the propagation of neutrinos is obtained by integrating out the bath degrees of freedom. We obtain the dispersion relations, mixing angles and relaxation rates of ``neutrino'' quasiparticles. The dispersion relations and mixing angles are of the same form as those of neutrinos in the medium, and the relaxation rates are given by $\\Gamma_1(k) = \\Gamma_{ee}(k) \\cos^2\\theta_m(k)+\\Gamma_{\\mu\\mu}(k)\\sin^2\\theta_m(k); \\Gamma_2(k)= \\Gamma_{\\mu\\mu}(k) \\cos^2\\theta_m(k)+\\Gamma_{ee}(k)\\sin^2\\theta_m(k) $ where $\\Gamma_{\\alpha\\alpha}(k)$ are the relaxation rates of the flavor fields in \\emph{absence} of mixing, and $\\theta_m(k)$ is the mixing angle in the medium. A Weisskopf-Wigner approximation that describes the asymptotic time evolution in terms of a non-hermitian Hamiltonian is derived. At long time $>>\\Gamma^{-1}_{1,2}$ ``neutrinos'' equilibrate with the bath. The equilibrium density matrix is nearly diagonal in the basis of eigenstates of an \\emph{effective Hamiltonian that includes self-energy corrections in the medium}. The equilibration of ``sterile neutrinos'' via active-sterile mixing is discussed.
Searching for Causality in AdS/CFT
Kelly, William R.
String theory with certain asymptotically AdS boundary conditions can be defined non-perturbatively using the AdS/CFT correspondence, which reformulates the theory in terms of a non-gravitational quantum field theory in a lower dimensional spacetime. In this way many of the subtleties of quantizing gravity are circumvented, however, the price of this simplification is that locality is no longer manifest, even in an approximate sense. In this dissertation we study features of asymptotically AdS spacetimes related to causality and search for these properties in the dual CFT description. We begin by reviewing some of the salient features of the correspondence and studying some puzzles related to the Ryu-Takayanagi conjecture. We then show that the notion of boundary causality associated with the Gao-Wald theorem implies that holographic CFT's on Minkowski space must satisfy the averaged null energy condition (ANEC). The ANEC is a quasilocal energy condition that requires the integrated null energy on a null line to be positive. Any violations of this condition in a holographic theory would result in "causal shortcuts'' through the bulk spacetime which would allow propagation outside of the light cone in the CFT. We next study causal wedges associated with subregions of the boundary and argue that these regions of the bulk spacetime are associated with a particular coarse-graining of the CFT reduced density matrix. In particular, we conjecture that the area of the codimension-two boundary of these wedges is equal to a particular coarse-grained entropy which we name the 'one-point entropy.' We present several suggestive examples in which the conjecture holds as well as a proof that it holds to leading order in a class of spacetimes with a bulk first law. In an appendix we explain how the conjecture is equivalent to a statement about the classical Einstein equation which in principle could be rigorously proven or falsified.
Lee, Mi Kyung; Bravaya, Ksenia B; Coker, David F
2017-06-14
There have been numerous efforts, both experimental and theoretical, that have attempted to parametrize model Hamiltonians to describe excited state energy transfer in photosynthetic light harvesting systems. The Frenkel exciton model, with its set of electronically coupled two level chromophores that are each linearly coupled to dissipative baths of harmonic oscillators, has become the workhorse of this field. The challenges to parametrizing such Hamiltonians have been their uniqueness, and physical interpretation. Here we present a computational approach that uses accurate first-principles electronic structure methods to compute unique model parameters for a collection of local minima that are sampled with molecular dynamics and QM geometry optimization enabling the construction of an ensemble of local models that captures fluctuations as these systems move between local basins of inherent structure. The accuracy, robustness, and reliability of the approach is demonstrated in an application to the phycobiliprotein light harvesting complexes from cryptophyte algae. Our computed Hamiltonian ensemble provides a first-principles description of inhomogeneous broadening processes, and a standard approximate non-Markovian reduced density matrix dynamics description is used to estimate lifetime broadening contributions to the spectral line shape arising from electronic-vibrational coupling. Despite the overbroadening arising from this approximate line shape theory, we demonstrate that our model Hamiltonian ensemble approach is able to provide a reliable fully first-principles method for computation of spectra and can distinguish the influence of different chromophore protonation states in experimental results. A key feature in the dynamics of these systems is the excitation of intrachromophore vibrations upon electronic excitation and energy transfer. We demonstrate that the Hamiltonian ensemble approach provides a reliable first-principles description of these
Modeling the surface photovoltage of silicon slabs with varying thickness.
Vazhappilly, Tijo; Kilin, Dmitri S; Micha, David A
2015-04-10
The variation with thickness of the energy band gap and photovoltage at the surface of a thin semiconductor film are of great interest in connection with their surface electronic structure and optical properties. In this work, the change of a surface photovoltage (SPV) with the number of layers of a crystalline silicon slab is extracted from models based on their atomic structure. Electronic properties of photoexcited slabs are investigated using generalized gradient and hybrid density functionals, and plane wave basis sets. Si(1 1 1) surfaces have been terminated by hydrogen atoms to compensate for dangling bonds and have been described by large supercells with periodic boundary conditions. Calculations of the SPV of the Si slabs have been done in terms of the reduced density matrix of the photoactive electrons including dissipative effects due to their interaction with medium phonons and excitons. Surface photovoltages have been calculated for model Si slabs with 4-12, and 16 layers, to determine convergence trends versus slab thickness. Band gaps and the inverse of the SPVs have been found to scale nearly linearly with the inverse thickness of the slab, while the electronic density of states increases quadratically with thickness. Our calculations show the same trends as experimental values indicating band gap reduction and absorption enhancement for Si films of increasing thickness. Simple arguments on confined electronic structures have been used to explain the main effects of changes with slab thickness. A procedure involving shifted electron excitation energies is described to improve results from generalized gradient functionals so they can be in better agreement with the more accurate but also more computer intensive values from screened exchange hybrid functionals.
Non-Sequential Double Recombination High Harmonic Generation in Molecular-like Systems
DEFF Research Database (Denmark)
Hansen, Kenneth Christian Klochmann; Madsen, Lars Bojer
Non-sequential double recombination (NSDR) high harmonic generation (HHG) is a strongly correlated two-electron HHG process where two electrons combine their potential and kinetic energy into emitting a single photon. We have studied this process in a molecular-like system and found that the two...
Quantum dissipation and decoherence of collective excitations in metallic nanoparticles
Energy Technology Data Exchange (ETDEWEB)
Weick, G.
2006-09-22
The treatment of the surface plasmon as a quantum particle provides a model system for the study of decoherence and quantum dissipation in confined nanoscopic systems, where the role of the electronic correlations is preponderant. Throughout this work we treat the metallic nanoparticle in the jellium approximation where the ionic structure is replaced by a continuous and homogeneous positive charge. The external laser field puts the center of mass into a coherent superposition of its ground and first excited state and thus creates a surface plasmon. The coupling between the center of mass and the relative coordinates causes decoherence and dissipation of this collective excitation. We have developed a theoretical formalism well adapted to the study of this dissipation, which is the reduced-density-matrix formalism. There are mainly two parameters which govern the surface plasmon dynamics: the decay rate of the plasmon, and the resonance frequency. For sizes smaller than 1 nm, presents oscillations as a function of the size. By means of a semiclassical formalism using Gutzwiller's trace formula for the density of states, we have shown that those oscillations are due to the correlations of the density of states of the particles and holes in the nanoparticle. If one considers a noble-metal nanoparticle in an inert matrix, we have shown that a naive application of the Kubo formula for the surface plasmon linewidth fails to reproduce the TDLDA numerical results, which are however consistent with experimental results. We have modified the Kubo theory in order to solve this discrepancy. We have shown, by extending our semiclassical theory to the nonlinear case, that the double plasmon is indeed well defined. We have calculated the lifetime of the double plasmon associated to this second-order effect. In addition to the width, we have also addressed the value of the resonance frequency. The classical electromagnetic Mie theory gives for the resonance frequency of the
Stochastic description of quantum Brownian dynamics
Yan, Yun-An; Shao, Jiushu
2016-08-01
Classical Brownian motion has well been investigated since the pioneering work of Einstein, which inspired mathematicians to lay the theoretical foundation of stochastic processes. A stochastic formulation for quantum dynamics of dissipative systems described by the system-plus-bath model has been developed and found many applications in chemical dynamics, spectroscopy, quantum transport, and other fields. This article provides a tutorial review of the stochastic formulation for quantum dissipative dynamics. The key idea is to decouple the interaction between the system and the bath by virtue of the Hubbard-Stratonovich transformation or Itô calculus so that the system and the bath are not directly entangled during evolution, rather they are correlated due to the complex white noises introduced. The influence of the bath on the system is thereby defined by an induced stochastic field, which leads to the stochastic Liouville equation for the system. The exact reduced density matrix can be calculated as the stochastic average in the presence of bath-induced fields. In general, the plain implementation of the stochastic formulation is only useful for short-time dynamics, but not efficient for long-time dynamics as the statistical errors go very fast. For linear and other specific systems, the stochastic Liouville equation is a good starting point to derive the master equation. For general systems with decomposable bath-induced processes, the hierarchical approach in the form of a set of deterministic equations of motion is derived based on the stochastic formulation and provides an effective means for simulating the dissipative dynamics. A combination of the stochastic simulation and the hierarchical approach is suggested to solve the zero-temperature dynamics of the spin-boson model. This scheme correctly describes the coherent-incoherent transition (Toulouse limit) at moderate dissipation and predicts a rate dynamics in the overdamped regime. Challenging problems
Solano-Altamirano, J. M.; Hernández-Pérez, Julio M.
2015-11-01
DensToolKit is a suite of cross-platform, optionally parallelized, programs for analyzing the molecular electron density (ρ) and several fields derived from it. Scalar and vector fields, such as the gradient of the electron density (∇ρ), electron localization function (ELF) and its gradient, localized orbital locator (LOL), region of slow electrons (RoSE), reduced density gradient, localized electrons detector (LED), information entropy, molecular electrostatic potential, kinetic energy densities K and G, among others, can be evaluated on zero, one, two, and three dimensional grids. The suite includes a program for searching critical points and bond paths of the electron density, under the framework of Quantum Theory of Atoms in Molecules. DensToolKit also evaluates the momentum space electron density on spatial grids, and the reduced density matrix of order one along lines joining two arbitrary atoms of a molecule. The source code is distributed under the GNU-GPLv3 license, and we release the code with the intent of establishing an open-source collaborative project. The style of DensToolKit's code follows some of the guidelines of an object-oriented program. This allows us to supply the user with a simple manner for easily implement new scalar or vector fields, provided they are derived from any of the fields already implemented in the code. In this paper, we present some of the most salient features of the programs contained in the suite, some examples of how to run them, and the mathematical definitions of the implemented fields along with hints of how we optimized their evaluation. We benchmarked our suite against both a freely-available program and a commercial package. Speed-ups of ˜2×, and up to 12× were obtained using a non-parallel compilation of DensToolKit for the evaluation of fields. DensToolKit takes similar times for finding critical points, compared to a commercial package. Finally, we present some perspectives for the future development and
Information carriers and (reading them through) information theory in quantum chemistry.
Geerlings, Paul; Borgoo, Alex
2011-01-21
This Perspective discusses the reduction of the electronic wave function via the second-order reduced density matrix to the electron density ρ(r), which is the key ingredient in density functional theory (DFT) as a basic carrier of information. Simplifying further, the 1-normalized density function turns out to contain essentially the same information as ρ(r) and is even of preferred use as an information carrier when discussing the periodic properties along Mendeleev's table where essentially the valence electrons are at stake. The Kullback-Leibler information deficiency turns out to be the most interesting choice to obtain information on the differences in ρ(r) or σ(r) between two systems. To put it otherwise: when looking for the construction of a functional F(AB) = F[ζ(A)(r),ζ(B)(r)] for extracting differences in information from an information carrier ζ(r) (i.e. ρ(r), σ(r)) for two systems A and B the Kullback-Leibler information measure ΔS is a particularly adequate choice. Examples are given, varying from atoms, to molecules and molecular interactions. Quantum similarity of atoms indicates that the shape function based KL information deficiency is the most appropriate tool to retrieve periodicity in the Periodic Table. The dissimilarity of enantiomers for which different information measures are presented at global and local (i.e. molecular and atomic) level leads to an extension of Mezey's holographic density theorem and shows numerical evidence that in a chiral molecule the whole molecule is pervaded by chirality. Finally Kullback-Leibler information profiles are discussed for intra- and intermolecular proton transfer reactions and a simple S(N)2 reaction indicating that the theoretical information profile can be used as a companion to the energy based Hammond postulate to discuss the early or late transition state character of a reaction. All in all this Perspective's answer is positive to the question of whether an even simpler carrier of
Energy Technology Data Exchange (ETDEWEB)
Appel, H.
2007-05-15
In part I of this work we present a double-pole approximation (DPA) to the response equations of time-dependent density functional theory (TDDFT). The double-pole approximation provides an exact description of systems with two strongly coupled excitations which are isolated from the rest of the spectrum. In contrast to the traditional single-pole approximation of TDDFT the DPA also yields corrections to the Kohn-Sham oscillator strengths. We also demonstrate how to invert the double-pole solution which allows us to predict matrix elements of the exchange-correlation kernel f{sub xc} from experimental input. We attempt some first steps towards a time-dependent generalization of reduced density matrix functional theory (RDMFT). In part II we derive equations of motion for natural orbitals and occupation numbers. Using the equation of motion for the occupation numbers we show that an adiabatic extension of presently known ground-state functionals of static RDMFT always leads to occupation numbers which are constant in time. From the stationary conditions of the equations of motion for the N-body correlations (correlated parts of the N-body matrices) we derive a new class of ground-state functionals which can be used in static RDMFT. Applications are presented for a one-dimensional model system where the time-dependent many-body Schroedinger equation can be propagated numerically. We use optimal control theory to find optimized laser pulses for transitions in a model for atomic Helium. From the numerically exact correlated wavefunction we extract the exact time evolution of natural orbitals and occupation numbers for (i) laser-driven Helium and (ii) electron-ion scattering. Part III of this work considers time-dependent quantum transport within TDDFT. We present an algorithm for the calculation of extended eigenstates of single-particle Hamiltonians which is especially tailored to a finite-difference discretization of the Schroedinger equation. We consider the
Orbital functionals in density-matrix- and current-density-functional theory
Energy Technology Data Exchange (ETDEWEB)
Helbig, N.
2006-05-15
Density-Functional Theory (DFT), although widely used and very successful in the calculation of several observables, fails to correctly describe strongly correlated materials. In the first part of this work we, therefore, introduce reduced-densitymatrix- functional theory (RDMFT) which is one possible way to treat electron correlation beyond DFT. Within this theory the one-body reduced density matrix (1- RDM) is used as the basic variable. Our main interest is the calculation of the fundamental gap which proves very problematic within DFT. In order to calculate the fundamental gap we generalize RDMFT to fractional particle numbers M by describing the system as an ensemble of an N and an N+1 particle system (with N{<=}M{<=}N+1). For each fixed particle number, M, the total energy is minimized with respect to the natural orbitals and their occupation numbers. This leads to the total energy as a function of M. The derivative of this function with respect to the particle number has a discontinuity at integer particle number which is identical to the gap. In addition, we investigate the necessary and sufficient conditions for the 1- RDM of a system with fractional particle number to be N-representable. Numerical results are presented for alkali atoms, small molecules, and periodic systems. Another problem within DFT is the description of non-relativistic many-electron systems in the presence of magnetic fields. It requires the paramagnetic current density and the spin magnetization to be used as basic variables besides the electron density. However, electron-gas-based functionals of current-spin-density-functional Theory (CSDFT) exhibit derivative discontinuities as a function of the magnetic field whenever a new Landau level is occupied, which makes them difficult to use in practice. Since the appearance of Landau levels is, intrinsically, an orbital effect it is appealing to use orbital-dependent functionals. We have developed a CSDFT version of the optimized
Mechanisms of double-electron ionization of atomic systems in a strong laser field.
Popov, A; Tikhonova, O; Volkova, E
2001-03-26
The field-induced double ionization of a model two-electron quantum system is investigated by direct numerical integration of the nonstationary Schroedinger equation. The contribution of different processes to a formation of doubly charged ions is analyzed.
Electron spin separation without magnetic field.
Pawłowski, J; Szumniak, P; Skubis, A; Bednarek, S
2014-08-27
A nanodevice capable of separating spins of two electrons confined in a quantum dot formed in a gated semiconductor nanowire is proposed. Two electrons confined initially in a single quantum dot in the singlet state are transformed into the system of two electrons confined in two spatially separated quantum dots with opposite spins. In order to separate the electrons' spins we exploit transitions between the singlet and the triplet state, which are induced by resonantly oscillating Rashba spin-orbit coupling strength. The proposed device is all electrically controlled and the electron spin separation can be realized within tens of picoseconds. The results are supported by solving numerically the quasi-one-dimensional time-dependent Schroedinger equation for two electrons, where the electron-electron correlations are taken into account in the exact manner.
An All-Optical Quantum Gate in a Semiconductor Quantum Dot
National Research Council Canada - National Science Library
Xiaoqin Li; Yanwen Wu; Duncan Steel; D. Gammon; T. H. Stievater; D. S. Katzer; D. Park; C. Piermarocchi; L. J. Sham
2003-01-01
We report coherent optical control of a biexciton (two electron-hole pairs), confined in a single quantum dot, that shows coherent oscillations similar to the excited-state Rabi flopping in an isolated atom...
A Quantum Dot with Spin-Orbit Interaction--Analytical Solution
Basu, B.; Roy, B.
2009-01-01
The practical applicability of a semiconductor quantum dot with spin-orbit interaction gives an impetus to study analytical solutions to one- and two-electron quantum dots with or without a magnetic field.
Institute of Scientific and Technical Information of China (English)
Tao Haiqiao; Long Jun; Zhou Han; Xie Chaogang; Dai Zhenyu; Wei Xiaoli
2009-01-01
The structure and energy of the carbonium ions formed upon protonation of butane were studied by the DFT methods. Four stable structures are identified for the protonated form of n-butane, the energy increases in the following order: C2HC3C1HC2>C2HH>C1HH. The stability of the penta-enordinated carbonium ions may be explained by the electron distribution in the three-center-two-electron bonds. The delocalization of the penta-eoordinated carbonium ion CHC with three-center-two-electron bonds on positive charges was stronger than that of the penta-coordinated carbonium ion CHH with three-center-two-electron bonds and its stability was higher than that of the penta-coordinated earbonium ion CHH with three-center-two-electron bonds.
Production of high-n strontium Rydberg atoms
Ye, S.; Zhang, X.; Killian, T. C.; Dunning, F. B.; Hiller, M.; Yoshida, S.; Burgdörfer, J.
2014-04-01
The photoexcitation of strontium Rydberg atoms with n ~ 300 is being examined using a crossed laser-atom beam approach to enable study of quasi-stable two-electron excited states and of strongly-coupled Rydberg systems.
349-IJBCS-Article-Adeniyi Adegoke
African Journals Online (AJOL)
Dr Gatsing
Kinetics of the reaction of compound III of horseradish peroxidase with hydrogen ... Key words: Ionic strength, rate constant, horseradish peroxidase, NADPH. INTRODUCTION ... enzyme and hydrogen peroxide involves a two-electron ...
A Quantum Dot with Spin-Orbit Interaction--Analytical Solution
Basu, B.; Roy, B.
2009-01-01
The practical applicability of a semiconductor quantum dot with spin-orbit interaction gives an impetus to study analytical solutions to one- and two-electron quantum dots with or without a magnetic field.
Fukuzumi, Shunichi; Yamada, Yusuke; Karlin, Kenneth D.
2012-01-01
This review describes homogeneous and heterogeneous catalytic reduction of dioxygen with metal complexes focusing on the catalytic two-electron reduction of dioxygen to produce hydrogen peroxide. Whether two-electron reduction of dioxygen to produce hydrogen peroxide or four-electron O2-reduction to produce water occurs depends on the types of metals and ligands that are utilized. Those factors controlling the two processes are discussed in terms of metal-oxygen intermediates involved in the ...
Asymptotic Structure in the Classically Forbidden Region of the Hooke's Atoms
Wang, Xue-Mei
2013-05-01
The two-electron Hooke's atom — a quantum mechanical system with two electrons bound in a harmonic potential — is well known for its exact analytical properties at certain oscillator strengths. The Hooke's atoms with more than two electrons offer more scope for valuable practical applications. In this work, we study the asymptotic structure of these Hooke's atoms in the classically forbidden region. The leading-order term of the long-range expression for the KS exchange-correlation potential vxc(r) is shown to be -1/r. The second and third higher order terms are also exactly obtained. Various components of vxc(r) are also studied. It is shown that the leading term of O(1/r) in vxc(r) is due to the pure Pauli correlation, while the leading contribution of the Coulomb correlation is of O(1/r3). Neither of them makes contribution to the term of O(1/r2), which is shown to be solely due to the kinetic correlation effect. Results for the two-electron Hooke's atom were obtained before in the literature. Our results reduce to those of the two-electron Hooke's atom as a special case.
Energy Technology Data Exchange (ETDEWEB)
Basilevsky, M. V.; Mitina, E. A. [Photochemistry Center, Russian Academy of Sciences, 7a, Novatorov ul., Moscow (Russian Federation); Odinokov, A. V. [Photochemistry Center, Russian Academy of Sciences, 7a, Novatorov ul., Moscow (Russian Federation); National Research Nuclear University “MEPhI,” 31, Kashirskoye shosse, Moscow (Russian Federation); Titov, S. V. [Karpov Institute of Physical Chemistry, 3-1/12, Building 6, Obuha pereulok, Moscow (Russian Federation)
2013-12-21
The algorithm for a theoretical calculation of transfer reaction rates for light quantum particles (i.e., the electron and H-atom transfers) in non-polar solid matrices is formulated and justified. The mechanism postulated involves a local mode (an either intra- or inter-molecular one) serving as a mediator which accomplishes the energy exchange between the reacting high-frequency quantum mode and the phonon modes belonging to the environment. This approach uses as a background the Fermi golden rule beyond the usually applied spin-boson approximation. The dynamical treatment rests on the one-dimensional version of the standard quantum relaxation equation for the reduced density matrix, which describes the frequency fluctuation spectrum for the local mode under consideration. The temperature dependence of a reaction rate is controlled by the dimensionless parameter ξ{sub 0}=ℏω{sub 0}/k{sub B}T where ω{sub 0} is the frequency of the local mode and T is the temperature. The realization of the computational scheme is different for the high/intermediate (ξ{sub 0} < 1 − 3) and for low (ξ{sub 0}≫ 1) temperature ranges. For the first (quasi-classical) kinetic regime, the Redfield approximation to the solution of the relaxation equation proved to be sufficient and efficient in practical applications. The study of the essentially quantum-mechanical low-temperature kinetic regime in its asymptotic limit requires the implementation of the exact relaxation equation. The coherent mechanism providing a non-vanishing reaction rate has been revealed when T→ 0. An accurate computational methodology for the cross-over kinetic regime needs a further elaboration. The original model of the hopping mechanism for electronic conduction in photosensitive organic materials is considered, based on the above techniques. The electron transfer (ET) in active centers of such systems proceeds via local intra- and intermolecular modes. The active modes, as a rule, operate beyond the
Pouranvari, Mohammad
In this thesis, we study the entanglement properties of quantum systems to characterize quantum phases and phase transitions. We focus on the free fermion lattice systems and we use numerical calculation to verify our ideas. Behavior of the entanglement entropy is used to distinguish different phases, in addition the area law of the entanglement entropy is studied. We propose that beside the entanglement entropy, there is physical information in the entanglement Hamiltonian of the reduced density matrix of a chosen subsystem. We verify our ideas by studying different free fermion models. The verification is made by comparing the results we obtain from studying the behavior of the entanglement Hamiltonian with the known previous results. As starting point, to show that entanglement Hamiltonian eigenmodes have physical information, we employ the XX spin chain model. Real space renormalization group method predicts that the ground state is the product state of singlet states and thus those singlet that cross the boundary make the entanglement. We use the entanglement Hamiltonian to show that its single particle eigenmode shows the location of the entangled singlet spins. This is done in the case of ground state at T = 0. We also studied the entanglement properties of the highly excited eigenstate of the system. We use modified version of real space renormalization group for excited state and we show that in T ≠ 0 case where singlet and triplet state with total SZ = 0 make entanglement, entanglement Hamiltonian eigenmode shows the location of the entangled spins. We distinguish one eigenmode of the entanglement Hamiltonian as the maximally entangled mode. This mode corresponds to the smallest entanglement energy and thus contributes the most to the entanglement entropy. In addition, we use two one-dimensional free fermion models, namely the random dimer model and power law random banded model to show that for a localized-delocalized phase transition, behavior of the
Chacón, Alexis; Ciappina, Marcelo F.; Lewenstein, Maciej
2016-10-01
We present theoretical studies of high-order harmonic generation (HHG) driven by plasmonic fields in two-electron atomic systems. Comparing the single- and two-electron active approximation models of the hydrogen negative ion, we provide strong evidence that a nonsequential double-electron recombination mechanism appears to be mainly responsible for the HHG cutoff extension. Our analysis is carried out by means of a reduced one-dimensional numerical integration of the two-electron time-dependent Schrödinger equation, and on investigations of the classical electron trajectories, resulting from the Newton's equation of motion. Additional comparisons between the hydrogen negative ion and the helium atom suggest that the double recombination process depends distinctly on the atomic target. Our research paves the way to the understanding of strong field processes in multielectronic systems driven by spatially inhomogeneous fields.
The origin of linear scaling Fock matrix calculation with density prescreening
Energy Technology Data Exchange (ETDEWEB)
Mitin, Alexander V., E-mail: mitin@phys.chem.msu.ru [Chemistry Department, Moscow State University, Moscow, 119991 (Russian Federation)
2015-12-31
A theorem was proven, which reads that the number of nonzero two-electron integrals scales linearly with respect to the number of basis functions for large molecular systems. This permits to show that linear scaling property of the Fock matrix calculation with using density prescreening arises due to linear scaling properties of the number of nonzero two-electron integrals and the number of leading matrix elements of density matrix. This property is reinforced by employing the density prescreening technique. The use of the density difference prescreening further improves the linear scaling property of the Fock matrix calculation method. As a result, the linear scaling regime of the Fock matrix calculation can begin from the number of basis functions of 2000–3000 in dependence on the basis function type in molecular calculations. It was also shown that the conventional algorithm of Fock matrix calculation from stored nonzero two-electron integrals with density prescreening possesses linear scaling property.
Lewis, Alan M; Hore, P J
2014-01-01
We describe how the semiclassical theory of radical pair recombination reactions recently introduced by two of us [D. E. Manolopoulos and P. J. Hore, J. Chem. Phys. 139, 124106 (2013)] can be generalised to allow for different singlet and triplet recombination rates. This is a non-trivial generalisation because when the recombination rates are different the recombination process is dynamically coupled to the coherent electron spin dynamics of the radical pair. Furthermore, because the recombination operator is a two-electron operator, it is no longer sufficient simply to consider the two electrons as classical vectors: one has to consider the complete set of 16 two-electron spin operators as independent classical variables. The resulting semiclassical theory is first validated by comparison with exact quantum mechanical results for a model radical pair containing 12 nuclear spins. It is then used to shed light on the spin dynamics of a carotenoid-porphyrin-fullerene (CPF) triad containing considerably more nu...
Chacón, A; Lewenstein, M
2015-01-01
We present theoretical studies of high-order harmonic generation (HHG) driven by plasmonic fields in two-electron atomic systems. Comparing the two-active electron and single-active electron approximation models of the negative hydrogen ion atom, we provide strong evidence that a double non-sequential two-electron recombination appears to be the main responsible for the HHG cutoff extension. Our analysis is carried out by means of a reduced one-dimensional numerical integration of the two-electron time-dependent Schr\\"odinger equation (TDSE), and on investigations of the classical electron trajectories resulting from the Newton's equation of motion. Additional comparisons between the negative hydrogen ion and the helium atom suggest that the double recombination process depends distinctly on the atomic target. Our research paves the way to the understanding of strong field processes in multi-electronic systems driven by spatially inhomogeneous fields.
High-frequency manipulation of few-electron double quantum dots-toward spin qubits
Kodera, T.; van der Wiel, W. G.; Ono, K.; Sasaki, S.; Fujisawa, T.; Tarucha, S.
2004-04-01
We use a photon-assisted tunneling (PAT) technique to study the high-frequency response of one- and two-electron states in a semiconductor vertically coupled double-dot system. In particular, PAT associated with two-electron spin states in the spin-blockade regime is observed up to the absorption of 10 photons, indicating the preservation of long relaxation times and hence the robustness of our electron spin device under strong microwave irradiation. An alternative double-dot structure with greater flexibility in tuning the inter-dot coupling is presented and its transport characteristics are discussed. This structure is proposed for high-frequency control of two-electron spin states, as required for quantum computation schemes using electron spins in quantum dots.
Harada, Ken
2012-02-01
A method of Lorentz electron microscopy, which enables observation two Foucault images simultaneously by using an electron biprism instead of an objective aperture, was developed. The electron biprism is installed between two electron beams deflected by 180° magnetic domains. Potential applied to the biprism deflects the two electron beams further, and two Foucault images with reversed contrast are then obtained in one visual field. The twin Foucault images are able to extract the magnetic domain structures and to reconstruct an ordinary electron micrograph. The developed Foucault method was demonstrated with a 180° domain structure of manganite La0.825Sr0.175MnO3.
Microcanonical distribution for one-electron triatomic molecules
Lazarou, C; Emmanouilidou, A
2015-01-01
We formulate a microcanonical distribution for an arbitrary one-electron triatomic molecule. This distribution can be used to describe the initial state in strongly-driven two-electron triatomic molecules. Namely, in many semiclassical models that describe ionization of two-electron molecules driven by intense infrared laser fields in the tunneling regime initially one electron tunnels while the other electron is bound. The microcanonical distribution presented in this work can be used to describe the initial state of this bound electron.
Enhanced Orbital Degeneracy in Momentum Space for LaOFeAs
Institute of Scientific and Technical Information of China (English)
ZHANG Hai-Jun; XU Gang; DAI Xi; FANG Zhong
2009-01-01
The Fermi surfaces (FS) of LaOFeAs (in kz= 0 plane) consist of two hole-type circles around F point, which do not touch each other, and two electron-type co-centred ellipses around the M point, which are degenerate along the M - X line. By first-principles calculations, here we show that additional degeneracy exists for the two electron-type FS, and the crucial role ofF-doping and pressure is to enhance this orbital degeneracy. It is therefore suggested that the inter-orbital fluctuation is important to understand the unconventional superconductivity in these materials.
Controlling double ionization of atoms in pump-probe experiments
Bauch, S; Bonitz, M
2010-01-01
The ionization dynamics of a two-electron atom in an attosecond XUV-infrared pump-probe experiment is simulated by solving the time-dependent two-electron Schr\\"odinger equation. A dramatic change of the double ionization (DI) yield with variation of the pump-probe delay is reported and the governing role of electron-electron correlations is shown. The results allow for a direct control of the DI yield and of the relative strength of double and single ionization.
Double strand breaks in DNA resulting from double-electron-emission events
Surdutovich, Eugene
2012-01-01
A mechanism of double strand breaking (DSB) in DNA due to the action of two electrons is considered. These are the electrons produced in the vicinity of DNA molecules due to ionization of water molecules with a consecutive emission of two electrons, making such a mechanism possible. This effect qualitatively solves a puzzle of large yields of DSBs following irradiation of DNA molecules. The transport of secondary electrons, including the additional electrons, is studied in relation to the assessment of radiation damage due to incident ions. This work is a stage in the inclusion of Auger mechanism and like effects into the multiscale approach to ion-beam cancer therapy.
Halász, Gábor J; Lasorne, Benjamin; Robb, Mike A; Gatti, Fabien; Vibók, Ágnes
2013-01-01
A coherent superposition of two electronic states of ozone (ground and Hartley B) is prepared with a UV pump pulse. Using the multiconfiguration time-dependent Hartree approach, we calculate the subsequent time evolution of the two corresponding nuclear wave packets and the coherence between them. The resulting wave packet shows an oscillation between the two chemical bonds. Even more interesting, the coherence between the two electronics states reappears after the laser pulse is switched off, which could be observed experimentally with an attosecond probe pulse.
Theory of coherent dynamic nuclear polarization in quantum dots
DEFF Research Database (Denmark)
Neder, Izhar; Rudner, Mark Spencer; Halperin, Bertrand
2014-01-01
We consider the production of dynamic nuclear spin polarization (DNP) in a two-electron double quantum dot, in which the electronic levels are repeatedly swept through a singlet-triplet avoided crossing. Our analysis helps to elucidate the intriguing interplay between electron-nuclear hyperfine...
Hydrogenases from the Hyperthermophilic Archaeon Pyrococcus furiosus
van Haaster, D.J.
2007-01-01
Hydrogenase is an electron-transfer protein and catalyses the simplest chemical redox reaction, the reversible two-electron oxidation of molecular hydrogen in aerobic and anaerobic microorganisms. A kinetic study of the hydrogen oxidation reaction by Fe-hydrogenase from Desulfovibrio vulgaris
Bis(pyrrolo)tetrathiafulvalene - An Efficient Pi-Donor in Supramolecular Chemistry
DEFF Research Database (Denmark)
Lau, Jesper; Nielsen, Mogens Brøndsted; Thorup, Niels
1999-01-01
The synthesis of three novel macrocycles 3-5 based on the two electron donors bis(2,5-dimethyl- pyrrolo)[3,4-d]tetrathiafulvalene (1) and 1,4-hydroquinone is presented. Their abilities to include the electron acceptor paraquat (6) have been investigated by UV/Vis and sup 1 H NMR spectroscopy...
Riboflavin : A multifunctional vitamin.
de Souza, ACS; Ferreira, CV; Juca, MB; Aoyama, H; Cavagis, ADM; Peppelenbosch, MP
2005-01-01
Riboflavin, a component of the B-2 vitaminic complex, plays important roles in biochemistry, especially in redox reactions, due to the ability to participate in both one- and two-electron transfers as well as acting as a photosensitizer. Accordingly, low intakes of this vitamin have been associated
Directory of Open Access Journals (Sweden)
Mota Claudio J. A.
2000-01-01
Full Text Available Carbonium ions are carbocations with a pentacoordinated carbon atom, where the electronic octet is maintained. They possess a three center two electron bond in order to keep the tetravalence of the carbon atom. This paper reviews the concept of carbonium ions, their formation, stability and reactions.
Low-energy electron beams through ultra-thin foils, applications for electron microscopy
Van Aken, R.H.
2005-01-01
This thesis has discussed two electron microscopy applications that make use of ultra-thin foils: the tunnel junction emitter and the low-energy foil corrector. Both applications have in common that the electron beam is sent through the thin foil at low energy. Part of the electrons will scatter in
Quantum efficiencies exceeding unity due to impact ionization in silicon solar cells
Kolodinski, Sabine; Werner, Jürgen H.; Wittchen, Thomas; Queisser, Hans J.
1993-10-01
Absolute measurements demonstrate internal quantum efficiencies in silicon solar cells to exceed unity for photon energies above the first direct band gap and to show distinct spectral features that correspond to specific points in the Brillouin zone. Ultraviolet radiation can generate hot carriers with sufficient energy to cause impact ionization which results in two electron hole pairs per incident photon.
Ponderomotive dressing of doubly-excited states with intensity-controlled laser light
Directory of Open Access Journals (Sweden)
Ding Thomas
2013-03-01
Full Text Available We laser-dress several doubly-excited states in helium. Tuning the coupling-laser intensity from perturbative to the strong-coupling regime, we are able to measure phases imprinted on the two-electron wavefunctions, and observe a new continuum coupling mechanism.
KK—vacancy sharing and TET energy shift in near—symmetric heavy—ion atom collision
Institute of Scientific and Technical Information of China (English)
LiJing－Wen; JiangLi－Yang; 等
1998-01-01
The two-electron-one photon transitions(TET) are measured in 75MeV Ni+q+Cu collisons.The KK-vacancy sharing ratio RKK is deduced,which is in agreement with the theoretical prediction of Lennard.The emission energy of TET is slightly larger than twice the correspoding K transition energy.
DEFF Research Database (Denmark)
Fromager, Emmanuel; Cimiraglia, Renzo; Jensen, Hans Jørgen Aagaard
2010-01-01
A rigorous combination of multireference perturbation theory and density functional theory (DFT) is proposed. Based on a range separation of the regular two-electron Coulomb interaction, it combines a short-range density functional with second-order strongly contracted n-electron valence state pe...
Soncini, A.; Domene, C.; Engelberts, J.J.; Fowler, P.W.; Rassat, A.; Lenthe, J.H. van; Havenith, R.W.A.; Jenneskens, L.W.
2005-01-01
Why are some (4n+2)π systems aromatic, and some not? The ipsocentric approach to the calculation of the current density induced in a molecule by an external magnetic field predicts a four-electron diatropic (aromatic) ring current for (4n+2)π carbocycles and a two-electron paratropic (antiaromatic)
Snik, A.F.M.; Noten, J.F.P.; Cremers, C.W.R.J.
2004-01-01
We compared the output of two electronic middle ear implants: the Otologics MET device and the Vibrant Soundbridge device. Both devices were programmed in the linear amplification mode. Aided minus unaided sound pressure levels recorded in the ear canal (objective gain) were compared to unaided minu
Connection between noise and quantum correlations in a double quantum dot
Bodoky, F.; Belzig, W.; Bruder, C.
We investigate the current and noise characteristics of a double quantum dot system. The strong correlations induced by the Coulomb interaction and the Pauli principle create entangled two-electron states and lead to signatures in the transport properties. We show that the interaction parameter Ø,
Fukuzumi, Shunichi; Yamada, Yusuke; Karlin, Kenneth D
2012-11-01
This review describes homogeneous and heterogeneous catalytic reduction of dioxygen with metal complexes focusing on the catalytic two-electron reduction of dioxygen to produce hydrogen peroxide. Whether two-electron reduction of dioxygen to produce hydrogen peroxide or four-electron O2-reduction to produce water occurs depends on the types of metals and ligands that are utilized. Those factors controlling the two processes are discussed in terms of metal-oxygen intermediates involved in the catalysis. Metal complexes acting as catalysts for selective two-electron reduction of oxygen can be utilized as metal complex-modified electrodes in the electrocatalytic reduction to produce hydrogen peroxide. Hydrogen peroxide thus produced can be used as a fuel in a hydrogen peroxide fuel cell. A hydrogen peroxide fuel cell can be operated with a one-compartment structure without a membrane, which is certainly more promising for the development of low-cost fuel cells as compared with two compartment hydrogen fuel cells that require membranes. Hydrogen peroxide is regarded as an environmentally benign energy carrier because it can be produced by the electrocatalytic two-electron reduction of O2, which is abundant in air, using solar cells; the hydrogen peroxide thus produced could then be readily stored and then used as needed to generate electricity through the use of hydrogen peroxide fuel cells.
Bis(pyrrolo)tetrathiafulvalene - An Efficient Pi-Donor in Supramolecular Chemistry
DEFF Research Database (Denmark)
Lau, Jesper; Nielsen, Mogens Brøndsted; Thorup, Niels
1999-01-01
The synthesis of three novel macrocycles 3-5 based on the two electron donors bis(2,5-dimethyl- pyrrolo)[3,4-d]tetrathiafulvalene (1) and 1,4-hydroquinone is presented. Their abilities to include the electron acceptor paraquat (6) have been investigated by UV/Vis and sup 1 H NMR spectroscopy and ...
Atomic physics with highly charged ions
Energy Technology Data Exchange (ETDEWEB)
Richard, P.
1991-08-01
This report discusses: One electron outer shell processes in fast ion-atom collisions; role of electron-electron interaction in two-electron processes; multi-electron processes at low energy; multi-electron processes at high energy; inner shell processes; molecular fragmentation studies; theory; and, JRM laboratory operations.
Atomic physics with highly charged ions. Progress report, FY 1989--91
Energy Technology Data Exchange (ETDEWEB)
Richard, P.
1991-08-01
This report discusses: One electron outer shell processes in fast ion-atom collisions; role of electron-electron interaction in two-electron processes; multi-electron processes at low energy; multi-electron processes at high energy; inner shell processes; molecular fragmentation studies; theory; and, JRM laboratory operations.
Superlattice Multinanolayered Thin Films of SiO2/SiO2 + Ge for Thermoelectric Device Applications
2013-04-05
REPORT Superlattice multinanolayered thin films of SiO2/SiO2 + Ge for thermoelectric device applications 14. ABSTRACT 16. SECURITY CLASSIFICATION OF...used as a physical vapor deposition ( PVD ) system since we have used only two electron guns to evaporate the crucibles without any gas assistance. The
Otter, den Matthijs Willem
2000-01-01
Mixed conducting oxygen ion conductors can be applied as membranes for the separation of oxygen from air, as electrodes for both oxygen pumps and solid oxide fuel cells. In these applications, oxygen molecules dissociate on the surface of the material. The atomic oxygen species pick up two electrons
New Organometallic Polymeric Materials: The Search for X(2) NLO organometallic Polymers.
1994-05-28
copolymer 6. Cyclic voltametry of complex 7 shows two reversible oxidation events, one at +0.11 V (two-electron event) and another at +0.71 V (one...award). A special thanks to Prof. Vernon Parker for helpful discussions and Dr. Kishan Handoo for obtaining the cyclic voltammetry data for compounds 6
van Gastel, Maurice
2009-09-28
Spin polarization effects play an important role in the theory of isotropic hyperfine interactions for aromatic protons. The spin polarization gives rise to significant isotropic proton hyperfine interactions--spin-dependent one-electron properties--smaller than 0 MHz and the effect has been theoretically described [H. M. McConnell and D. B. J. Chesnut, Chem. Phys. 28, 107 (1958)]. The influence of spin polarization on the zero field splitting parameters, which are spin-dependent two-electron properties, has not been clearly identified yet. A phenomenological equation is proposed here for the contribution of spin polarization to the zero field splitting parameter D in analogy to McConnell's equation for hyperfine interactions. The presence of the effect is demonstrated in a series of calculations on polyacenes in the triplet state and turns out to be responsible for up to 50% of the D parameter in the case of naphthalene! It is found that spin-unrestricted single-determinant methods, including the widely used density functional theory methods, do not accurately reproduce the two-electron reduced electron density required for the evaluation of two-electron spin-dependent properties. For the accurate calculation of zero field splitting parameters by quantum chemical methods, it thus seems necessary to resort to correlated ab initio methods which do not give rise to spin contamination and which do provide an accurate description of the two-electron reduced electron density.
CTM4DOC : Electronic structure analysis from X-ray spectroscopy
Delgado-Jaime, Mario Ulises; Zhang, Kaili; Vura-Weis, Josh; De Groot, Frank M F
2016-01-01
Two electronic structure descriptions, one based on orbitals and the other based on term symbols, have been implemented in a new Matlab-based program, CTM4DOC. The program includes a graphical user interface that allows the user to explore the dependence of details of electronic structure in transit
Electronic Collaboration in Electronic Commerce%电子商务中的电子协作
Institute of Scientific and Technical Information of China (English)
胡翠华
2001-01-01
During the transformation from business electronization to Electronic Commerce,electronic collaboration is a core management technology.Based on the two electronic collaboration models inside and outside an enterprise,this paper analyzes the environment of electronic collaboration.The characters and functions of the supporting system are mentioned,too.