Nguyen, Thuong T.; Székely, Eszter; Imbalzano, Giulio; Behler, Jörg; Csányi, Gábor; Ceriotti, Michele; Götz, Andreas W.; Paesani, Francesco
2018-06-01
The accurate representation of multidimensional potential energy surfaces is a necessary requirement for realistic computer simulations of molecular systems. The continued increase in computer power accompanied by advances in correlated electronic structure methods nowadays enables routine calculations of accurate interaction energies for small systems, which can then be used as references for the development of analytical potential energy functions (PEFs) rigorously derived from many-body (MB) expansions. Building on the accuracy of the MB-pol many-body PEF, we investigate here the performance of permutationally invariant polynomials (PIPs), neural networks, and Gaussian approximation potentials (GAPs) in representing water two-body and three-body interaction energies, denoting the resulting potentials PIP-MB-pol, Behler-Parrinello neural network-MB-pol, and GAP-MB-pol, respectively. Our analysis shows that all three analytical representations exhibit similar levels of accuracy in reproducing both two-body and three-body reference data as well as interaction energies of small water clusters obtained from calculations carried out at the coupled cluster level of theory, the current gold standard for chemical accuracy. These results demonstrate the synergy between interatomic potentials formulated in terms of a many-body expansion, such as MB-pol, that are physically sound and transferable, and machine-learning techniques that provide a flexible framework to approximate the short-range interaction energy terms.
Permutationally invariant state reconstruction
DEFF Research Database (Denmark)
Moroder, Tobias; Hyllus, Philipp; Tóth, Géza
2012-01-01
Feasible tomography schemes for large particle numbers must possess, besides an appropriate data acquisition protocol, an efficient way to reconstruct the density operator from the observed finite data set. Since state reconstruction typically requires the solution of a nonlinear large-scale opti...... optimization, which has clear advantages regarding speed, control and accuracy in comparison to commonly employed numerical routines. First prototype implementations easily allow reconstruction of a state of 20 qubits in a few minutes on a standard computer.......-scale optimization problem, this is a major challenge in the design of scalable tomography schemes. Here we present an efficient state reconstruction scheme for permutationally invariant quantum state tomography. It works for all common state-of-the-art reconstruction principles, including, in particular, maximum...
Many-Body Localization Dynamics from Gauge Invariance
Brenes, Marlon; Dalmonte, Marcello; Heyl, Markus; Scardicchio, Antonello
2018-01-01
We show how lattice gauge theories can display many-body localization dynamics in the absence of disorder. Our starting point is the observation that, for some generic translationally invariant states, the Gauss law effectively induces a dynamics which can be described as a disorder average over gauge superselection sectors. We carry out extensive exact simulations on the real-time dynamics of a lattice Schwinger model, describing the coupling between U(1) gauge fields and staggered fermions. Our results show how memory effects and slow, double-logarithmic entanglement growth are present in a broad regime of parameters—in particular, for sufficiently large interactions. These findings are immediately relevant to cold atoms and trapped ion experiments realizing dynamical gauge fields and suggest a new and universal link between confinement and entanglement dynamics in the many-body localized phase of lattice models.
Permutation-invariant distance between atomic configurations
Ferré, Grégoire; Maillet, Jean-Bernard; Stoltz, Gabriel
2015-09-01
We present a permutation-invariant distance between atomic configurations, defined through a functional representation of atomic positions. This distance enables us to directly compare different atomic environments with an arbitrary number of particles, without going through a space of reduced dimensionality (i.e., fingerprints) as an intermediate step. Moreover, this distance is naturally invariant through permutations of atoms, avoiding the time consuming associated minimization required by other common criteria (like the root mean square distance). Finally, the invariance through global rotations is accounted for by a minimization procedure in the space of rotations solved by Monte Carlo simulated annealing. A formal framework is also introduced, showing that the distance we propose verifies the property of a metric on the space of atomic configurations. Two examples of applications are proposed. The first one consists in evaluating faithfulness of some fingerprints (or descriptors), i.e., their capacity to represent the structural information of a configuration. The second application concerns structural analysis, where our distance proves to be efficient in discriminating different local structures and even classifying their degree of similarity.
Permutation-invariant distance between atomic configurations
International Nuclear Information System (INIS)
Ferré, Grégoire; Maillet, Jean-Bernard; Stoltz, Gabriel
2015-01-01
We present a permutation-invariant distance between atomic configurations, defined through a functional representation of atomic positions. This distance enables us to directly compare different atomic environments with an arbitrary number of particles, without going through a space of reduced dimensionality (i.e., fingerprints) as an intermediate step. Moreover, this distance is naturally invariant through permutations of atoms, avoiding the time consuming associated minimization required by other common criteria (like the root mean square distance). Finally, the invariance through global rotations is accounted for by a minimization procedure in the space of rotations solved by Monte Carlo simulated annealing. A formal framework is also introduced, showing that the distance we propose verifies the property of a metric on the space of atomic configurations. Two examples of applications are proposed. The first one consists in evaluating faithfulness of some fingerprints (or descriptors), i.e., their capacity to represent the structural information of a configuration. The second application concerns structural analysis, where our distance proves to be efficient in discriminating different local structures and even classifying their degree of similarity
Yarloo, H.; Langari, A.; Vaezi, A.
2018-02-01
We enquire into the quasi many-body localization in topologically ordered states of matter, revolving around the case of Kitaev toric code on the ladder geometry, where different types of anyonic defects carry different masses induced by environmental errors. Our study verifies that the presence of anyons generates a complex energy landscape solely through braiding statistics, which suffices to suppress the diffusion of defects in such clean, multicomponent anyonic liquid. This nonergodic dynamics suggests a promising scenario for investigation of quasi many-body localization. Computing standard diagnostics evidences that a typical initial inhomogeneity of anyons gives birth to a glassy dynamics with an exponentially diverging time scale of the full relaxation. Our results unveil how self-generated disorder ameliorates the vulnerability of topological order away from equilibrium. This setting provides a new platform which paves the way toward impeding logical errors by self-localization of anyons in a generic, high energy state, originated exclusively in their exotic statistics.
International Nuclear Information System (INIS)
Arnold, Vladimir I
2009-01-01
Decompositions into cycles for random permutations of a large number of elements are very different (in their statistics) from the same decompositions for algebraic permutations (defined by linear or projective transformations of finite sets). This paper presents tables giving both these and other statistics, as well as a comparison of them with the statistics of involutions or permutations with all their cycles of even length. The inclusions of a point in cycles of various lengths turn out to be equiprobable events for random permutations. The number of permutations of 2N elements with all cycles of even length turns out to be the square of an integer (namely, of (2N-1)!!). The number of cycles of projective permutations (over a field with an odd prime number of elements) is always even. These and other empirically discovered theorems are proved in the paper. Bibliography: 6 titles.
Energy Technology Data Exchange (ETDEWEB)
Li, Jun; Jiang, Bin; Guo, Hua, E-mail: hguo@unm.edu [Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131 (United States)
2013-11-28
A rigorous, general, and simple method to fit global and permutation invariant potential energy surfaces (PESs) using neural networks (NNs) is discussed. This so-called permutation invariant polynomial neural network (PIP-NN) method imposes permutation symmetry by using in its input a set of symmetry functions based on PIPs. For systems with more than three atoms, it is shown that the number of symmetry functions in the input vector needs to be larger than the number of internal coordinates in order to include both the primary and secondary invariant polynomials. This PIP-NN method is successfully demonstrated in three atom-triatomic reactive systems, resulting in full-dimensional global PESs with average errors on the order of meV. These PESs are used in full-dimensional quantum dynamical calculations.
International Nuclear Information System (INIS)
Schmid, K.W.
2001-01-01
The mathematical tools to restore Galilei invariance in the nuclear many-body problem with the help of projection techniques are presented. For simple oscillator configurations recursion relations for the various elementary contractions are derived. The method is then applied to simple configurations for the ground states of 4 He, 16 O and 40 Ca as well as to the corresponding one-hole and one-particle states. As a first application the spectral functions and spectroscopic factors for the above-mentioned doubly even nuclei are investigated. It turns out that the conventional picture of an uncorrelated system underestimates the single-particle strengths of the hole states from the last occupied shell while that of the higher excited hole states is overestimated considerably. These results are in complete agreement with those derived by Dieperink and de Forest using different methods. Similar effects are seen for the particle states which have not been studied before. All the calculations presented here are performed analytically and thus can be checked explicitly by the interested reader. (orig.)
International Nuclear Information System (INIS)
Schwesinger, B.
1978-01-01
The solution of the many-body oscillator problem is used as a basis for a RPA-calculation of 16 O. The calculation is performed in a LS-coupling scheme with an interaction containing central, spin-orbit and tensor forces. The main differences with conventional RPA-calculations occur for the transition probabilities. (orig.) [de
Linear algebra of the permutation invariant Crow-Kimura model of prebiotic evolution.
Bratus, Alexander S; Novozhilov, Artem S; Semenov, Yuri S
2014-10-01
A particular case of the famous quasispecies model - the Crow-Kimura model with a permutation invariant fitness landscape - is investigated. Using the fact that the mutation matrix in the case of a permutation invariant fitness landscape has a special tridiagonal form, a change of the basis is suggested such that in the new coordinates a number of analytical results can be obtained. In particular, using the eigenvectors of the mutation matrix as the new basis, we show that the quasispecies distribution approaches a binomial one and give simple estimates for the speed of convergence. Another consequence of the suggested approach is a parametric solution to the system of equations determining the quasispecies. Using this parametric solution we show that our approach leads to exact asymptotic results in some cases, which are not covered by the existing methods. In particular, we are able to present not only the limit behavior of the leading eigenvalue (mean population fitness), but also the exact formulas for the limit quasispecies eigenvector for special cases. For instance, this eigenvector has a geometric distribution in the case of the classical single peaked fitness landscape. On the biological side, we propose a mathematical definition, based on the closeness of the quasispecies to the binomial distribution, which can be used as an operational definition of the notorious error threshold. Using this definition, we suggest two approximate formulas to estimate the critical mutation rate after which the quasispecies delocalization occurs. Copyright © 2014 Elsevier Inc. All rights reserved.
International Nuclear Information System (INIS)
Hubbard, J.
1980-01-01
The evolution of the discipline of many-body theory during the past 25 years is outlined and the developments originated in the Theoretical Physics Division, AERE, are discussed. Topics considered include; the connection between plasma oscillations and the dielectric properties of an electron gas, superconductivity, Fermi levels, ferromagnetism in metals, phase transformations, scaling laws, and quasi-one-dimensional solids. (UK)
Quantum tests for the linearity and permutation invariance of Boolean functions
Energy Technology Data Exchange (ETDEWEB)
Hillery, Mark [Department of Physics, Hunter College of the City University of New York, 695 Park Avenue, New York, New York 10021 (United States); Andersson, Erika [SUPA, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom)
2011-12-15
The goal in function property testing is to determine whether a black-box Boolean function has a certain property or is {epsilon}-far from having that property. The performance of the algorithm is judged by how many calls need to be made to the black box in order to determine, with high probability, which of the two alternatives is the case. Here we present two quantum algorithms, the first to determine whether the function is linear and the second to determine whether it is symmetric (invariant under permutations of the arguments). Both require order {epsilon}{sup -2/3} calls to the oracle, which is better than known classical algorithms. In addition, in the case of linearity testing, if the function is linear, the quantum algorithm identifies which linear function it is. The linearity test combines the Bernstein-Vazirani algorithm and amplitude amplification, while the test to determine whether a function is symmetric uses projective measurements and amplitude amplification.
Finally! A valid test of configural invariance using permutation in multigroup CFA
Jorgensen, T.D.; Kite, B.A.; Chen, P.-Y.; Short, S.D.; van der Ark, L.A.; Wiberg, M.; Culpepper, S.A.; Douglas, J.A.; Wang, W.-C.
2017-01-01
In multigroup factor analysis, configural measurement invariance is accepted as tenable when researchers either (a) fail to reject the null hypothesis of exact fit using a χ2 test or (b) conclude that a model fits approximately well enough, according to one or more alternative fit indices (AFIs).
International Nuclear Information System (INIS)
Li, Jun; Chen, Jun; Zhao, Zhiqiang; Zhang, Dong H.; Xie, Daiqian; Guo, Hua
2015-01-01
We report a permutationally invariant global potential energy surface (PES) for the H + CH 4 system based on ∼63 000 data points calculated at a high ab initio level (UCCSD(T)-F12a/AVTZ) using the recently proposed permutation invariant polynomial-neural network method. The small fitting error (5.1 meV) indicates a faithful representation of the ab initio points over a large configuration space. The rate coefficients calculated on the PES using tunneling corrected transition-state theory and quasi-classical trajectory are found to agree well with the available experimental and previous quantum dynamical results. The calculated total reaction probabilities (J tot = 0) including the abstraction and exchange channels using the new potential by a reduced dimensional quantum dynamic method are essentially the same as those on the Xu-Chen-Zhang PES [Chin. J. Chem. Phys. 27, 373 (2014)
Many body calculations in atomic physics
International Nuclear Information System (INIS)
Kelly, H.P.
1985-01-01
The use of the many-body perturbation theory for atomic calculations are reviewed. The major emphasis is on the use of the linked-cluster many-body perturbation theory derived by Brueckner and Goldstone. Applications of many-body theory to calculations of hyperfine structure are examined. Auger rates and parity violation are discussed. Photoionization is reviewed, and the authors show how many-body perturbation theory can be applied to problems ranging from structural properties such as correlation energies and hyperfine structure to dynamical properties such as transitions induced by weak neutral currents and photoionization cross sections
General coordinate invariance in quantum many-body systems
Czech Academy of Sciences Publication Activity Database
Brauner, Tomáš; Endlich, S.; Monin, A.; Penco, R.
2014-01-01
Roč. 90, č. 10 (2014), s. 105016 ISSN 1550-7998 Institutional support: RVO:61389005 Keywords : Chiral Perturbation-Theory * Planar Galilei Group * Lagrangians Subject RIV: BE - Theoretical Physics Impact factor: 4.643, year: 2014
Introduction to many-body physics
Coleman, Piers
2015-01-01
A modern, graduate-level introduction to many-body physics in condensed matter, this textbook explains the tools and concepts needed for a research-level understanding of the correlated behavior of quantum fluids. Starting with an operator-based introduction to the quantum field theory of many-body physics, this textbook presents the Feynman diagram approach, Green's functions and finite-temperature many body physics before developing the path integral approach to interacting systems. Special chapters are devoted to the concepts of Fermi liquid theory, broken symmetry, conduction in disordered systems, superconductivity and the physics of local-moment metals. A strong emphasis on concepts and numerous exercises make this an invaluable course book for graduate students in condensed matter physics. It will also interest students in nuclear, atomic and particle physics.
International Nuclear Information System (INIS)
Brueckner, K.A.
1980-01-01
This paper reviews the major steps in the development of many-body theory since the early 1950's. Very few systems permit an exact solution by selective diagram summation or by exact solution of a truncated Hamiltonian. Formal methods have usually had little success for real physical systems. Examples are all the quantum liquids such as nuclear matter, liquid He 3 , liquid He 4 , superconductors and metallic conductors. Atomic and molecular systems and finite nuclei present additional problems. Many-body theory has probably had its greatest success in the application to atomic properties and the development in recent years is reviewed. (Auth.)
The relativistic atomic many-body problem
International Nuclear Information System (INIS)
Brown, G.E.
1987-01-01
Problems connected with the infinite negative energy sea of electrons in the atomic many-body problem are discussed. It is shown that as long as one works in mean-field approximations, wave functions do not need to suffer from continuum dissociation. Various effects from virtual pairs in the wave functions are discussed. (orig.)
Many body perturbation calculations of photoionization
International Nuclear Information System (INIS)
Kelly, H.P.
1979-01-01
The application of many body perturbation theory to the calculation of atomic photoionization cross sections is reviewed. The choice of appropriate potential for the single-particle state is discussed and results are presented for several atoms including resonance structure. In addition to single photoionization, the process of double photoionization is considered and is found to be significant. (Auth.)
Review of many-body calculations
International Nuclear Information System (INIS)
Kelly, H.P.
1981-01-01
A brief review is given of many-body perturbation theory and its application to atomic physics. Particular attention is given to the choice of single-particle potential used to generate excited states. Applications to many atomic properties are discussed including hyperfine structure, photoabsorption including multiple processes, and parity non-conserving transitions in heavy atoms
Directory of Open Access Journals (Sweden)
Mikel Aickin
2010-01-01
Full Text Available Permutation tests are often presented in a rather casual manner, in both introductory and advanced statistics textbooks. The appeal of the cleverness of the procedure seems to replace the need for a rigorous argument that it produces valid hypothesis tests. The consequence of this educational failing has been a widespread belief in a “permutation principle”, which is supposed invariably to give tests that are valid by construction, under an absolute minimum of statistical assumptions. Several lines of argument are presented here to show that the permutation principle itself can be invalid, concentrating on the Fisher-Pitman permutation test for two means. A simple counterfactual example illustrates the general problem, and a slightly more elaborate counterfactual argument is used to explain why the main mathematical proof of the validity of permutation tests is mistaken. Two modifications of the permutation test are suggested to be valid in a very modest simulation. In instances where simulation software is readily available, investigating the validity of a specific permutation test can be done easily, requiring only a minimum understanding of statistical technicalities.
Dynamically induced many-body localization
Choi, Soonwon; Abanin, Dmitry A.; Lukin, Mikhail D.
2018-03-01
We show that a quantum phase transition from ergodic to many-body localized (MBL) phases can be induced via periodic pulsed manipulation of spin systems. Such a transition is enabled by the interplay between weak disorder and slow heating rates. Specifically, we demonstrate that the Hamiltonian of a weakly disordered ergodic spin system can be effectively engineered, by using sufficiently fast coherent controls, to yield a stable MBL phase, which in turn completely suppresses the energy absorption from external control field. Our results imply that a broad class of existing many-body systems can be used to probe nonequilibrium phases of matter for a long time, limited only by coupling to external environment.
Many-body orthogonal polynomial systems
International Nuclear Information System (INIS)
Witte, N.S.
1997-03-01
The fundamental methods employed in the moment problem, involving orthogonal polynomial systems, the Lanczos algorithm, continued fraction analysis and Pade approximants has been combined with a cumulant approach and applied to the extensive many-body problem in physics. This has yielded many new exact results for many-body systems in the thermodynamic limit - for the ground state energy, for excited state gaps, for arbitrary ground state avenges - and are of a nonperturbative nature. These results flow from a confluence property of the three-term recurrence coefficients arising and define a general class of many-body orthogonal polynomials. These theorems constitute an analytical solution to the Lanczos algorithm in that they are expressed in terms of the three-term recurrence coefficients α and β. These results can also be applied approximately for non-solvable models in the form of an expansion, in a descending series of the system size. The zeroth order order this expansion is just the manifestation of the central limit theorem in which a Gaussian measure and hermite polynomials arise. The first order represents the first non-trivial order, in which classical distribution functions like the binomial distributions arise and the associated class of orthogonal polynomials are Meixner polynomials. Amongst examples of systems which have infinite order in the expansion are q-orthogonal polynomials where q depends on the system size in a particular way. (author)
Correlation functions for Hermitian many-body systems: Necessary conditions
International Nuclear Information System (INIS)
Brown, E.B.
1994-01-01
Lee [Phys. Rev. B 47, 8293 (1993)] has shown that the odd-numbered derivatives of the Kubo autocorrelation function vanish at t=0. We show that this condition is based on a more general property of nondiagonal Kubo correlation functions. This general property provides that certain functional forms (e.g., simple exponential decay) are not admissible for any symmetric or antisymmetric Kubo correlation function in a Hermitian many-body system. Lee's result emerges as a special case of this result. Applications to translationally invariant systems and systems with rotational symmetries are also demonstrated
Many Body Structure of Strongly Interacting Systems
Arenhövel, Hartmuth; Drechsel, Dieter; Friedrich, Jörg; Kaiser, Karl-Heinz; Walcher, Thomas; Symposium on 20 Years of Physics at the Mainz Microtron MAMI
2006-01-01
This carefully edited proceedings volume provides an extensive review and analysis of the work carried out over the past 20 years at the Mainz Microtron (MAMI). This research centered around the application of Quantum Chromodynamics in the strictly nonperturbative regime at hadronic scales of about 1 fm. Due to the many degrees of freedom in hadrons at this scale the leitmotiv of this research is "Many body structure of strongly interacting systems". Further, an outlook on the research with the forthcoming upgrade of MAMI is given. This volume is an authoritative source of reference for everyone interested in the field of the electro-weak probing of the structure of hadrons.
Nuclear, particle and many body physics
Morse, Philip M; Feshbach, Herman
2013-01-01
Nuclear, Particle and Many Body Physics, Volume II, is the second of two volumes dedicated to the memory of physicist Amos de-Shalit. The contributions in this volume are a testament to the respect he earned as a physicist and of the warm and rich affection he commanded as a personal friend. The book contains 41 chapters and begins with a study on the renormalization of rational Lagrangians. Separate chapters cover the scattering of high energy protons by light nuclei; approximation of the dynamics of proton-neutron systems; the scattering amplitude for the Gaussian potential; Coulomb excitati
Seniority in quantum many-body systems
International Nuclear Information System (INIS)
Van Isacker, P.
2010-01-01
The use of the seniority quantum number in many-body systems is reviewed. A brief summary is given of its introduction by Racah in the context of atomic spectroscopy. Several extensions of Racah's original idea are discussed: seniority for identical nucleons in a single-j shell, its extension to the case of many, non-degenerate j shells and to systems with neutrons and protons. To illustrate its usefulness to this day, a recent application of seniority is presented in Bose-Einstein condensates of atoms with spin.
Non-equilibrium many body dynamics
International Nuclear Information System (INIS)
Creutz, M.; Gyulassy, M.
1997-01-01
This Riken BNL Research Center Symposium on Non-Equilibrium Many Body Physics was held on September 23-25, 1997 as part of the official opening ceremony of the Center at Brookhaven National Lab. A major objective of theoretical work at the center is to elaborate on the full spectrum of strong interaction physics based on QCD, including the physics of confinement and chiral symmetry breaking, the parton structure of hadrons and nuclei, and the phenomenology of ultra-relativistic nuclear collisions related to the up-coming experiments at RHIC. The opportunities and challenges of nuclear and particle physics in this area naturally involve aspects of the many body problem common to many other fields. The aim of this symposium was to find common theoretical threads in the area of non-equilibrium physics and modern transport theories. The program consisted of invited talks on a variety topics from the fields of atomic, condensed matter, plasma, astrophysics, cosmology, and chemistry, in addition to nuclear and particle physics. Separate abstracts have been indexed into the database for contributions to this workshop
Non-equilibrium many body dynamics
Energy Technology Data Exchange (ETDEWEB)
Creutz, M.; Gyulassy, M.
1997-09-22
This Riken BNL Research Center Symposium on Non-Equilibrium Many Body Physics was held on September 23-25, 1997 as part of the official opening ceremony of the Center at Brookhaven National Lab. A major objective of theoretical work at the center is to elaborate on the full spectrum of strong interaction physics based on QCD, including the physics of confinement and chiral symmetry breaking, the parton structure of hadrons and nuclei, and the phenomenology of ultra-relativistic nuclear collisions related to the up-coming experiments at RHIC. The opportunities and challenges of nuclear and particle physics in this area naturally involve aspects of the many body problem common to many other fields. The aim of this symposium was to find common theoretical threads in the area of non-equilibrium physics and modern transport theories. The program consisted of invited talks on a variety topics from the fields of atomic, condensed matter, plasma, astrophysics, cosmology, and chemistry, in addition to nuclear and particle physics. Separate abstracts have been indexed into the database for contributions to this workshop.
CIME School on Quantum Many Body Systems
Rivasseau, Vincent; Solovej, Jan Philip; Spencer, Thomas
2012-01-01
The book is based on the lectures given at the CIME school "Quantum many body systems" held in the summer of 2010. It provides a tutorial introduction to recent advances in the mathematics of interacting systems, written by four leading experts in the field: V. Rivasseau illustrates the applications of constructive Quantum Field Theory to 2D interacting electrons and their relation to quantum gravity; R. Seiringer describes a proof of Bose-Einstein condensation in the Gross-Pitaevski limit and explains the effects of rotating traps and the emergence of lattices of quantized vortices; J.-P. Solovej gives an introduction to the theory of quantum Coulomb systems and to the functional analytic methods used to prove their thermodynamic stability; finally, T. Spencer explains the supersymmetric approach to Anderson localization and its relation to the theory of random matrices. All the lectures are characterized by their mathematical rigor combined with physical insights.
Photon Subtraction by Many-Body Decoherence
DEFF Research Database (Denmark)
Murray, C. R.; Mirgorodskiy, I.; Tresp, C.
2018-01-01
We experimentally and theoretically investigate the scattering of a photonic quantum field from another stored in a strongly interacting atomic Rydberg ensemble. Considering the many-body limit of this problem, we derive an exact solution to the scattering-induced spatial decoherence of multiple...... stored photons, allowing for a rigorous understanding of the underlying dissipative quantum dynamics. Combined with our experiments, this analysis reveals a correlated coherence-protection process in which the scattering from one excitation can shield all others from spatial decoherence. We discuss how...... this effect can be used to manipulate light at the quantum level, providing a robust mechanism for single-photon subtraction, and experimentally demonstrate this capability....
International Nuclear Information System (INIS)
Amusia, M Ya
2011-01-01
Contrary to common wisdom, not everything is clear and simple in the structure of many-electron atoms. Complexity in atoms is mainly a result of interelectron interaction that leads to rather unusual behaviour. Most transparently this is manifested in photo-ionization processes of many-electron atoms and some multi-atomic objects e.g. endohedrals. Particular attention will be given to the approach describing the interaction of photons with many-electron atoms in the frame of the many-body theory based on the Feynman diagrams technique. As a suitable one-electron approximation the Hartree - Fock (HF) approach will be presented. On its ground we will include the so-called electron correlation effects and discuss the frequently used Random Phase Approximation with Exchange - RPAE. Some results of recent calculations will be presented.
Energy Technology Data Exchange (ETDEWEB)
Amusia, M Ya, E-mail: amusia@vms.huji.ac.il [Racah Institute of Physics, The Hebrew University, Jerusalem (Israel); Ioffe Physical-technical Institute, RAS, St. Petersburg (Russian Federation)
2011-09-16
Contrary to common wisdom, not everything is clear and simple in the structure of many-electron atoms. Complexity in atoms is mainly a result of interelectron interaction that leads to rather unusual behaviour. Most transparently this is manifested in photo-ionization processes of many-electron atoms and some multi-atomic objects e.g. endohedrals. Particular attention will be given to the approach describing the interaction of photons with many-electron atoms in the frame of the many-body theory based on the Feynman diagrams technique. As a suitable one-electron approximation the Hartree - Fock (HF) approach will be presented. On its ground we will include the so-called electron correlation effects and discuss the frequently used Random Phase Approximation with Exchange - RPAE. Some results of recent calculations will be presented.
Intermittent many-body dynamics at equilibrium
Danieli, C.; Campbell, D. K.; Flach, S.
2017-06-01
The equilibrium value of an observable defines a manifold in the phase space of an ergodic and equipartitioned many-body system. A typical trajectory pierces that manifold infinitely often as time goes to infinity. We use these piercings to measure both the relaxation time of the lowest frequency eigenmode of the Fermi-Pasta-Ulam chain, as well as the fluctuations of the subsequent dynamics in equilibrium. The dynamics in equilibrium is characterized by a power-law distribution of excursion times far off equilibrium, with diverging variance. Long excursions arise from sticky dynamics close to q -breathers localized in normal mode space. Measuring the exponent allows one to predict the transition into nonergodic dynamics. We generalize our method to Klein-Gordon lattices where the sticky dynamics is due to discrete breathers localized in real space.
Current algebras and many-body physics
International Nuclear Information System (INIS)
Albertin, U.K.
1989-01-01
Several applications of current algebras in many body physics are examined. The first is the interacting Bose gas in three dimensions. Theories for phonons, vortices and rotons are all described within the current algebra formalism. Next the one dimensional electron gas is examined within the approximation of linear dispersion so that relativistic current algebra techniques may be used. The relation with Thirring strings and compactified boson models is examined, and points of enhanced symmetry in the compactified boson models are shown to lie on phase transition lines for the electron gas. Finally, mathematical aspects of the current algebra are studied. The theory of induced representations of the diffeomorphism group are used to describe the Aharanov-Bohm effect, the thermodynamics of the Bose gas, and the Bose gas in the presence of vortex filaments
Interferometric probes of many-body localization.
Serbyn, M; Knap, M; Gopalakrishnan, S; Papić, Z; Yao, N Y; Laumann, C R; Abanin, D A; Lukin, M D; Demler, E A
2014-10-03
We propose a method for detecting many-body localization (MBL) in disordered spin systems. The method involves pulsed coherent spin manipulations that probe the dephasing of a given spin due to its entanglement with a set of distant spins. It allows one to distinguish the MBL phase from a noninteracting localized phase and a delocalized phase. In particular, we show that for a properly chosen pulse sequence the MBL phase exhibits a characteristic power-law decay reflecting its slow growth of entanglement. We find that this power-law decay is robust with respect to thermal and disorder averaging, provide numerical simulations supporting our results, and discuss possible experimental realizations in solid-state and cold-atom systems.
Many-body approaches to nuclear physics
International Nuclear Information System (INIS)
Hjorth-Jensen, M.
1993-10-01
This thesis deals with applications of perturbative many-body theories to selected nuclear systems at low and intermediate energies. Examples are the properties of neutron stars, the calculation of shell-model effective interactions and the microscopic derivation of the optical-model potential for finite nuclei. The line of research leans on the microscopic approach, i.e. an approach which aims at describing nuclear properties from the underlying free interaction between the various hadrons where parameters like meson coupling constants define the Lagrangians. The emphasis is on the behavior of the various components of the free interaction in different nuclear media in order to understand how these components are affected by the studied nuclear correlations. 159 refs
Prethermalization in an isolated many body system
International Nuclear Information System (INIS)
Gring, M.
2012-01-01
Understanding the relaxation dynamics of complex non-equilibrium many-body quantum systems is a fundamental problem, arising in many areas of physics. However, experimental examples of non-equilibrium systems that are both controllable and suitable for detailed study are extremely rare. In this thesis one such example in the form of a coherently split one-dimensional (1d) ultra cold Bose gas in a double-well potential is studied in detail. Typical for the analysis of non-equilibrium systems, the key challenge in this study is the characterization of the complex transient states of the system. In the presented work this task is solved by employing measurements of the time evolution of the full quantum mechanical probability distribution functions (FDFs) of time-of-flight matter-wave interference patterns between the two halves of the split system. The dynamics of the FDFs reveal two distinct regimes of relaxation clearly demonstrating the multi-mode nature of 1d Bose gases. Moreover, after an initial rapid evolution, the FDFs exhibit the approach towards a thermal-like steady state of the system which however does not correspond to the true thermal equilibrium of the system. This surprising behaviour is also predicted by a recent theoretical work which puts the observations in a much broader context and classifies them as an example of prethermalization. Prethermalization is a general concept from relativistic quantum field theory and is currently the subject of intense theoretical research. Accordingly prethermalized states were recently predicted for a series of other many-body quantum systems. The work presented in this thesis represents a direct experimental observation of this phenomenon of prethermalization. (author) [de
Many-body formalism for fermions: The partition function
Watson, D. K.
2017-09-01
The partition function, a fundamental tenet in statistical thermodynamics, contains in principle all thermodynamic information about a system. It encapsulates both microscopic information through the quantum energy levels and statistical information from the partitioning of the particles among the available energy levels. For identical particles, this statistical accounting is complicated by the symmetry requirements of the allowed quantum states. In particular, for Fermi systems, the enforcement of the Pauli principle is typically a numerically demanding task, responsible for much of the cost of the calculations. The interplay of these three elements—the structure of the many-body spectrum, the statistical partitioning of the N particles among the available levels, and the enforcement of the Pauli principle—drives the behavior of mesoscopic and macroscopic Fermi systems. In this paper, we develop an approach for the determination of the partition function, a numerically difficult task, for systems of strongly interacting identical fermions and apply it to a model system of harmonically confined, harmonically interacting fermions. This approach uses a recently introduced many-body method that is an extension of the symmetry-invariant perturbation method (SPT) originally developed for bosons. It uses group theory and graphical techniques to avoid the heavy computational demands of conventional many-body methods which typically scale exponentially with the number of particles. The SPT application of the Pauli principle is trivial to implement since it is done "on paper" by imposing restrictions on the normal-mode quantum numbers at first order in the perturbation. The method is applied through first order and represents an extension of the SPT method to excited states. Our method of determining the partition function and various thermodynamic quantities is accurate and efficient and has the potential to yield interesting insight into the role played by the Pauli
Many-body physics using cold atoms
Sundar, Bhuvanesh
Advances in experiments on dilute ultracold atomic gases have given us access to highly tunable quantum systems. In particular, there have been substantial improvements in achieving different kinds of interaction between atoms. As a result, utracold atomic gases oer an ideal platform to simulate many-body phenomena in condensed matter physics, and engineer other novel phenomena that are a result of the exotic interactions produced between atoms. In this dissertation, I present a series of studies that explore the physics of dilute ultracold atomic gases in different settings. In each setting, I explore a different form of the inter-particle interaction. Motivated by experiments which induce artificial spin-orbit coupling for cold fermions, I explore this system in my first project. In this project, I propose a method to perform universal quantum computation using the excitations of interacting spin-orbit coupled fermions, in which effective p-wave interactions lead to the formation of a topological superfluid. Motivated by experiments which explore the physics of exotic interactions between atoms trapped inside optical cavities, I explore this system in a second project. I calculate the phase diagram of lattice bosons trapped in an optical cavity, where the cavity modes mediates effective global range checkerboard interactions between the atoms. I compare this phase diagram with one that was recently measured experimentally. In two other projects, I explore quantum simulation of condensed matter phenomena due to spin-dependent interactions between particles. I propose a method to produce tunable spin-dependent interactions between atoms, using an optical Feshbach resonance. In one project, I use these spin-dependent interactions in an ultracold Bose-Fermi system, and propose a method to produce the Kondo model. I propose an experiment to directly observe the Kondo effect in this system. In another project, I propose using lattice bosons with a large hyperfine spin
Nuclear many-body correlation dynamics--a nonperturbative approach in quantum many-body theory
International Nuclear Information System (INIS)
Wang Shunjin
1996-01-01
Based on the experimental results and theoretical experience in nuclear physics, the article has explored the basic physical ideas and theoretical methods in nuclear and quantum many-body correlation dynamics. The main theoretical results and important applications are introduced briefly. The paper addresses the fundamental ingredients and physical interpretation of theoretical results in a comprehensive way. Recent new results about correlation dynamics in quantum field theories are also presented. The perspectives of further application are viewed. (91 refs.)
Quantum Many-Body System in Presence of Time-Dependent Potential and Electric Field
Energy Technology Data Exchange (ETDEWEB)
Sobhani, Hadi; Hassanabadi, Hassan [Shahrood University of Technology, Shahrood (Iran, Islamic Republic of)
2017-07-15
In this article, a quantum many-body system is considered. Then two time-dependent interactions have been added to the system. Changing of them is assumed in general form. After that, by using algebraic method, time evolution of this many-body system has been investigated. In order to study the time evolution, Lewis-Riesenfeld dynamical invariant and time evolution operator method have been used. Appropriate dynamical invariants are constructed and their Eigenvalues are derived as well as appropriate time evolution operators are constructed. These calculations have been done in general form so there are no limiting assumptions on changing of time-dependent functions.
Nuclear collision theory with many-body correlations, 1
International Nuclear Information System (INIS)
Kurihara, Yukio.
1984-11-01
A generalized many-body correlation operator is introduced, following the Feshbach's formalism. Especially, the many-body correlation induced by the strong repulsion and attraction of the realistic NN interaction is concerned and the Feshbach's formalism is reformulated to describe such a many-body correlation well. And a method to estimate the many-body correlation operator is given from the multiple-scattering picture. The present formalism is compared with the resonating-group method. (author)
Bajaj, Pushp; Wang, Xiao-Gang; Carrington, Tucker; Paesani, Francesco
2018-03-01
Full-dimensional vibrational spectra are calculated for both X-(H2O) and X-(D2O) dimers (X = F, Cl, Br, I) at the quantum-mechanical level. The calculations are carried out on two sets of recently developed potential energy functions (PEFs), namely, Thole-type model energy (TTM-nrg) and many-body energy (MB-nrg), using the symmetry-adapted Lanczos algorithm with a product basis set including all six vibrational coordinates. Although both TTM-nrg and MB-nrg PEFs are derived from coupled-cluster single double triple-F12 data obtained in the complete basis set limit, they differ in how many-body effects are represented at short range. Specifically, while both models describe long-range interactions through the combination of two-body dispersion and many-body classical electrostatics, the relatively simple Born-Mayer functions employed in the TTM-nrg PEFs to represent short-range interactions are replaced in the MB-nrg PEFs by permutationally invariant polynomials to achieve chemical accuracy. For all dimers, the MB-nrg vibrational spectra are in close agreement with the available experimental data, correctly reproducing anharmonic and nuclear quantum effects. In contrast, the vibrational frequencies calculated with the TTM-nrg PEFs exhibit significant deviations from the experimental values. The comparison between the TTM-nrg and MB-nrg results thus reinforces the notion that an accurate representation of both short-range interactions associated with electron density overlap and long-range many-body electrostatic interactions is necessary for a correct description of hydration phenomena at the molecular level.
Passman, Donald S
2012-01-01
This volume by a prominent authority on permutation groups consists of lecture notes that provide a self-contained account of distinct classification theorems. A ready source of frequently quoted but usually inaccessible theorems, it is ideally suited for professional group theorists as well as students with a solid background in modern algebra.The three-part treatment begins with an introductory chapter and advances to an economical development of the tools of basic group theory, including group extensions, transfer theorems, and group representations and characters. The final chapter feature
International Nuclear Information System (INIS)
Bantay, P.
2002-01-01
A general theory of permutation orbifolds is developed for arbitrary twist groups. Explicit expressions for the number of primaries, the partition function, the genus one characters, the matrix elements of modular transformations and for fusion rule coefficients are presented, together with the relevant mathematical concepts, such as Λ-matrices and twisted dimensions. The arithmetic restrictions implied by the theory for the allowed modular representations in CFT are discussed. The simplest nonabelian example with twist group S 3 is described to illustrate the general theory
From few- to many-body quantum systems
Schiulaz, Mauro; Távora, Marco; Santos, Lea F.
2018-01-01
How many particles are necessary to make a many-body quantum system? To answer this question, we take as reference for the many-body limit a quantum system at half-filling and compare its properties with those of a system with $N$ particles, gradually increasing $N$ from 1. We show that the convergence of the static properties of the system with few particles to the many-body limit is fast. For $N \\gtrsim 4$, the density of states is already very close to Gaussian and signatures of many-body ...
EDITORIAL: Focus on Quantum Information and Many-Body Theory
Eisert, Jens; Plenio, Martin B.
2010-02-01
Quantum many-body models describing natural systems or materials and physical systems assembled piece by piece in the laboratory for the purpose of realizing quantum information processing share an important feature: intricate correlations that originate from the coherent interaction between a large number of constituents. In recent years it has become manifest that the cross-fertilization between research devoted to quantum information science and to quantum many-body physics leads to new ideas, methods, tools, and insights in both fields. Issues of criticality, quantum phase transitions, quantum order and magnetism that play a role in one field find relations to the classical simulation of quantum systems, to error correction and fault tolerance thresholds, to channel capacities and to topological quantum computation, to name but a few. The structural similarities of typical problems in both fields and the potential for pooling of ideas then become manifest. Notably, methods and ideas from quantum information have provided fresh approaches to long-standing problems in strongly correlated systems in the condensed matter context, including both numerical methods and conceptual insights. Focus on quantum information and many-body theory Contents TENSOR NETWORKS Homogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems M Rizzi, S Montangero, P Silvi, V Giovannetti and Rosario Fazio Concatenated tensor network states R Hübener, V Nebendahl and W Dür Entanglement renormalization in free bosonic systems: real-space versus momentum-space renormalization group transforms G Evenbly and G Vidal Finite-size geometric entanglement from tensor network algorithms Qian-Qian Shi, Román Orús, John Ove Fjærestad and Huan-Qiang Zhou Characterizing symmetries in a projected entangled pair state D Pérez-García, M Sanz, C E González-Guillén, M M Wolf and J I Cirac Matrix product operator representations B Pirvu, V Murg, J I Cirac
Many-body localization from one particle density matrix
Energy Technology Data Exchange (ETDEWEB)
Bera, Soumya; Bardarson, Jens [Max Planck Institute for the Physics of Complex Systems, Dresden (Germany); Schomerus, Henning [Lancaster University, Lancaster (United Kingdom); Heidrich-Meisner, Fabian [Ludwig-Maximilians-Universitaet Muenchen (Germany)
2016-07-01
We show that the one-particle density matrix ρ can be used to characterize the interaction-driven many-body localization transition in isolated fermionic systems. The natural orbitals (the eigenstates) are localized in the many-body localized phase and spread out when one enters the delocalized phase, while the occupation spectrum (the set of eigenvalues) reveals the distinctive Fock- space structure of the many-body eigenstates, exhibiting a step-like discontinuity in the localized phase. The associated one-particle occupation entropy is small in the localized phase and large in the delocalized phase, with diverging fluctuations at the transition.
Aspects of Strongly Correlated Many-Body Fermi Systems
Porter, William J., III
which we use to characterize the entanglement properties of the two-body sector across a broad range of attractive couplings. In the many-body case, we determine universal scaling properties of this system, and for the two-body case, we compute the entanglement spectrum exactly, successfully characterizing a vast range of entanglement behavior across the BCS-BEC crossover.
Detecting a many-body mobility edge with quantum quenches
Directory of Open Access Journals (Sweden)
Piero Naldesi, Elisa Ercolessi, Tommaso Roscilde
2016-10-01
Full Text Available The many-body localization (MBL transition is a quantum phase transition involving highly excited eigenstates of a disordered quantum many-body Hamiltonian, which evolve from "extended/ergodic" (exhibiting extensive entanglement entropies and fluctuations to "localized" (exhibiting area-law scaling of entanglement and fluctuations. The MBL transition can be driven by the strength of disorder in a given spectral range, or by the energy density at fixed disorder - if the system possesses a many-body mobility edge. Here we propose to explore the latter mechanism by using "quantum-quench spectroscopy", namely via quantum quenches of variable width which prepare the state of the system in a superposition of eigenstates of the Hamiltonian within a controllable spectral region. Studying numerically a chain of interacting spinless fermions in a quasi-periodic potential, we argue that this system has a many-body mobility edge; and we show that its existence translates into a clear dynamical transition in the time evolution immediately following a quench in the strength of the quasi-periodic potential, as well as a transition in the scaling properties of the quasi-stationary state at long times. Our results suggest a practical scheme for the experimental observation of many-body mobility edges using cold-atom setups.
Mathematical methods of many-body quantum field theory
Lehmann, Detlef
2004-01-01
Mathematical Methods of Many-Body Quantum Field Theory offers a comprehensive, mathematically rigorous treatment of many-body physics. It develops the mathematical tools for describing quantum many-body systems and applies them to the many-electron system. These tools include the formalism of second quantization, field theoretical perturbation theory, functional integral methods, bosonic and fermionic, and estimation and summation techniques for Feynman diagrams. Among the physical effects discussed in this context are BCS superconductivity, s-wave and higher l-wave, and the fractional quantum Hall effect. While the presentation is mathematically rigorous, the author does not focus solely on precise definitions and proofs, but also shows how to actually perform the computations.Presenting many recent advances and clarifying difficult concepts, this book provides the background, results, and detail needed to further explore the issue of when the standard approximation schemes in this field actually work and wh...
Vortex matter stabilized by many-body interactions
Wolf, S.; Vagov, A.; Shanenko, A. A.; Axt, V. M.; Aguiar, J. Albino
2017-10-01
This work investigates interactions of vortices in superconducting materials between standard types I and II, in the domain of the so-called intertype (IT) superconductivity. Contrary to common expectations, the many-body (many-vortex) contribution is not a correction to the pair-vortex interaction here but plays a crucial role in the formation of the IT vortex matter. In particular, the many-body interactions stabilize vortex clusters that otherwise could not exist. Furthermore, clusters with large numbers of vortices become more stable when approaching the boundary between the intertype domain and type I. This indicates that IT superconductors develop a peculiar unconventional type of the vortex matter governed by the many-body interactions of vortices.
The quantum mechanics of many-body systems
Thouless, David James; Brueckner, Keith A
1961-01-01
The Quantum Mechanics of Many-Body Systems provides an introduction to that field of theoretical physics known as """"many-body theory."""" It is concerned with problems that are common to nuclear physics, atomic physics, the electron theory of metals, and to the theories of liquid helium three and four, and it describes the methods which have recently been developed to solve such problems. The aim has been to produce a unified account of the field, rather than to describe all the parallel methods that have been developed; as a result, a number of important papers are not mentioned. The main
Short history of nuclear many-body problem
International Nuclear Information System (INIS)
Köhler, H.S.
2014-01-01
This is a very short presentation regarding developments in the theory of nuclear many-body problems, as seen and experienced by the author during the past 60 years with particular emphasis on the contributions of Gerry Brown and his research-group. Much of his work was based on Brueckner's formulation of the nuclear many-body problem. It is reviewed briefly together with the Moszkowski–Scott separation method that was an important part of his early work. The core polarisation and his work related to effective interactions in general are also addressed
Nonlocality in many-body quantum systems detected with two-body correlators
Energy Technology Data Exchange (ETDEWEB)
Tura, J., E-mail: jordi.tura@icfo.es [ICFO—Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona) (Spain); Augusiak, R.; Sainz, A.B. [ICFO—Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona) (Spain); Lücke, B.; Klempt, C. [Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover (Germany); Lewenstein, M.; Acín, A. [ICFO—Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona) (Spain); ICREA—Institució Catalana de Recerca i Estudis Avançats, Lluis Campanys 3, 08010 Barcelona (Spain)
2015-11-15
Contemporary understanding of correlations in quantum many-body systems and in quantum phase transitions is based to a large extent on the recent intensive studies of entanglement in many-body systems. In contrast, much less is known about the role of quantum nonlocality in these systems, mostly because the available multipartite Bell inequalities involve high-order correlations among many particles, which are hard to access theoretically, and even harder experimentally. Standard, “theorist- and experimentalist-friendly” many-body observables involve correlations among only few (one, two, rarely three...) particles. Typically, there is no multipartite Bell inequality for this scenario based on such low-order correlations. Recently, however, we have succeeded in constructing multipartite Bell inequalities that involve two- and one-body correlations only, and showed how they revealed the nonlocality in many-body systems relevant for nuclear and atomic physics [Tura et al., Science 344 (2014) 1256]. With the present contribution we continue our work on this problem. On the one hand, we present a detailed derivation of the above Bell inequalities, pertaining to permutation symmetry among the involved parties. On the other hand, we present a couple of new results concerning such Bell inequalities. First, we characterize their tightness. We then discuss maximal quantum violations of these inequalities in the general case, and their scaling with the number of parties. Moreover, we provide new classes of two-body Bell inequalities which reveal nonlocality of the Dicke states—ground states of physically relevant and experimentally realizable Hamiltonians. Finally, we shortly discuss various scenarios for nonlocality detection in mesoscopic systems of trapped ions or atoms, and by atoms trapped in the vicinity of designed nanostructures.
Many-body localization of bosons in optical lattices
Sierant, Piotr; Zakrzewski, Jakub
2018-04-01
Many-body localization for a system of bosons trapped in a one-dimensional lattice is discussed. Two models that may be realized for cold atoms in optical lattices are considered. The model with a random on-site potential is compared with previously introduced random interactions model. While the origin and character of the disorder in both systems is different they show interesting similar properties. In particular, many-body localization appears for a sufficiently large disorder as verified by a time evolution of initial density wave states as well as using statistical properties of energy levels for small system sizes. Starting with different initial states, we observe that the localization properties are energy-dependent which reveals an inverted many-body localization edge in both systems (that finding is also verified by statistical analysis of energy spectrum). Moreover, we consider computationally challenging regime of transition between many body localized and extended phases where we observe a characteristic algebraic decay of density correlations which may be attributed to subdiffusion (and Griffiths-like regions) in the studied systems. Ergodicity breaking in the disordered Bose–Hubbard models is compared with the slowing-down of the time evolution of the clean system at large interactions.
Computational Nuclear Quantum Many-Body Problem: The UNEDF Project
Bogner, Scott; Bulgac, Aurel; Carlson, Joseph A.; Engel, Jonathan; Fann, George; Furnstahl, Richard J.; Gandolfi, Stefano; Hagen, Gaute; Horoi, Mihai; Johnson, Calvin W.; Kortelainen, Markus; Lusk, Ewing; Maris, Pieter; Nam, Hai Ah; Navratil, Petr
2013-01-01
The UNEDF project was a large-scale collaborative effort that applied high-performance computing to the nuclear quantum many-body problem. UNEDF demonstrated that close associations among nuclear physicists, mathematicians, and computer scientists can lead to novel physics outcomes built on algorithmic innovations and computational developments. This review showcases a wide range of UNEDF science results to illustrate this interplay.
Many body effects in the van der Waals force
International Nuclear Information System (INIS)
Perez, P.; Claro, F.
1985-08-01
A classical model of fluctuating dipoles is proposed for the evaluation of many-body effects in the van der Waals force between neutral polarizable particles. The method is applied to solid xenon giving the correct low temperature stable structure, unlike the usual two-body potential result. (author)
Thermodynamical and Green function many-body Wick theorems
International Nuclear Information System (INIS)
Westwanski, B.
1987-01-01
The thermodynamical and Green function many-body reduction theorems of Wick type are proved for the arbitrary mixtures of the fermion, boson and spin systems. ''Many-body'' means that the operators used are the products of the arbitrary number of one-body standard basis operators [of the fermion or (and) spin types] with different site (wave vector) indices, but having the same ''time'' (in the interaction representation). The method of proving is based on'' 1) the first-order differential equation of Schwinger type for: 1a) anti T-product of operators; 1b) its average value; 2) KMS boundary conditions for this average. It is shown that the fermion, boson and spin systems can be unified in the many-body formulation (bosonification of the fermion systems). It is impossible in the one-body approach. Both of the many-body versions of the Wick theorem have the recurrent feature: nth order moment diagrams for the free energy or Green functions can be expressed by the (n-1)th order ones. This property corresponds to the automatic realization of: (i) summations over Bose-Einstein or (and) Fermi-Dirac frequencies; (ii) elimination of Bose-Einstein or (and) Fermi-Dirac distributions. The procedures (i) and (ii), being the results of using the Green function one-body reduction theorem, have constituted the significant difficulty up to now in the treatment of quantum systems. (orig.)
Properties of exponential many-body interatomic potentials
Czech Academy of Sciences Publication Activity Database
Ostapovets, Andrej; Paidar, Václav
2009-01-01
Roč. 47, č. 3 (2009), s. 193-199 ISSN 0023-432X R&D Projects: GA AV ČR IAA100100920 Institutional research plan: CEZ:AV0Z10100520 Keywords : many-body potentials * elastic constants * multilayer surface relaxations Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.345, year: 2007
Q-deformed algebras and many-body physics
Energy Technology Data Exchange (ETDEWEB)
Galetti, D; Lunardi, J T; Pimentel, B M [Instituto de Fisica Teorica (IFT), Sao Paulo, SP (Brazil); Lima, C L [Sao Paulo Univ., SP (Brazil). Inst. de Fisica
1995-11-01
A review is presented of some applications of q-deformed algebras to many-body systems. The rotational and pairing nuclear problems will be discussed in the context of q-deformed algebras, before presenting a more microscopically based application of q-deformed concepts to many-fermion systems. (author). 30 refs., 5 figs.
Thermalization dynamics in a quenched many-body state
Kaufman, Adam; Preiss, Philipp; Tai, Eric; Lukin, Alex; Rispoli, Matthew; Schittko, Robert; Greiner, Markus
2016-05-01
Quantum and classical many-body systems appear to have disparate behavior due to the different mechanisms that govern their evolution. The dynamics of a classical many-body system equilibrate to maximally entropic states and quickly re-thermalize when perturbed. The assumptions of ergodicity and unbiased configurations lead to a successful framework of describing classical systems by a sampling of thermal ensembles that are blind to the system's microscopic details. By contrast, an isolated quantum many-body system is governed by unitary evolution: the system retains memory of past dynamics and constant global entropy. However, even with differing characteristics, the long-term behavior for local observables in quenched, non-integrable quantum systems are often well described by the same thermal framework. We explore the onset of this convergence in a many-body system of bosonic atoms in an optical lattice. Our system's finite size allows us to verify full state purity and measure local observables. We observe rapid growth and saturation of the entanglement entropy with constant global purity. The combination of global purity and thermalized local observables agree with the Eigenstate Thermalization Hypothesis in the presence of a near-volume law in the entanglement entropy.
Many-body forces in nuclear shell-model
International Nuclear Information System (INIS)
Rath, P.K.
1985-01-01
In the microscopic derivation of the effective Hamiltonian for the nuclear shell model many-body forces between the valence nucleons occur. These many-body forces can be discriminated in ''real'' many-body forces, which can be related to mesonic and internal degrees of freedom of the nucleons, and ''effective'' many-body forces, which arise by the confinement of the nucleonic Hilbert space to the finite-dimension shell-model space. In the present thesis the influences of such three-body forces on the spectra of sd-shell nuclei are studied. For this the two common techniques for shell-model calculations (Oak Ridge-Rochester and Glasgow representation) are extended in such way that a general three-body term in the Hamiltonian can be regarded. The studies show that the repulsive contributions of the considered three-nucleon forces become more important with increasing number of valence nucleons. By this the particle-number dependence of empirical two-nucleon forces can be qualitatively explained. A special kind of effective many-body force occurs in the folded diagram expansion of the energy-dependent effective Hamiltonian for the shell model. Thereby it is shown that the contributions of the folded diagrams with three nucleons are just as important as those with two nucleons. Thus it is to be suspected that the folded diagram expansion contains many-particle terms with arbitrary particle number. The present studies however show that four nucleon effects are neglegible so that the folded diagram expansion can be confined to two- and three-particle terms. In shell-model calculations which extend over several main shells the influences of the spurious center-of-mass motion must be regarded. A procedure is discussed by which these spurious degrees of freedom can be exactly separated. (orig.) [de
Quantum Markov processes and applications in many-body systems
International Nuclear Information System (INIS)
Temme, P. K.
2010-01-01
This thesis is concerned with the investigation of quantum as well as classical Markov processes and their application in the field of strongly correlated many-body systems. A Markov process is a special kind of stochastic process, which is determined by an evolution that is independent of its history and only depends on the current state of the system. The application of Markov processes has a long history in the field of statistical mechanics and classical many-body theory. Not only are Markov processes used to describe the dynamics of stochastic systems, but they predominantly also serve as a practical method that allows for the computation of fundamental properties of complex many-body systems by means of probabilistic algorithms. The aim of this thesis is to investigate the properties of quantum Markov processes, i.e. Markov processes taking place in a quantum mechanical state space, and to gain a better insight into complex many-body systems by means thereof. Moreover, we formulate a novel quantum algorithm which allows for the computation of the thermal and ground states of quantum many-body systems. After a brief introduction to quantum Markov processes we turn to an investigation of their convergence properties. We find bounds on the convergence rate of the quantum process by generalizing geometric bounds found for classical processes. We generalize a distance measure that serves as the basis for our investigations, the chi-square divergence, to non-commuting probability spaces. This divergence allows for a convenient generalization of the detailed balance condition to quantum processes. We then devise the quantum algorithm that can be seen as the natural generalization of the ubiquitous Metropolis algorithm to simulate quantum many-body Hamiltonians. By this we intend to provide further evidence, that a quantum computer can serve as a fully-fledged quantum simulator, which is not only capable of describing the dynamical evolution of quantum systems, but
Nonlinear many-body reaction theories from nuclear mean field approximations
International Nuclear Information System (INIS)
Griffin, J.J.
1983-01-01
Several methods of utilizing nonlinear mean field propagation in time to describe nuclear reaction have been studied. The property of physical asymptoticity is analyzed in this paper, which guarantees that the prediction by a reaction theory for the physical measurement of internal fragment properties shall not depend upon the precise location of the measuring apparatus. The physical asymptoticity is guaranteed in the Schroedinger collision theory of a scuttering system with translationally invariant interaction by the constancy of the S-matrix elements and by the translational invariance of the internal motion for well-separated fragments. Both conditions are necessary for the physical asymptoticity. The channel asymptotic single-determinantal propagation can be described by the Dirac-TDHF (time dependent Hartree-Fock) time evolution. A new asymptotic Hartree-Fock stationary phase (AHFSP) description together with the S-matrix time-dependent Hartree-Fock (TD-S-HF) theory constitute the second example of a physically asymptotic nonlinear many-body reaction theory. A review of nonlinear mean field many-body reaction theories shows that initial value TDHF is non-asymptotic. The TD-S-HF theory is asymptotic by the construction. The gauge invariant periodic quantized solution of the exact Schroedinger problem has been considered to test whether it includes all of the exact eigenfunctions as it ought to. It did, but included as well an infinity of all spurions solutions. (Kato, T.)
Almost conserved operators in nearly many-body localized systems
Pancotti, Nicola; Knap, Michael; Huse, David A.; Cirac, J. Ignacio; Bañuls, Mari Carmen
2018-03-01
We construct almost conserved local operators, that possess a minimal commutator with the Hamiltonian of the system, near the many-body localization transition of a one-dimensional disordered spin chain. We collect statistics of these slow operators for different support sizes and disorder strengths, both using exact diagonalization and tensor networks. Our results show that the scaling of the average of the smallest commutators with the support size is sensitive to Griffiths effects in the thermal phase and the onset of many-body localization. Furthermore, we demonstrate that the probability distributions of the commutators can be analyzed using extreme value theory and that their tails reveal the difference between diffusive and subdiffusive dynamics in the thermal phase.
Universal Properties of Many-Body Delocalization Transitions
Directory of Open Access Journals (Sweden)
Andrew C. Potter
2015-09-01
Full Text Available We study the dynamical melting of “hot” one-dimensional many-body localized systems. As disorder is weakened below a critical value, these nonthermal quantum glasses melt via a continuous dynamical phase transition into classical thermal liquids. By accounting for collective resonant tunneling processes, we derive and numerically solve an effective model for such quantum-to-classical transitions and compute their universal critical properties. Notably, the classical thermal liquid exhibits a broad regime of anomalously slow subdiffusive equilibration dynamics and energy transport. The subdiffusive regime is characterized by a continuously evolving dynamical critical exponent that diverges with a universal power at the transition. Our approach elucidates the universal long-distance, low-energy scaling structure of many-body delocalization transitions in one dimension, in a way that is transparently connected to the underlying microscopic physics. We discuss experimentally testable signatures of the predicted scaling properties.
Quasiparticle many-body dynamics of the Anderson model
International Nuclear Information System (INIS)
Kuzemskij, A.L.
1996-01-01
The paper addresses the many-body quasiparticle dynamics of the Anderson impurity model at finite temperatures in the framework of the equation-of-motion method. We find a new exact identity relating the one-particle and many-particle Green's Functions. Using this identity we present a consistent and general scheme for a construction of generalised mean fields (elastic scattering corrections) and self-energy (inelastic scattering) in terms of the Dyson equation. A new approach for the complex expansion for the single-particle propagator in terms of the Coulomb repulsion U and hybridization V is proposed. Using the exact identity, the essentially new many-body dynamical solution of SIAM has been derived. This approach offers a new way for the systematic construction of the approximative interpolating dynamical solutions of the strongly correlated electron systems. 47 refs
Solvable Family of Driven-Dissipative Many-Body Systems
Foss-Feig, Michael; Young, Jeremy T.; Albert, Victor V.; Gorshkov, Alexey V.; Maghrebi, Mohammad F.
2017-11-01
Exactly solvable models have played an important role in establishing the sophisticated modern understanding of equilibrium many-body physics. Conversely, the relative scarcity of solutions for nonequilibrium models greatly limits our understanding of systems away from thermal equilibrium. We study a family of nonequilibrium models, some of which can be viewed as dissipative analogues of the transverse-field Ising model, in that an effectively classical Hamiltonian is frustrated by dissipative processes that drive the system toward states that do not commute with the Hamiltonian. Surprisingly, a broad and experimentally relevant subset of these models can be solved efficiently. We leverage these solutions to compute the effects of decoherence on a canonical trapped-ion-based quantum computation architecture, and to prove a no-go theorem on steady-state phase transitions in a many-body model that can be realized naturally with Rydberg atoms or trapped ions.
Integrals of motion in the many-body localized phase
Directory of Open Access Journals (Sweden)
V. Ros
2015-02-01
Full Text Available We construct a complete set of quasi-local integrals of motion for the many-body localized phase of interacting fermions in a disordered potential. The integrals of motion can be chosen to have binary spectrum {0,1}, thus constituting exact quasiparticle occupation number operators for the Fermi insulator. We map the problem onto a non-Hermitian hopping problem on a lattice in operator space. We show how the integrals of motion can be built, under certain approximations, as a convergent series in the interaction strength. An estimate of its radius of convergence is given, which also provides an estimate for the many-body localization–delocalization transition. Finally, we discuss how the properties of the operator expansion for the integrals of motion imply the presence or absence of a finite temperature transition.
Many-body interactions in quasi-freestanding graphene
Energy Technology Data Exchange (ETDEWEB)
Siegel, David; Park, Cheol-Hwan; Hwang, Choongyu; Deslippe, Jack; Fedorov, Alexei; Louie, Steven; Lanzara, Alessandra
2011-06-03
The Landau-Fermi liquid picture for quasiparticles assumes that charge carriers are dressed by many-body interactions, forming one of the fundamental theories of solids. Whether this picture still holds for a semimetal such as graphene at the neutrality point, i.e., when the chemical potential coincides with the Dirac point energy, is one of the long-standing puzzles in this field. Here we present such a study in quasi-freestanding graphene by using high-resolution angle-resolved photoemission spectroscopy. We see the electron-electron and electron-phonon interactions go through substantial changes when the semimetallic regime is approached, including renormalizations due to strong electron-electron interactions with similarities to marginal Fermi liquid behavior. These findings set a new benchmark in our understanding of many-body physics in graphene and a variety of novel materials with Dirac fermions.
Theory of many-body localization in periodically driven systems
International Nuclear Information System (INIS)
Abanin, Dmitry A.; De Roeck, Wojciech; Huveneers, François
2016-01-01
We present a theory of periodically driven, many-body localized (MBL) systems. We argue that MBL persists under periodic driving at high enough driving frequency: The Floquet operator (evolution operator over one driving period) can be represented as an exponential of an effective time-independent Hamiltonian, which is a sum of quasi-local terms and is itself fully MBL. We derive this result by constructing a sequence of canonical transformations to remove the time-dependence from the original Hamiltonian. When the driving evolves smoothly in time, the theory can be sharpened by estimating the probability of adiabatic Landau–Zener transitions at many-body level crossings. In all cases, we argue that there is delocalization at sufficiently low frequency. We propose a phase diagram of driven MBL systems.
Nonlinear Quantum Metrology of Many-Body Open Systems
Beau, M.; del Campo, A.
2017-07-01
We introduce general bounds for the parameter estimation error in nonlinear quantum metrology of many-body open systems in the Markovian limit. Given a k -body Hamiltonian and p -body Lindblad operators, the estimation error of a Hamiltonian parameter using a Greenberger-Horne-Zeilinger state as a probe is shown to scale as N-[k -(p /2 )], surpassing the shot-noise limit for 2 k >p +1 . Metrology equivalence between initial product states and maximally entangled states is established for p ≥1 . We further show that one can estimate the system-environment coupling parameter with precision N-(p /2 ), while many-body decoherence enhances the precision to N-k in the noise-amplitude estimation of a fluctuating k -body Hamiltonian. For the long-range Ising model, we show that the precision of this parameter beats the shot-noise limit when the range of interactions is below a threshold value.
Efficient numerical simulations of many-body localized systems
Energy Technology Data Exchange (ETDEWEB)
Pollmann, Frank [Max-Planck-Institut fuer Physik komplexer Systeme, 01187 Dresden (Germany); Khemani, Vedika; Sondhi, Shivaji [Physics Department, Princeton University, Princeton, NJ 08544 (United States)
2016-07-01
Many-body localization (MBL) occurs in isolated quantum systems when Anderson localization persists in the presence of finite interactions. To understand this phenomenon, the development of new, efficient numerical methods to find highly excited eigenstates is essential. We introduce a variant of the density-matrix renormalization group (DMRG) method that obtains individual highly excited eigenstates of MBL systems to machine precision accuracy at moderate-large disorder. This method explicitly takes advantage of the local spatial structure characterizing MBL eigenstates.
Many body quantum physics at the condensed matter
International Nuclear Information System (INIS)
Llano, M. de
1981-01-01
The non-relativistic, continuous (as opposed to spin) many-body problem as it relates to condensed matter at absolute zero temperature is reviewed in simple, non-technical terms, mainly from the standpoint of infinite order perturbation theory, for physical systems where all the particles have the same mass but which otherwise interact with arbitrary short- or long-ranged two-body forces. (author)
Entanglement replication in driven dissipative many-body systems.
Zippilli, S; Paternostro, M; Adesso, G; Illuminati, F
2013-01-25
We study the dissipative dynamics of two independent arrays of many-body systems, locally driven by a common entangled field. We show that in the steady state the entanglement of the driving field is reproduced in an arbitrarily large series of inter-array entangled pairs over all distances. Local nonclassical driving thus realizes a scale-free entanglement replication and long-distance entanglement distribution mechanism that has immediate bearing on the implementation of quantum communication networks.
Many-Body Coulomb Gauge Exotic and Charmed Hybrids
Llanes-Estrada, Felipe J.; Cotanch, Stephen R.
2000-01-01
Utilizing a QCD Coulomb gauge Hamiltonian with linear confinement specified by lattice, we report a relativistic many-body calculation for the light exotic and charmed hybrid mesons. The Hamiltonian successfully describes both quark and gluon sectors, with vacuum and quasiparticle properties generated by a BCS transformation and more elaborate TDA and RPA diagonalizations for the meson ($q\\bar{q}$) and glueball ($gg$) masses. Hybrids entail a computationally intense relativistic three quasipa...
Few-body correlations in many-body physics
Energy Technology Data Exchange (ETDEWEB)
Barth, Marcus
2015-12-01
In this thesis, various systems are analyzed in parameter regimes where the few-body aspects are dominant over the many-body behavior. Using the Operator Product Expansion from Quantum Field Theory, exact relations for observables of the electron gas as well as two-dimensional Fermi gases are derived. In addition, properties of both two-dimensional and three-dimensional cold quantum gases at small to moderate degeneracy are determined by means of a diagrammatic virial expansion.
General many-body formalism for composite quantum particles.
Combescot, M; Betbeder-Matibet, O
2010-05-21
This Letter provides a formalism capable of exactly treating Pauli blocking between n-fermion particles. This formalism is based on an operator algebra made of commutators and anticommutators which contrasts with the usual scalar formalism of Green functions developed half a century ago for elementary quantum particles. We also provide the diagrams which visualize the very specific many-body physics induced by fermion exchanges between composite quantum particles.
Chiral symmetry and many-body forces in nuclei
International Nuclear Information System (INIS)
Nyman, E.M.; Rho, M.
1976-01-01
It is demonstrated that when quantum corrections are added, chiral Lagrangians need not generate strong many-body forces as they do in tree approximation. It is suggested that a physically reasonable procedure is to adjust the sigma-model parameters so as not to conflict with the current status of nuclear theory. As a consequence, the equilibrium density of abnormal states could be pushed up further, and the binding energy be considerably reduced. (Auth.)
On nonequilibrium many-body systems III: nonlinear transport theory
International Nuclear Information System (INIS)
Luzzi, R.; Vasconcellos, A.R.; Algarte, A.C.S.
1986-01-01
A nonlinear transport theory for many-body systems arbitrarily away from equilibrium, based on the nonequilibrium statistical operator (NSO) method, is presented. Nonlinear transport equations for a basis set of dynamical quantities are derived using two equivalent treatments that may be considered far reaching generalizations of the Hilbert-Chapman-Enskog method and Mori's generalized Langevin equations method. The first case is considered in some detail and the general characteristics of the theory are discussed. (Author) [pt
Probing many-body interactions in an optical lattice clock
Energy Technology Data Exchange (ETDEWEB)
Rey, A.M., E-mail: arey@jilau1.colorado.edu [JILA, NIST and University of Colorado, Department of Physics, Boulder, CO 80309 (United States); Gorshkov, A.V. [Joint Quantum Institute, NIST and University of Maryland, Department of Physics, College Park, MD 20742 (United States); Kraus, C.V. [Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck (Austria); Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck (Austria); Martin, M.J. [JILA, NIST and University of Colorado, Department of Physics, Boulder, CO 80309 (United States); Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125 (United States); Bishof, M.; Swallows, M.D.; Zhang, X.; Benko, C.; Ye, J. [JILA, NIST and University of Colorado, Department of Physics, Boulder, CO 80309 (United States); Lemke, N.D.; Ludlow, A.D. [National Institute of Standards and Technology, Boulder, CO 80305 (United States)
2014-01-15
We present a unifying theoretical framework that describes recently observed many-body effects during the interrogation of an optical lattice clock operated with thousands of fermionic alkaline earth atoms. The framework is based on a many-body master equation that accounts for the interplay between elastic and inelastic p-wave and s-wave interactions, finite temperature effects and excitation inhomogeneity during the quantum dynamics of the interrogated atoms. Solutions of the master equation in different parameter regimes are presented and compared. It is shown that a general solution can be obtained by using the so called Truncated Wigner Approximation which is applied in our case in the context of an open quantum system. We use the developed framework to model the density shift and decay of the fringes observed during Ramsey spectroscopy in the JILA {sup 87}Sr and NIST {sup 171}Yb optical lattice clocks. The developed framework opens a suitable path for dealing with a variety of strongly-correlated and driven open-quantum spin systems. -- Highlights: •Derived a theoretical framework that describes many-body effects in a lattice clock. •Validated the analysis with recent experimental measurements. •Demonstrated the importance of beyond mean field corrections in the dynamics.
Atomic many-body theory of giant resonances
International Nuclear Information System (INIS)
Kelly, H.P.; Altun, Z.
1987-01-01
In this paper the use of many-body perturbation theory (MBPT) to include effects of electron correlations is discussed. The various physical processes contributing to the broad photoionization cross sections of the rare gases are studied in terms of the relevant many-body diagrams. Use of the random phase approximation with exchange (RPAE) is discussed by Amusia and Cherepkov. Calculations using the relativistic RPAE are reviewed by Johnson. In addition, many-body perturbation theory (MBPT) is used to study resonances which are due to excitation of bound states degenerate with the continuum. Very interesting giant resonance structure can occur when an inner shell electron is excited into a vacant open-shell orbital of the same principal quantum number. A particular example which is studied is the neutral manganese atom 3p 6 3d 5 4s 2 ( 6 S), in which the spins of the five 3d electrons are aligned. A very large resonance occurs in the 3d and 4s cross sections due to 3p → 3d excitation near 51 eV, and calculations of this resonance by MBPT and RPAE are discussed. A second example of this type of resonance occurs in open-shell rare-earth atoms with configurations 4d 10 4f/sup n/5s 2 5p 6 s 2 . Calculations and experimental results will be discussed for the case of europium with a half-filled sub-shell 4f 7 . 71 references, 15 figures
Entanglement between noncomplementary parts of many-body systems
International Nuclear Information System (INIS)
Wichterich, Hannu Christian
2011-01-01
This thesis investigates the structure and behaviour of entanglement, the purely quantum mechanical part of correlations, in many-body systems, employing both numerical and analytical techniques at the interface of condensed matter theory and quantum information theory. Entanglement can be seen as a precious resource which, for example, enables the noiseless and instant transmission of quantum information, provided the communicating parties share a sufficient ''amount'' of it. Furthermore, measures of entanglement of a quantum mechanical state are perceived as useful probes of collective properties of many-body systems. For instance, certain measures are capable of detecting and classifying ground-state phases and, particularly, transition (or critical) points separating such phases. Chapters 2 and 3 focus on entanglement in many-body systems and its use as a potential resource for communication protocols. They address the questions of how a substantial amount of entanglement can be established between distant subsystems, and how efficiently this entanglement could be ''harvested'' by way of measurements. The subsequent chapters 4 and 5 are devoted to universality of entanglement between large collections of particles undergoing a quantum phase transition, where, despite the enormous complexity of these systems, collective properties including entanglement no longer depend crucially on the microscopic details. (orig.)
Probing many-body localization with neural networks
Schindler, Frank; Regnault, Nicolas; Neupert, Titus
2017-06-01
We show that a simple artificial neural network trained on entanglement spectra of individual states of a many-body quantum system can be used to determine the transition between a many-body localized and a thermalizing regime. Specifically, we study the Heisenberg spin-1/2 chain in a random external field. We employ a multilayer perceptron with a single hidden layer, which is trained on labeled entanglement spectra pertaining to the fully localized and fully thermal regimes. We then apply this network to classify spectra belonging to states in the transition region. For training, we use a cost function that contains, in addition to the usual error and regularization parts, a term that favors a confident classification of the transition region states. The resulting phase diagram is in good agreement with the one obtained by more conventional methods and can be computed for small systems. In particular, the neural network outperforms conventional methods in classifying individual eigenstates pertaining to a single disorder realization. It allows us to map out the structure of these eigenstates across the transition with spatial resolution. Furthermore, we analyze the network operation using the dreaming technique to show that the neural network correctly learns by itself the power-law structure of the entanglement spectra in the many-body localized regime.
Many-body perturbation theory for ab initio nuclear structure
International Nuclear Information System (INIS)
Tichai, Alexander
2017-01-01
The solution of the quantum many-body problem for medium-mass nuclei using realistic nuclear interactions poses a superbe challenge for nuclear structure research. Because an exact solution can only be provided for the lightest nuclei, one has to rely on approximate solutions when proceeding to heavier systems. Over the past years, tremendous progress has been made in the development and application of systematically improvable expansion methods and an accurate description of nuclear observables has become viable up to mass number A ∼ 100. While closed-shell systems are consistently described via a plethora of different many-body methods, the extension to genuine open-shell systems still remains a major challenge and up to now there is no ab initio many-body method which applies equally well to systems with even and odd mass numbers. The goal of this thesis is the development and implementation of innovative perturbative approaches with genuine open-shell capabilities. This requires the extension of well-known single-reference approaches to more general vacua. In this work we choose two complementary routes for the usage of generalized reference states. First, we derive a new ab initio approach based on multi-configurational reference states that are conveniently derived from a prior no-core shell model calculation. Perturbative corrections are derived via second-order many-body perturbation theory, thus, merging configuration interaction and many-body perturbation theory. The generality of this ansatz enables for a treatment of medium-mass systems with arbitrary mass number, as well as the extension to low-lying excited states such that ground and excited states are treated on an equal footing. In a complementary approach, we use reference states that break a symmetry of the underlying Hamiltonian. In the simplest case this corresponds to the expansion around a particle-number-broken Hartree-Fock-Bogolyubov vacuum which is obtained from a mean-field calculation
The mean field in many body quantum physics
International Nuclear Information System (INIS)
Llano, M. de
1984-01-01
As an introduction to the quantum problem of many bodies we present a panoramic view of the most elementary theories called mean field theories. They comprise: i) the fermions ideal gas theory which implies, in a simple manner, the stability of white dwarf stars and of neutron stars, ii) the Hartree-Fock approximation for thermodynamical systems which is presented here in the context of a liquid-crystal phase transition, and iii) the Thomas-Fermi theory which is applied to the total binding energy of neutral atoms. (author)
Density functional and many-body theories of Hydrogen plasmas
International Nuclear Information System (INIS)
Perrot, F.; Dharma-Wardana, M.W.C.
1983-11-01
This work is an attempt to go beyond the standard description of hot condensed matter using the well-known ''average atom model''. The first part describes a static model using ''Density functional theory'' to calculate self-consistent coupled electron and ion density profiles of the plasma not restricted to a single average atomic sphere. In a second part, the results are used as ingredients for a many-body approach to electronic properties: the one-particle Green-function self-energy is calculated, from which shifted levels, populations and level-widths are deduced. Results for the Hydrogen plasma are reported, with emphasis on the 1s bound state
Computational nuclear quantum many-body problem: The UNEDF project
Bogner, S.; Bulgac, A.; Carlson, J.; Engel, J.; Fann, G.; Furnstahl, R. J.; Gandolfi, S.; Hagen, G.; Horoi, M.; Johnson, C.; Kortelainen, M.; Lusk, E.; Maris, P.; Nam, H.; Navratil, P.; Nazarewicz, W.; Ng, E.; Nobre, G. P. A.; Ormand, E.; Papenbrock, T.; Pei, J.; Pieper, S. C.; Quaglioni, S.; Roche, K. J.; Sarich, J.; Schunck, N.; Sosonkina, M.; Terasaki, J.; Thompson, I.; Vary, J. P.; Wild, S. M.
2013-10-01
The UNEDF project was a large-scale collaborative effort that applied high-performance computing to the nuclear quantum many-body problem. The primary focus of the project was on constructing, validating, and applying an optimized nuclear energy density functional, which entailed a wide range of pioneering developments in microscopic nuclear structure and reactions, algorithms, high-performance computing, and uncertainty quantification. UNEDF demonstrated that close associations among nuclear physicists, mathematicians, and computer scientists can lead to novel physics outcomes built on algorithmic innovations and computational developments. This review showcases a wide range of UNEDF science results to illustrate this interplay.
Neural network models: from biology to many - body phenomenology
International Nuclear Information System (INIS)
Clark, J.W.
1993-01-01
Theoretical work in neural networks has a strange feel for most physicists. In some cases the aspect of design becomes paramount. More comfortable ground at least for many body theorists may be found in realistic biological simulation, although the complexity of most problems is so awesome that incisive results will be hard won. It has also shown the impressive capabilities of artificial networks in pattern recognition and classification may be exploited to solve management problems in experimental physics and for discovery of radically new theoretical description of physical systems. This advance represents an important step towards the ultimate goal of neuro biological paradigm. (A.B.)
Many-Body Mean-Field Equations: Parallel implementation
International Nuclear Information System (INIS)
Vallieres, M.; Umar, S.; Chinn, C.; Strayer, M.
1993-01-01
We describe the implementation of Hartree-Fock Many-Body Mean-Field Equations on a Parallel Intel iPSC/860 hypercube. We first discuss the Nuclear Mean-Field approach in physical terms. Then we describe our parallel implementation of this approach on the Intel iPSC/860 hypercube. We discuss and compare the advantages and disadvantages of the domain partition versus the Hilbert space partition for this problem. We conclude by discussing some timing experiments on various computing platforms
Many-Body Green Function of Degenerate Systems
International Nuclear Information System (INIS)
Brouder, Christian; Panati, Gianluca; Stoltz, Gabriel
2009-01-01
A rigorous nonperturbative adiabatic approximation of the evolution operator in the many-body physics of degenerate systems is derived. This approximation is used to solve the long-standing problem of the choice of the initial states of H 0 leading to eigenstates of H 0 +V for degenerate systems. These initial states are eigenstates of P 0 VP 0 , where P 0 is the projection onto a degenerate eigenspace of H 0 . This result is used to give the proper definition of the Green function, the statistical Green function and the nonequilibrium Green function of degenerate systems. The convergence of these Green functions is established.
Many-body physics with circuit quantum electrodynamics
International Nuclear Information System (INIS)
Leib, Martin H.
2015-01-01
We present proposals to simulate many-body physics with superconducting circuits. The ''body'' to work with for superconducting circuits is the microwave photon and interaction is induced by the nonlinearity of the Josephson effect. We present two different approaches to simulate Bose-Hubbard physics, one based on a polariton scheme and another with nonlinear resonators. We also present a Dicke-model like simulator for ultrastrongly coupled Josephson junctions to a resonator and show a scheme for implementing long range interactions.
Many-Body Theory for Positronium-Atom Interactions
Green, D. G.; Swann, A. R.; Gribakin, G. F.
2018-05-01
A many-body-theory approach has been developed to study positronium-atom interactions. As first applications, we calculate the elastic scattering and momentum-transfer cross sections and the pickoff annihilation rate 1Zeff for Ps collisions with He and Ne. For He the cross section is in agreement with previous coupled-state calculations, while comparison with experiment for both atoms highlights discrepancies between various sets of measured data. In contrast, the calculated 1Zeff (0.13 and 0.26 for He and Ne, respectively) are in excellent agreement with the measured values.
Porter-Thomas distribution in unstable many-body systems
International Nuclear Information System (INIS)
Volya, Alexander
2011-01-01
We use the continuum shell model approach to explore the resonance width distribution in unstable many-body systems. The single-particle nature of a decay, the few-body character of the interaction Hamiltonian, and the collectivity that emerges in nonstationary systems due to the coupling to the continuum of reaction states are discussed. Correlations between the structures of the parent and daughter nuclear systems in the common Fock space are found to result in deviations of decay width statistics from the Porter-Thomas distribution.
Many-Body Potentials For Binary Immiscible liquid Metal Alloys
International Nuclear Information System (INIS)
Karaguelle, H.
2004-01-01
The modified analytic embedded atom method (MAEAM) type many- body potentials have been constructed for three binary liquid immiscible alloy systems: Al-Pb, Ag-Ni, Ag- Cu. The MAEAM potential functions are fitted to both solid and liquid state properties for only liquid pure metals which consist the immiscible alloy. In order to test the reliability of the constructed MAEAM effective potentials, partial structure factors and pair distribution functions of these binary liquid metal alloys have been calculated using the thermodynamically self-consistent variational modified hypernetted chain (VMHNC) theory of liquids. A good agreement with the available experimental data for structure has
Efficient tomography of a quantum many-body system
Lanyon, B. P.; Maier, C.; Holzäpfel, M.; Baumgratz, T.; Hempel, C.; Jurcevic, P.; Dhand, I.; Buyskikh, A. S.; Daley, A. J.; Cramer, M.; Plenio, M. B.; Blatt, R.; Roos, C. F.
2017-12-01
Quantum state tomography is the standard technique for estimating the quantum state of small systems. But its application to larger systems soon becomes impractical as the required resources scale exponentially with the size. Therefore, considerable effort is dedicated to the development of new characterization tools for quantum many-body states. Here we demonstrate matrix product state tomography, which is theoretically proven to allow for the efficient and accurate estimation of a broad class of quantum states. We use this technique to reconstruct the dynamical state of a trapped-ion quantum simulator comprising up to 14 entangled and individually controlled spins: a size far beyond the practical limits of quantum state tomography. Our results reveal the dynamical growth of entanglement and describe its complexity as correlations spread out during a quench: a necessary condition for future demonstrations of better-than-classical performance. Matrix product state tomography should therefore find widespread use in the study of large quantum many-body systems and the benchmarking and verification of quantum simulators and computers.
Chiral Floquet Phases of Many-Body Localized Bosons
Directory of Open Access Journals (Sweden)
Hoi Chun Po
2016-12-01
Full Text Available We construct and classify chiral topological phases in driven (Floquet systems of strongly interacting bosons, with finite-dimensional site Hilbert spaces, in two spatial dimensions. The construction proceeds by introducing exactly soluble models with chiral edges, which in the presence of many-body localization (MBL in the bulk are argued to lead to stable chiral phases. These chiral phases do not require any symmetry and in fact owe their existence to the absence of energy conservation in driven systems. Surprisingly, we show that they are classified by a quantized many-body index, which is well defined for any MBL Floquet system. The value of this index, which is always the logarithm of a positive rational number, can be interpreted as the entropy per Floquet cycle pumped along the edge, formalizing the notion of quantum-information flow. We explicitly compute this index for specific models and show that the nontrivial topology leads to edge thermalization, which provides an interesting link between bulk topology and chaos at the edge. We also discuss chiral Floquet phases in interacting fermionic systems and their relation to chiral bosonic phases.
Quantum simulations and many-body physics with light.
Noh, Changsuk; Angelakis, Dimitris G
2017-01-01
In this review we discuss the works in the area of quantum simulation and many-body physics with light, from the early proposals on equilibrium models to the more recent works in driven dissipative platforms. We start by describing the founding works on Jaynes-Cummings-Hubbard model and the corresponding photon-blockade induced Mott transitions and continue by discussing the proposals to simulate effective spin models and fractional quantum Hall states in coupled resonator arrays (CRAs). We also analyse the recent efforts to study out-of-equilibrium many-body effects using driven CRAs, including the predictions for photon fermionisation and crystallisation in driven rings of CRAs as well as other dynamical and transient phenomena. We try to summarise some of the relatively recent results predicting exotic phases such as super-solidity and Majorana like modes and then shift our attention to developments involving 1D nonlinear slow light setups. There the simulation of strongly correlated phases characterising Tonks-Girardeau gases, Luttinger liquids, and interacting relativistic fermionic models is described. We review the major theory results and also briefly outline recent developments in ongoing experimental efforts involving different platforms in circuit QED, photonic crystals and nanophotonic fibres interfaced with cold atoms.
Quantum theory of many-body systems techniques and applications
Zagoskin, Alexandre
2014-01-01
This text presents a self-contained treatment of the physics of many-body systems from the point of view of condensed matter. The approach, quite traditionally, uses the mathematical formalism of quasiparticles and Green’s functions. In particular, it covers all the important diagram techniques for normal and superconducting systems, including the zero-temperature perturbation theory and the Matsubara, Keldysh and Nambu-Gor'kov formalism, as well as an introduction to Feynman path integrals. This new edition contains an introduction to the methods of theory of one-dimensional systems (bosonization and conformal field theory) and their applications to many-body problems. Intended for graduate students in physics and related fields, the aim is not to be exhaustive, but to present enough detail to enable the student to follow the current research literature, or to apply the techniques to new problems. Many of the examples are drawn from mesoscopic physics, which deals with systems small enough that quantum...
Scalar meson field and many-body forces. Chapter 23
International Nuclear Information System (INIS)
Nyman, E.M.
1979-01-01
In applications of field theory to the theory of the nuclear forces, one has frequently assumed that there is a scalar meson. It will then be responsible for most of the medium-range attraction between the nucleons. According to current ideas, however, it is possible to account for the medium-range attraction without an elementary sigma meson. This approach requires a careful treatment of the exchange of interacting pairs of π mesons, such as to include those ππ interactions which are responsible for the formation and decay of the sigma meson. Recently, the scalar field in the nuclear many-body problem has begun to receive more attention. There are two reasons for this change of philosophy. One reason is the discovery of neutron stars. In neutron stars, the nucleon number density can be much higher than in nuclei. One therefore wants to derive the equation of state from a relativistic many-body theory. This forces one to deal explicitly with a set of mesons, such that in the non-relativistic limit one recovers the one-boson-exchange potential. (Auth.)
Relativistic many-body XMCD theory including core degenerate effects
Fujikawa, Takashi
2009-11-01
A many-body relativistic theory to analyze X-ray Magnetic Circular Dichroism (XMCD) spectra has been developed on the basis of relativistic quantum electrodynamic (QED) Keldysh Green's function approach. This theoretical framework enables us to handle relativistic many-body effects in terms of correlated nonrelativistic Green's function and relativistic correction operator Q, which naturally incorporates radiation field screening and other optical field effects in addition to electron-electron interactions. The former can describe the intensity ratio of L2/L3 which deviates from the statistical weight (branching ratio) 1/2. In addition to these effects, we consider the degenerate or nearly degenerate effects of core levels from which photoelectrons are excited. In XPS spectra, for example in Rh 3d sub level excitations, their peak shapes are quite different: This interesting behavior is explained by core-hole moving after the core excitation. We discuss similar problems in X-ray absorption spectra in particular excitation from deep 2p sub levels which are degenerate in each sub levels and nearly degenerate to each other in light elements: The hole left behind is not frozen there. We derive practical multiple scattering formulas which incorporate all those effects.
Neural network models: from biology to many - body phenomenology
International Nuclear Information System (INIS)
Clark, J.W.
1993-01-01
The current surge of research on practical side of neural networks and their utility in memory storage/recall, pattern recognition and classification is given in this article. The initial attraction of neural networks as dynamical and statistical system has been investigated. From the view of many-body theorist, the neurons may be thought of as particles, and the weighted connection between the units, as the interaction between these particles. Finally, the author has seen the impressive capabilities of artificial neural networks in pattern recognition and classification may be exploited to solve data management problems in experimental physics and the discovery of radically new theoretically description of physical problems and neural networks can be used in physics. (A.B.)
The mathematical description of resonances in many-body systems
International Nuclear Information System (INIS)
Orth, A.
1985-01-01
We introduce a characterization for quantum-mechanical resonance and use it in order to detect for certain distinct physical states an especially slow decay behaviour. We apply these results to a model of the quantum-mechanical many-body problem and obtain so a mathematical description of the Auger effect (self-ionization of atoms). The class of the interaction potentials admitted for our theory is compared with other theories on resonances extremely large. We establish differentiability conditions and conditions on the fading behaviour in the infinite. Especially the Coulomb potential and the Yukawa potential belong to our class but also non-spherical-symmetric and non-analytic potentials with a Coulomb-like singularity in the origin, two- to threefold differentiable which tend to zero at the infinite. In the introduction we discuss extensively also by means of some examples the problematics of the quantum-mechanical resonance. (orig.) [de
Modified potentials in many-body perturbation theory
International Nuclear Information System (INIS)
Silver, D.M.; Bartlett, R.J.
1976-01-01
Many-body perturbation-theory calculations of the pair-correlation energy within the regime of various finite expansions in two-center Slater-type basis sets are performed using a wide variety of modified potentials for the determination of unoccupied orbitals. To achieve meaningful convergence, it appears that the perturbation series must be carried through third order, using shifted denominators to include contributions from various higher-order diagrams. Moreover, certain denominator shifts are found necessary to ensure that a negative-definite resolvent accompanies the perturbation scheme when an arbitrary modified potential is employed. Through third order with denominator shifts, well-behaved modified potentials are found to give results that are equivalent, within 1 kcal/mole, to those obtained for pair-correlation energies with the standard self-consistent-field-V/sup N/ potential
Structure of the many-body wavefunction for scattering
International Nuclear Information System (INIS)
L'Huillier, M.; Redish, E.F.; Tandy, P.C.
1978-01-01
We show that the scattered part of the many-body wavefunction initiated by two incoming clusters is given by a fully connected operator acting on the initial channel state. The structure of this operator suggests a division of the full wavefunction into two-cluster components. A set of coupled equations in both the differential and integral form is then derived for these components. These equations have structure and properties similar to the three-body equations of Faddeev. We demonstrate that each component has outgoing waves in a unique two-cluster partition. The transition amplitude for any final arrangement can therefore be extracted directly from the outgoing waves in the relevant components
The partition function of an interacting many body system
International Nuclear Information System (INIS)
Rummel, C.; Ankerhold, J.
2002-01-01
Based on the path integral approach the partition function of a many body system with separable two body interaction is calculated in the sense of a semiclassical approximation. The commonly used Gaussian type of approximation, known as the perturbed static path approximation (PSPA), breaks down near a crossover temperature due to instabilities of the classical mean field solution. It is shown how the PSPA is systematically improved within the crossover region by taking into account large non-Gaussian fluctuation and an approximation applicable down to very low temperatures is carried out. These findings are tested against exact results for the archetypical cases of a particle moving in a one dimensional double well and the exactly solvable Lipkin-Meshkov-Glick model. The extensions should have applications in finite systems at low temperatures as in nuclear physics and mesoscopic systems, e. g. for gap fluctuations in nano-scale superconducting devices previously studied within a PSPA type of approximation. (author)
Classical and quantum simulations of many-body systems
Energy Technology Data Exchange (ETDEWEB)
Murg, Valentin
2008-04-07
This thesis is devoted to recent developments in the fields of classical and quantum simulations of many-body systems. We describe new classical algorithms that overcome problems apparent in conventional renormalization group and Monte Carlo methods. These algorithms make possible the detailed study of finite temperature properties of 2-D classical and 1-D quantum systems, the investigation of ground states of 2-D frustrated or fermionic systems and the analysis of time evolutions of 2-D quantum systems. Furthermore, we propose new 'analog' quantum simulators that are able to realize interesting models such as a Tonks-Girardeau gas or a frustrated spin-1/2 XY model on a trigonal lattice. These quantum simulators make use of optical lattices and trapped ions and are technically feasible. In fact, the Tonks-Girardeau gas has been realized experimentally and we provide a detailed comparison between the experimental data and the theoretical predictions. (orig.)
Dynamical stability of a many-body Kapitza pendulum
Energy Technology Data Exchange (ETDEWEB)
Citro, Roberta, E-mail: citro@sa.infn.it [Dipartimento di Fisica “E. R. Caianiello” and Spin-CNR, Universita’ degli Studi di Salerno, Via Giovanni Paolo II, I-84084 Fisciano (Italy); Dalla Torre, Emanuele G., E-mail: emanuele.dalla-torre@biu.ac.il [Department of Physics, Bar Ilan University, Ramat Gan 5290002 (Israel); Department of Physics, Harvard University, Cambridge, MA 02138 (United States); D’Alessio, Luca [Department of Physics, The Pennsylvania State University, University Park, PA 16802 (United States); Department of Physics, Boston University, Boston, MA 02215 (United States); Polkovnikov, Anatoli [Department of Physics, Boston University, Boston, MA 02215 (United States); Babadi, Mehrtash [Department of Physics, Harvard University, Cambridge, MA 02138 (United States); Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125 (United States); Oka, Takashi [Department of Applied Physics, University of Tokyo, Tokyo, 113-8656 (Japan); Demler, Eugene [Department of Physics, Harvard University, Cambridge, MA 02138 (United States)
2015-09-15
We consider a many-body generalization of the Kapitza pendulum: the periodically-driven sine–Gordon model. We show that this interacting system is dynamically stable to periodic drives with finite frequency and amplitude. This finding is in contrast to the common belief that periodically-driven unbounded interacting systems should always tend to an absorbing infinite-temperature state. The transition to an unstable absorbing state is described by a change in the sign of the kinetic term in the Floquet Hamiltonian and controlled by the short-wavelength degrees of freedom. We investigate the stability phase diagram through an analytic high-frequency expansion, a self-consistent variational approach, and a numeric semiclassical calculation. Classical and quantum experiments are proposed to verify the validity of our results.
Nuclear collision theory with many-body correlations, 2
International Nuclear Information System (INIS)
Kurihara, Yukio.
1984-12-01
A nuclear collision theory, in which the many-body correlation induced by the strong short-ranged repulsion and medium-ranged attraction of the realistic NN interaction is explicitly included, is applied to the deuteron+deuteron elastic scattering at low energies. Pair correlation functions calculated by the present theory are very different from the Hackenbroich et al. 's one. They contain not only the short-ranged suppressive correlation, but also the medium-ranged enhancing correlation. The former changes the shape of the d-d potential from the wine-bottle one. And the latter makes the d-d potential much more attractive. This effect is necessary for reproducing a bump around thatesub(cm)=90 0 in the experimental elastic differential cross section. The phase shifts evaluated by the present theory are compared with those from the resonating-group method. (author)
Exactly solvable models in many-body theory
March, N H
2016-01-01
The book reviews several theoretical, mostly exactly solvable, models for selected systems in condensed states of matter, including the solid, liquid, and disordered states, and for systems of few or many bodies, both with boson, fermion, or anyon statistics. Some attention is devoted to models for quantum liquids, including superconductors and superfluids. Open problems in relativistic fields and quantum gravity are also briefly reviewed.The book ranges almost comprehensively, but concisely, across several fields of theoretical physics of matter at various degrees of correlation and at different energy scales, with relevance to molecular, solid-state, and liquid-state physics, as well as to phase transitions, particularly for quantum liquids. Mostly exactly solvable models are presented, with attention also to their numerical approximation and, of course, to their relevance for experiments.
Resonating-group method for nuclear many-body problems
International Nuclear Information System (INIS)
Tang, Y.C.; LeMere, M.; Thompson, D.R.
1977-01-01
The resonating-group method is a microscopic method which uses fully antisymmetric wave functions, treats correctly the motion of the total center of mass, and takes cluster correlation into consideration. In this review, the formulation of this method is discussed for various nuclear many-body problems, and a complex-generator-coordinate technique which has been employed to evaluate matrix elements required in resonating-group calculations is described. Several illustrative examples of bound-state, scattering, and reaction calculations, which serve to demonstrate the usefulness of this method, are presented. Finally, by utilization of the results of these calculations, the role played by the Pauli principle in nuclear scattering and reaction processes is discussed. 21 figures, 2 tables, 185 references
Classical and quantum simulations of many-body systems
International Nuclear Information System (INIS)
Murg, Valentin
2008-01-01
This thesis is devoted to recent developments in the fields of classical and quantum simulations of many-body systems. We describe new classical algorithms that overcome problems apparent in conventional renormalization group and Monte Carlo methods. These algorithms make possible the detailed study of finite temperature properties of 2-D classical and 1-D quantum systems, the investigation of ground states of 2-D frustrated or fermionic systems and the analysis of time evolutions of 2-D quantum systems. Furthermore, we propose new ''analog'' quantum simulators that are able to realize interesting models such as a Tonks-Girardeau gas or a frustrated spin-1/2 XY model on a trigonal lattice. These quantum simulators make use of optical lattices and trapped ions and are technically feasible. In fact, the Tonks-Girardeau gas has been realized experimentally and we provide a detailed comparison between the experimental data and the theoretical predictions. (orig.)
Relativistic many-body theory of atomic structures
International Nuclear Information System (INIS)
Cheng, K.T.
1983-01-01
The main objective of this program is to improve our understanding of the effect of relativity and electron correlations on atomic processes. Current efforts include hyperfine structure (hfs) studies using the multiconfiguration Dirac-Fock (MCDF) technique. Atomic hfs are known to be sensitive to relativity and electron correlations, and provide important tests of relativistic atomic many-body theories. Preliminary results on the hfs of the 4f 12 3 H ground state of 68 Er 167 are shown and are in good agreement with experiment. This shows that the MCDF technique can be an efficient and powerful method for atomic hfs studies. Further tests of this method are in progress. We are also studying the absorption spectra for Xe-like ions in the region of 4d → nf, epsilonf transitions
Many-body theory and Energy Density Functionals
Energy Technology Data Exchange (ETDEWEB)
Baldo, M. [INFN, Catania (Italy)
2016-07-15
In this paper a method is first presented to construct an Energy Density Functional on a microscopic basis. The approach is based on the Kohn-Sham method, where one introduces explicitly the Nuclear Matter Equation of State, which can be obtained by an accurate many-body calculation. In this way it connects the functional to the bare nucleon-nucleon interaction. It is shown that the resulting functional can be performing as the best Gogny force functional. In the second part of the paper it is shown how one can go beyond the mean-field level and the difficulty that can appear. The method is based on the particle-vibration coupling scheme and a formalism is presented that can handle the correct use of the vibrational degrees of freedom within a microscopic approach. (orig.)
Many-body physics with alkaline-earth Rydberg lattices
Energy Technology Data Exchange (ETDEWEB)
Mukherjee, R; Nath, R; Pohl, T [Max Planck Institute for the Physics of Complex Systems, Noethnitzer Strasse 38, 01187 Dresden (Germany); Millen, J; Jones, M P A, E-mail: rick@pks.mpg.de [Department of Physics, Durham University, Durham DH1 3LE (United Kingdom)
2011-09-28
We explore the prospects for confining alkaline-earth Rydberg atoms in an optical lattice via optical dressing of the secondary core-valence electron. Focussing on the particular case of strontium, we identify experimentally accessible magic wavelengths for simultaneous trapping of ground and Rydberg states. A detailed analysis of relevant loss mechanisms shows that the overall lifetime of such a system is limited only by the spontaneous decay of the Rydberg state, and is not significantly affected by photoionization or autoionization. The van der Waals C{sub 6} coefficients for the Sr(5sns {sup 1}S{sub 0}) Rydberg series are calculated, and we find that the interactions are attractive. Finally we show that the combination of magic-wavelength lattices and attractive interactions could be exploited to generate many-body Greenberger-Horne-Zeilinger states.
Experimental statistical signature of many-body quantum interference
Giordani, Taira; Flamini, Fulvio; Pompili, Matteo; Viggianiello, Niko; Spagnolo, Nicolò; Crespi, Andrea; Osellame, Roberto; Wiebe, Nathan; Walschaers, Mattia; Buchleitner, Andreas; Sciarrino, Fabio
2018-03-01
Multi-particle interference is an essential ingredient for fundamental quantum mechanics phenomena and for quantum information processing to provide a computational advantage, as recently emphasized by boson sampling experiments. Hence, developing a reliable and efficient technique to witness its presence is pivotal in achieving the practical implementation of quantum technologies. Here, we experimentally identify genuine many-body quantum interference via a recent efficient protocol, which exploits statistical signatures at the output of a multimode quantum device. We successfully apply the test to validate three-photon experiments in an integrated photonic circuit, providing an extensive analysis on the resources required to perform it. Moreover, drawing upon established techniques of machine learning, we show how such tools help to identify the—a priori unknown—optimal features to witness these signatures. Our results provide evidence on the efficacy and feasibility of the method, paving the way for its adoption in large-scale implementations.
Finite Cycle Gibbs Measures on Permutations of
Armendáriz, Inés; Ferrari, Pablo A.; Groisman, Pablo; Leonardi, Florencia
2015-03-01
We consider Gibbs distributions on the set of permutations of associated to the Hamiltonian , where is a permutation and is a strictly convex potential. Call finite-cycle those permutations composed by finite cycles only. We give conditions on ensuring that for large enough temperature there exists a unique infinite volume ergodic Gibbs measure concentrating mass on finite-cycle permutations; this measure is equal to the thermodynamic limit of the specifications with identity boundary conditions. We construct as the unique invariant measure of a Markov process on the set of finite-cycle permutations that can be seen as a loss-network, a continuous-time birth and death process of cycles interacting by exclusion, an approach proposed by Fernández, Ferrari and Garcia. Define as the shift permutation . In the Gaussian case , we show that for each , given by is an ergodic Gibbs measure equal to the thermodynamic limit of the specifications with boundary conditions. For a general potential , we prove the existence of Gibbs measures when is bigger than some -dependent value.
Many-body quantum simulation with Rydberg atoms and ions
International Nuclear Information System (INIS)
Mueller, M.
2010-01-01
This thesis presents my work that is located at the interface between the fields of atomic physics, quantum optics and quantum information. The work was performed at the Institute of Theoretical Physics of the University of Innsbruck and the Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences under the supervision of Prof. Peter Zoller. The main topic of this thesis is the investigation of new schemes for quantum simulation of interacting many-body systems. The thesis is divided into three parts, which cover my work on i) chains of trapped Rydberg ions ii) quantum information processing and simulation with Rydberg atoms and iii) quantum simulation with ground state ions. The first part of this thesis is concerned with the study of Rydberg ions trapped in a linear Paul trap. The properties of ionic Rydberg states in the presence of the static and time-dependent electric trapping fields are investigated. First it is analyzed under which conditions laser-excited Rydberg ions can be trapped in a stable configuration. Furthermore, it is shown that strong dipole-dipole interactions among the ions can be achieved by microwave dressing fields. These interactions can give rise to dynamics of Rydberg excitations through the ion crystal, which take place on a nanosecond timescale and can be described by effective spin-models. In addition, it is discussed how to achieve fast two-qubit entangling gates between pairs of Rydberg ions. In the second part of this thesis, novel possibilities of using neutral Rydberg atoms for quantum-information processing and quantum simulation are investigated. A new scheme for a multi-atom quantum gate is proposed and theoretically analyzed. This parallelized gate allows one to entangle a mesoscopic ensemble of atoms with a single control atom in a single step, with high fidelity and on a microsecond time scale. The operation relies on strong and long-ranged interactions between Rydberg atoms triggering a
Universality in driven-dissipative quantum many-body systems
International Nuclear Information System (INIS)
Sieberer, L.M.
2015-01-01
Recent experimental investigations of condensation phenomena in driven-dissipative quantum many-body systems raise the question of what kind of novel universal behavior can emerge under non-equilibrium conditions. We explore various aspects of universality in this context. Our results are of relevance for a variety of open quantum systems on the interface of quantum optics and condensed matter physics, ranging from exciton-polariton condensates to cold atomic gases. In Part I we characterize the dynamical critical behavior at the Bose-Einstein condensation phase transition in driven open quantum systems in three spatial dimensions. Although thermodynamic equilibrium conditions are emergent at low frequencies, the approach to this thermalized low-frequency regime is described by a critical exponent which is specific to the non-equilibrium transition, and places the latter beyond the standard classification of equilibrium dynamical critical behavior. Our theoretical approach is based on the functional renormalization group within the framework of Keldysh non-equilibrium field theory, which is equivalent to a microscopic description of the open system dynamics in terms of a many-body quantum master equation. Universal behavior in the coherence properties of driven-dissipative condensates in reduced dimensions is investigated in Part II. We show that driven two-dimensional Bose systems cannot exhibit algebraic order as in thermodynamic equilibrium, unless they are sufficiently anisotropic. However, we find evidence that even isotropic systems may have a finite superfluidity fraction. In one-dimensional systems, non-equilibrium conditions are traceable in the behavior of the autocorrelation function. We obtain these results by mapping the long-wavelength condensate dynamics onto the Kardar-Parisi-Zhang equation. In Part III we show that systems in thermodynamic equilibrium have a specific symmetry, which makes them distinct from generic driven open systems. The novel
Ruelle resonances in quantum many-body dynamics
International Nuclear Information System (INIS)
Prosen, Tomaz
2002-01-01
We define a quantum Perron-Frobenius master operator over a suitable normed space of translationally invariant states adjoint to the quasi-local C* algebra of quantum lattice gasses (e.g. spin chains), whose spectrum determines the exponents of decay of time correlation functions. The theoretical ideas are applied to a generic example of kicked Ising spin 1/2 chains. We show that the 'chaotic eigenmodes' corresponding to leading eigenvalue resonances have fractal structure in the basis of local operators. (letter to the editor)
Communication: Random phase approximation renormalized many-body perturbation theory
International Nuclear Information System (INIS)
Bates, Jefferson E.; Furche, Filipp
2013-01-01
We derive a renormalized many-body perturbation theory (MBPT) starting from the random phase approximation (RPA). This RPA-renormalized perturbation theory extends the scope of single-reference MBPT methods to small-gap systems without significantly increasing the computational cost. The leading correction to RPA, termed the approximate exchange kernel (AXK), substantially improves upon RPA atomization energies and ionization potentials without affecting other properties such as barrier heights where RPA is already accurate. Thus, AXK is more balanced than second-order screened exchange [A. Grüneis et al., J. Chem. Phys. 131, 154115 (2009)], which tends to overcorrect RPA for systems with stronger static correlation. Similarly, AXK avoids the divergence of second-order Møller-Plesset (MP2) theory for small gap systems and delivers a much more consistent performance than MP2 across the periodic table at comparable cost. RPA+AXK thus is an accurate, non-empirical, and robust tool to assess and improve semi-local density functional theory for a wide range of systems previously inaccessible to first-principles electronic structure calculations
Many-body delocalization with random vector potentials
Cheng, Chen; Mondaini, Rubem
In this talk we present the ergodic properties of excited states in a model of interacting fermions in quasi-one dimensional chains subjected to a random vector potential. In the non-interacting limit, we show that arbitrarily small values of this complex off-diagonal disorder triggers localization for the whole spectrum; the divergence of the localization length in the single particle basis is characterized by a critical exponent ν which depends on the energy density being investigated. However, when short-ranged interactions are included, the localization is lost and the system is ergodic regardless of the magnitude of disorder in finite chains. Our numerical results suggest a delocalization scheme for arbitrary small values of interactions. This finding indicates that the standard scenario of the many-body localization cannot be obtained in a model with random gauge fields. This research is financially supported by the National Natural Science Foundation of China (NSFC) (Grant Nos. U1530401 and 11674021). RM also acknowledges support from NSFC (Grant No. 11650110441).
Relativistic many-body theory of high density matter
International Nuclear Information System (INIS)
Chin, S.A.
1977-01-01
A fully relativistic quantum many-body theory is applied to the study of high-density matter. The latter is identified with the zero-temperature ground state of a system of interacting baryons. In accordance with the observed short-range repulsive and long-range attractive character of the nucleon--nucleon force, baryons are described as interacting with each other via a massive scalar and a massive vector meson exchange. In the Hartree approximation, the theory yields the same result as the mean-field theory, but with additional vacuum fluctuation corrections. The resultant equation of state for neutron matter is used to determine properties of neutron stars. The relativistic exchange energy, its corresponding single-particle excitation spectrum, and its effect on the neutron matter equation of state, are calculated. The correlation energy from summing the set of ring diagrams is derived directly from the energy-momentum tensor, with renormalization carried out by adding counterterms to the original Lagrangian and subtracting purely vacuum expectation values. Terms of order g 4 lng 2 are explicitly given. Effects of scalar-vector mixing are discussed. Collective modes corresponding to macroscopic density fluctuation are investigated. Two basic modes are found, a plasma-like mode and zero sound, with the latter dominant at high density. The stability and damping of these modes are studied. Last, the effect of vacuum polarization in high-density matter is examined
Petascale Many Body Methods for Complex Correlated Systems
Pruschke, Thomas
2012-02-01
Correlated systems constitute an important class of materials in modern condensed matter physics. Correlation among electrons are at the heart of all ordering phenomena and many intriguing novel aspects, such as quantum phase transitions or topological insulators, observed in a variety of compounds. Yet, theoretically describing these phenomena is still a formidable task, even if one restricts the models used to the smallest possible set of degrees of freedom. Here, modern computer architectures play an essential role, and the joint effort to devise efficient algorithms and implement them on state-of-the art hardware has become an extremely active field in condensed-matter research. To tackle this task single-handed is quite obviously not possible. The NSF-OISE funded PIRE collaboration ``Graduate Education and Research in Petascale Many Body Methods for Complex Correlated Systems'' is a successful initiative to bring together leading experts around the world to form a virtual international organization for addressing these emerging challenges and educate the next generation of computational condensed matter physicists. The collaboration includes research groups developing novel theoretical tools to reliably and systematically study correlated solids, experts in efficient computational algorithms needed to solve the emerging equations, and those able to use modern heterogeneous computer architectures to make then working tools for the growing community.
Detecting many-body-localization lengths with cold atoms
Guo, Xuefei; Li, Xiaopeng
2018-03-01
Considering ultracold atoms in optical lattices, we propose experimental protocols to study many-body-localization (MBL) length and criticality in quench dynamics. Through numerical simulations with exact diagonalization, we show that in the MBL phase the perturbed density profile following a local quench remains exponentially localized in postquench dynamics. The size of this density profile after long-time-dynamics defines a localization length, which tends to diverge at the MBL-to-ergodic transition as we increase the system size. The determined localization transition point agrees with previous exact diagonalization calculations using other diagnostics. Our numerical results provide evidence for violation of the Harris-Chayes bound for the MBL criticality. The critical exponent ν can be extracted from our proposed dynamical procedure, which can then be used directly in experiments to determine whether the Harris-Chayes-bound holds for the MBL transition. These proposed protocols to detect localization criticality are justified by benchmarking to the well-established results for the noninteracting three-dimensional Anderson localization.
Quantum many-body physics in a nutshell
Shuryak, Edward
2018-01-01
This book provides an essential introduction to the physics of quantum many-body systems, which are at the heart of atomic and nuclear physics, condensed matter, and particle physics. Unlike other textbooks on the subject, it covers topics across a broad range of physical fields―phenomena as well as theoretical tools―and does so in a simple and accessible way. Edward Shuryak begins with Feynman diagrams of the quantum and statistical mechanics of a particle―in these applications, the diagrams are easy to calculate and there are no divergencies. He discusses the renormalization group and illustrates its uses and covers systems such as weakly and strongly coupled Bose and Fermi gases, electron gas, nuclear matter, and quark-gluon plasmas. Phenomena include Bose condensation and superfluidity. Shuryak also looks at Cooper pairing and superconductivity for electrons in metals, liquid 3He, nuclear matter, and quark-gluon plasma. A recurring topic throughout is topological matter, ranging from ensembles of q...
Nuclear many-body problem with repulsive hard core interactions
Energy Technology Data Exchange (ETDEWEB)
Haddad, L M
1965-07-01
The nuclear many-body problem is considered using the perturbation-theoretic approach of Brueckner and collaborators. This approach is outlined with particular attention paid to the graphical representation of the terms in the perturbation expansion. The problem is transformed to centre-of-mass coordinates in configuration space and difficulties involved in ordinary methods of solution of the resulting equation are discussed. A new technique, the 'reference spectrum method', devised by Bethe, Brandow and Petschek in an attempt to simplify the numerical work in presented. The basic equations are derived in this approximation and considering the repulsive hard core part of the interaction only, the effective mass is calculated at high momentum (using the same energy spectrum for both 'particle' and 'hole' states). The result of 0.87m is in agreement with that of Bethe et al. A more complete treatment using the reference spectrum method in introduced and a self-consistent set of equations is established for the reference spectrum parameters again for the case of hard core repulsions. (author)
Many-body problem in one-dimension
International Nuclear Information System (INIS)
Emery, V.J.
1979-11-01
This work attempts to give a qualitative feeling for the more important physical ideas involved with the study of many-body systems in one dimension, and considers a particular strong-coupling model. This model provides an excellent description of the chains of mercury ions in Hg/sub 3-delta/AsF 6 ; some of the predictions of the theory can be checked by x-ray and neutron diffraction. Much of the physics of nearly one-dimensional materials is concerned with understanding the possible types of phase transition that may take place, and establishing the conditions in which one or another will be predominant. The most significant feature of purely one-dimensional systems is the dominant effect of fluctuations. The paper is organized as follows: introduction; qualitative aspects of one-dimensional systems (general survey, mathematical model, qualitative discussion of strong coupling - strong attractive U, strong repulsive U, large V); strong coupling between parallel spins (independent spin systems, coupling between opposite spins); mercury chains; electrons with arbitrary coupling; boson representations of operators; and classical Coulomb gas
Spectral statistics of chaotic many-body systems
International Nuclear Information System (INIS)
Dubertrand, Rémy; Müller, Sebastian
2016-01-01
We derive a trace formula that expresses the level density of chaotic many-body systems as a smooth term plus a sum over contributions associated to solutions of the nonlinear Schrödinger (or Gross–Pitaevski) equation. Our formula applies to bosonic systems with discretised positions, such as the Bose–Hubbard model, in the semiclassical limit as well as in the limit where the number of particles is taken to infinity. We use the trace formula to investigate the spectral statistics of these systems, by studying interference between solutions of the nonlinear Schrödinger equation. We show that in the limits taken the statistics of fully chaotic many-particle systems becomes universal and agrees with predictions from the Wigner–Dyson ensembles of random matrix theory. The conditions for Wigner–Dyson statistics involve a gap in the spectrum of the Frobenius–Perron operator, leaving the possibility of different statistics for systems with weaker chaotic properties. (paper)
Many-body theory of effective mass in degenerate semiconductors
Tripathi, G. S.; Shadangi, S. K.
2018-03-01
We derive the many-body theory of the effective mass in the effective mass representation (EMR). In the EMR, we need to solve the equation of motion of an electron in the presence of electron-electron interactions, where the wavefunction is expanded over a complete set of Luttinger-Kohn wavefunctions. We use the Luttinger-Ward thermodynamic potential and the Green’s function perturbation to derive an expression for the band effective mass by taking into account the electron-electron interactions. Both quasi-particle and the correlation contributions are considered. We show that had we considered only the quasi-particle contribution, we would have missed important cancellations. Thus the correlated motion of electrons has important effects in the renormalization of the effective mass. Considering the exchange self-energy in the band model, we derive a tractable expression for the band effective mass. We apply the theory to n-type degenerate semiconductors, PbTe and SnTe, and analyze the impact of the theory on the anisotropic effective mass of the conduction bands in these systems.
From Discrete Breathers to Many Body Localization and Flatbands
Flach, Sergej
Discrete breathers (DB) and intrinsic localized modes (ILM) are synonymic dynamical states on nonlinear lattices - periodic in time and localized in space, and widely observed in many applications. I will discuss the connections between DBs and many-body localization (MBL) and the properties of DBs on flatband networks. A dense quantized gas of strongly excited DBs can lead to a MBL phase in a variety of different lattice models. Its classical counterpart corresponds to a 'nonergodic metal' in the MBL language, or to a nonGibbsean selftrapped state in the language of nonlinear dynamics. Flatband networks are lattices with small amplitude waves exhibiting macroscopic degeneracy in their band structure due to local symmetries, destructive interference, compact localized eigenstates and horizontal flat bands. DBs can preserve the compactness of localization in the presence of nonlinearity with properly tuned internal phase relationships, making them promising tools for control of the phase coherence of waves. Also at New Zealand Institute of Advanced Study, Massey University, Auckland, New Zealand.
Many body effects in nuclear matter QCD sum rules
Drukarev, E. G.; Ryskin, M. G.; Sadovnikova, V. A.
2017-12-01
We calculate the single-particle nucleon characteristics in symmetric nuclear matter with inclusion of the 3N and 4N interactions. We calculated the contribution of the 3N interactions earlier, now we add that of the 4N ones. The contribution of the 4N forces to nucleon self energies is expressed in terms of the nonlocal scalar condensate (d = 3) and of the configurations of the vector-scalar and the scalar-scalar quark condensates (d = 6) in which two diquark operators act on two different nucleons of the matter.These four-quark condensates are obtained in the model-independent way. The density dependence of the nucleon effective mass, of the vector self energy and of the single-particle potential energy are obtained. We traced the dependence of the nucleon characteristics on the actual value of the pion-nucleon sigma term. We obtained also the nucleon characteristics in terms of the quasifree nucleons, with the noninteracting nucleons surrounded by their pion clouds as the starting point. This approach leads to strict hierarchy of the many body forces.
Another New Solvable Many-Body Model of Goldfish Type
Directory of Open Access Journals (Sweden)
Francesco Calogero
2012-07-01
Full Text Available A new solvable many-body problem is identified. It is characterized by nonlinear Newtonian equations of motion (''acceleration equal force'' featuring one-body and two-body velocity-dependent forces ''of goldfish type'' which determine the motion ofan arbitrary number $N$ of unit-mass point-particles in a plane. The $N$ (generally complex values $z_{n}(t$ at time $t$ ofthe $N$ coordinates of these moving particles are given by the $N$eigenvalues of a time-dependent $Nimes N$ matrix $U(t$explicitly known in terms of the $2N$ initial data $z_{n}(0$and $dot{z}_{n}(0 $. This model comes in two dif/ferentvariants, one featuring 3 arbitrary coupling constants, the other only 2; for special values of these parameters all solutions are completely periodic with the same period independent of the initial data (''isochrony''; for other special values of these parameters this property holds up to corrections vanishing exponentially as $tightarrow infty$ (''asymptotic isochrony''. Other isochronous variants of these models are also reported. Alternative formulations, obtained by changing the dependent variables from the $N$ zeros of a monic polynomial of degree $N$ to its $N$ coefficients, are also exhibited. Some mathematical findings implied by some of these results - such as Diophantine properties of the zeros of certain polynomials - are outlined, but their analysis is postponed to a separate paper.
Many-body localization in disorder-free systems: The importance of finite-size constraints
Energy Technology Data Exchange (ETDEWEB)
Papić, Z., E-mail: zpapic@perimeterinstitute.ca [School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT (United Kingdom); Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5 (Canada); Stoudenmire, E. Miles [Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5 (Canada); Abanin, Dmitry A. [Department of Theoretical Physics, University of Geneva, 24 quai Ernest-Ansermet, 1211 Geneva (Switzerland); Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5 (Canada)
2015-11-15
Recently it has been suggested that many-body localization (MBL) can occur in translation-invariant systems, and candidate 1D models have been proposed. We find that such models, in contrast to MBL systems with quenched disorder, typically exhibit much more severe finite-size effects due to the presence of two or more vastly different energy scales. In a finite system, this can artificially split the density of states (DOS) into bands separated by large gaps. We argue for such models to faithfully represent the thermodynamic limit behavior, the ratio of relevant coupling must exceed a certain system-size depedent cutoff, chosen such that various bands in the DOS overlap one another. Setting the parameters this way to minimize finite-size effects, we study several translation-invariant MBL candidate models using exact diagonalization. Based on diagnostics including entanglement and local observables, we observe thermal (ergodic), rather than MBL-like behavior. Our results suggest that MBL in translation-invariant systems with two or more very different energy scales is less robust than perturbative arguments suggest, possibly pointing to the importance of non-perturbative effects which induce delocalization in the thermodynamic limit.
A quantum information perspective of fermionic quantum many-body systems
Energy Technology Data Exchange (ETDEWEB)
Kraus, Christina V.
2009-11-02
In this Thesis fermionic quantum many-body system are theoretically investigated from a quantum information perspective. Quantum correlations in fermionic many-body systems, though central to many of the most fascinating effects of condensed matter physics, are poorly understood from a theoretical perspective. Even the notion of ''paired'' fermions which is widely used in the theory of superconductivity and has a clear physical meaning there, is not a concept of a systematic and mathematical theory so far. Applying concepts and tools from entanglement theory, we close this gap, developing a pairing theory allowing to unambiguously characterize paired states. We develop methods for the detection and quantification of pairing according to our definition which are applicable to current experimental setups. Pairing is shown to be a quantum correlation distinct from any notion of entanglement proposed for fermionic systems, giving further understanding of the structure of highly correlated quantum states. In addition, we show the resource character of paired states for precision metrology, proving that BCS-states allow phase measurements at the Heisenberg limit. Next, the power of fermionic systems is considered in the context of quantum simulations, where we study the possibility to simulate Hamiltonian time evolutions on a cubic lattice under the constraint of translational invariance. Given a set of translationally invariant local Hamiltonians and short range interactions we determine time evolutions which can and those which can not be simulated. Bosonic and finite-dimensional quantum systems (''spins'') are included in our investigations. Furthermore, we develop new techniques for the classical simulation of fermionic many-body systems. First, we introduce a new family of states, the fermionic Projected Entangled Pair States (fPEPS) on lattices in arbitrary spatial dimension. These are the natural generalization of the PEPS
A quantum information perspective of fermionic quantum many-body systems
International Nuclear Information System (INIS)
Kraus, Christina V.
2009-01-01
In this Thesis fermionic quantum many-body system are theoretically investigated from a quantum information perspective. Quantum correlations in fermionic many-body systems, though central to many of the most fascinating effects of condensed matter physics, are poorly understood from a theoretical perspective. Even the notion of ''paired'' fermions which is widely used in the theory of superconductivity and has a clear physical meaning there, is not a concept of a systematic and mathematical theory so far. Applying concepts and tools from entanglement theory, we close this gap, developing a pairing theory allowing to unambiguously characterize paired states. We develop methods for the detection and quantification of pairing according to our definition which are applicable to current experimental setups. Pairing is shown to be a quantum correlation distinct from any notion of entanglement proposed for fermionic systems, giving further understanding of the structure of highly correlated quantum states. In addition, we show the resource character of paired states for precision metrology, proving that BCS-states allow phase measurements at the Heisenberg limit. Next, the power of fermionic systems is considered in the context of quantum simulations, where we study the possibility to simulate Hamiltonian time evolutions on a cubic lattice under the constraint of translational invariance. Given a set of translationally invariant local Hamiltonians and short range interactions we determine time evolutions which can and those which can not be simulated. Bosonic and finite-dimensional quantum systems (''spins'') are included in our investigations. Furthermore, we develop new techniques for the classical simulation of fermionic many-body systems. First, we introduce a new family of states, the fermionic Projected Entangled Pair States (fPEPS) on lattices in arbitrary spatial dimension. These are the natural generalization of the PEPS known for spin systems, and they
General variational many-body theory with complete self-consistency for trapped bosonic systems
International Nuclear Information System (INIS)
Streltsov, Alexej I.; Alon, Ofir E.; Cederbaum, Lorenz S.
2006-01-01
In this work we develop a complete variational many-body theory for a system of N trapped bosons interacting via a general two-body potential. The many-body solution of this system is expanded over orthogonal many-body basis functions (configurations). In this theory both the many-body basis functions and the respective expansion coefficients are treated as variational parameters. The optimal variational parameters are obtained self-consistently by solving a coupled system of noneigenvalue--generally integro-differential--equations to get the one-particle functions and by diagonalizing the secular matrix problem to find the expansion coefficients. We call this theory multiconfigurational Hartree theory for bosons or MCHB(M), where M specifies explicitly the number of one-particle functions used to construct the configurations. General rules for evaluating the matrix elements of one- and two-particle operators are derived and applied to construct the secular Hamiltonian matrix. We discuss properties of the derived equations. We show that in the limiting cases of one configuration the theory boils down to the well-known Gross-Pitaevskii and the recently developed multi-orbital mean fields. The invariance of the complete solution with respect to unitary transformations of the one-particle functions is utilized to find the solution with the minimal number of contributing configurations. In the second part of our work we implement and apply the developed theory. It is demonstrated that for any practical computation where the configurational space is restricted, the description of trapped bosonic systems strongly depends on the choice of the many-body basis set used, i.e., self-consistency is of great relevance. As illustrative examples we consider bosonic systems trapped in one- and two-dimensional symmetric and asymmetric double well potentials. We demonstrate that self-consistency has great impact on the predicted physical properties of the ground and excited states
Permutation orbifolds and chaos
Belin, A.
2017-01-01
We study out-of-time-ordered correlation functions in permutation orbifolds at large central charge. We show that they do not decay at late times for arbitrary choices of low-dimension operators, indicating that permutation orbifolds are non-chaotic theories. This is in agreement with the fact they
Stochastic many-body perturbation theory for anharmonic molecular vibrations
Energy Technology Data Exchange (ETDEWEB)
Hermes, Matthew R. [Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801 (United States); Hirata, So, E-mail: sohirata@illinois.edu [Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801 (United States); CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012 (Japan)
2014-08-28
A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm{sup −1} and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.
Energy Technology Data Exchange (ETDEWEB)
Padmanabhan, Pramod [Fields, Gravity & Strings, CTPU, Institute for Basic Science,Daejeon 34037 (Korea, Republic of); Rey, Soo-Jong [Fields, Gravity & Strings, CTPU, Institute for Basic Science,Daejeon 34037 (Korea, Republic of); School of Physics and Astronomy & Center for Theoretical Physics, Seoul National University,Seoul 06544 (Korea, Republic of); Department of Basic Sciences, University of Science and Technology, Daejeon 34113 (Korea, Republic of); Teixeira, Daniel; Trancanelli, Diego [Institute of Physics, University of São Paulo, 05314-970 São Paulo (Brazil)
2017-05-25
Partial symmetries are described by generalized group structures known as symmetric inverse semigroups. We use the algebras arising from these structures to realize supersymmetry in (0+1) dimensions and to build many-body quantum systems on a chain. This construction consists in associating appropriate supercharges to chain sites, in analogy to what is done in spin chains. For simple enough choices of supercharges, we show that the resulting states have a finite non-zero Witten index, which is invariant under perturbations, therefore defining supersymmetric phases of matter protected by the index. The Hamiltonians we obtain are integrable and display a spectrum containing both product and entangled states. By introducing disorder and studying the out-of-time-ordered correlators (OTOC), we find that these systems are in the many-body localized phase and do not thermalize. Finally, we reformulate a theorem relating the growth of the second Rényi entropy to the OTOC on a thermal state in terms of partial symmetries.
Quantum phase transition in strongly correlated many-body system
You, Wenlong
The past decade has seen a substantial rejuvenation of interest in the study of quantum phase transitions (QPTs), driven by experimental advance on the cuprate superconductors, the heavy fermion materials, organic conductors, Quantum Hall effect, Fe-As based superconductors and other related compounds. It is clear that strong electronic interactions play a crucial role in the systems of current interest, and simple paradigms for the behavior of such systems near quantum critical points remain unclear. Furthermore, the rapid progress in Feshbach resonance and optical lattice provides a flexible platform to study QPT. Quantum Phase Transition (QPT) describes the non-analytic behaviors of the ground-state properties in a many-body system by varying a physical parameter at absolute zero temperature - such as magnetic field or pressure, driven by quantum fluctuations. Such quantum phase transitions can be first-order phase transition or continuous. The phase transition is usually accompanied by a qualitative change in the nature of the correlations in the ground state, and describing this change shall clearly be one of our major interests. We address this issue from three prospects in a few strong correlated many-body systems in this thesis, i.e., identifying the ordered phases, studying the properties of different phases, characterizing the QPT points. In chapter 1, we give an introduction to QPT, and take one-dimensional XXZ model as an example to illustrate the QPT therein. Through this simple example, we would show that when the tunable parameter is varied, the system evolves into different phases, across two quantum QPT points. The distinct phases exhibit very different behaviors. Also a schematic phase diagram is appended. In chapter 2, we are engaged in research on ordered phases. Originating in the work of Landau and Ginzburg on second-order phase transition, the spontaneous symmetry breaking induces nonzero expectation of field operator, e.g., magnetization M
Many-Body Quantum Chaos: Analytic Connection to Random Matrix Theory
Kos, Pavel; Ljubotina, Marko; Prosen, Tomaž
2018-04-01
A key goal of quantum chaos is to establish a relationship between widely observed universal spectral fluctuations of clean quantum systems and random matrix theory (RMT). Most prominent features of such RMT behavior with respect to a random spectrum, both encompassed in the spectral pair correlation function, are statistical suppression of small level spacings (correlation hole) and enhanced stiffness of the spectrum at large spectral ranges. For single-particle systems with fully chaotic classical counterparts, the problem has been partly solved by Berry [Proc. R. Soc. A 400, 229 (1985), 10.1098/rspa.1985.0078] within the so-called diagonal approximation of semiclassical periodic-orbit sums, while the derivation of the full RMT spectral form factor K (t ) (Fourier transform of the spectral pair correlation function) from semiclassics has been completed by Müller et al. [Phys. Rev. Lett. 93, 014103 (2004), 10.1103/PhysRevLett.93.014103]. In recent years, the questions of long-time dynamics at high energies, for which the full many-body energy spectrum becomes relevant, are coming to the forefront even for simple many-body quantum systems, such as locally interacting spin chains. Such systems display two universal types of behaviour which are termed the "many-body localized phase" and "ergodic phase." In the ergodic phase, the spectral fluctuations are excellently described by RMT, even for very simple interactions and in the absence of any external source of disorder. Here we provide a clear theoretical explanation for these observations. We compute K (t ) in the leading two orders in t and show its agreement with RMT for nonintegrable, time-reversal invariant many-body systems without classical counterparts, a generic example of which are Ising spin-1 /2 models in a periodically kicking transverse field. In particular, we relate K (t ) to partition functions of a class of twisted classical Ising models on a ring of size t ; hence, the leading-order RMT behavior
Time-dependent, many-body scattering theory and nuclear reaction applications
International Nuclear Information System (INIS)
Levin, F.S.
1977-01-01
The channel component state form of the channel coupling array theory of many-body scattering is briefly reviewed. These states obey a non-hermitian matrix equation whose exact solution yields the Schroedinger eigenstates, eigenvalues and scattering amplitudes. A time-dependent formulation of the theory is introduced in analogy to the time-dependent Schrodinger equation and several consequences of the development are noted. These include an interaction picture, a single (matrix) S operator, and the usual connection between the t = 0 time-dependent and the time-independent scattering states. Finally, the channel component states (psi/sub j/) are shown to have the useful property that only psi/sub j/ has (two-body) outgoing waves in channel j: psi/sub m/, m not equal to j, is asymptotically zero in two-body channel j. This formalism is then considered as a means for direct nuclear reaction analysis. Typical bound state approximations are introduced and it is shown that a DWBA amplitude occurs in only one channel. The non-time-reversal invariance of the approximate theory is noted. Results of calculations based on a realistic model for two sets of light-ion induced, one-particle transfer reactions are discussed and compared with the coupled reaction channel (CRC) results using the CRC procedure of Cotanch and Vincent. Angular distributions for the two calculational methods are found to be similar in shape and magnitude. Higher ordercorrections are small as are time-reversal non-invariant effects. Post- and prior-type CRC calculations are seen to differ; the latter are closer to the full CRC results
Lee, Tsung-Han
Strongly correlated materials are a class of materials that cannot be properly described by the Density Functional Theory (DFT), which is a single-particle approximation to the original many-body electronic Hamiltonian. These systems contain d or f orbital electrons, i.e., transition metals, actinides, and lanthanides compounds, for which the electron-electron interaction (correlation) effects are too strong to be described by the single-particle approximation of DFT. Therefore, complementary many-body methods have been developed, at the model Hamiltonians level, to describe these strong correlation effects. Dynamical Mean Field Theory (DMFT) and Rotationally Invariant Slave-Boson (RISB) approaches are two successful methods that can capture the correlation effects for a broad interaction strength. However, these many-body methods, as applied to model Hamiltonians, treat the electronic structure of realistic materials in a phenomenological fashion, which only allow to describe their properties qualitatively. Consequently, the combination of DFT and many body methods, e.g., Local Density Approximation augmented by RISB and DMFT (LDA+RISB and LDA+DMFT), have been recently proposed to combine the advantages of both methods into a quantitative tool to analyze strongly correlated systems. In this dissertation, we studied the possible improvements of these approaches, and tested their accuracy on realistic materials. This dissertation is separated into two parts. In the first part, we studied the extension of DMFT and RISB in three directions. First, we extended DMFT framework to investigate the behavior of the domain wall structure in metal-Mott insulator coexistence regime by studying the unstable solution describing the domain wall. We found that this solution, differing qualitatively from both the metallic and the insulating solutions, displays an insulating-like behavior in resistivity while carrying a weak metallic character in its electronic structure. Second, we
Energy Technology Data Exchange (ETDEWEB)
Bourget, Antoine [Department of Physics, Universidad de Oviedo, Avenida Calvo Sotelo 18, 33007 Oviedo (Spain); Troost, Jan [Laboratoire de Physique Théorique de l’É cole Normale Supérieure, CNRS,PSL Research University, Sorbonne Universités, 75005 Paris (France)
2017-05-09
We discuss the permutation group G of massive vacua of four-dimensional gauge theories with N=1 supersymmetry that arises upon tracing loops in the space of couplings. We concentrate on superconformal N=4 and N=2 theories with N=1 supersymmetry preserving mass deformations. The permutation group G of massive vacua is the Galois group of characteristic polynomials for the vacuum expectation values of chiral observables. We provide various techniques to effectively compute characteristic polynomials in given theories, and we deduce the existence of varying symmetry breaking patterns of the duality group depending on the gauge algebra and matter content of the theory. Our examples give rise to interesting field extensions of spaces of modular forms.
Stochastic many-body problems in ecology, evolution, neuroscience, and systems biology
Butler, Thomas C.
Using the tools of many-body theory, I analyze problems in four different areas of biology dominated by strong fluctuations: The evolutionary history of the genetic code, spatiotemporal pattern formation in ecology, spatiotemporal pattern formation in neuroscience and the robustness of a model circadian rhythm circuit in systems biology. In the first two research chapters, I demonstrate that the genetic code is extremely optimal (in the sense that it manages the effects of point mutations or mistranslations efficiently), more than an order of magnitude beyond what was previously thought. I further show that the structure of the genetic code implies that early proteins were probably only loosely defined. Both the nature of early proteins and the extreme optimality of the genetic code are interpreted in light of recent theory [1] as evidence that the evolution of the genetic code was driven by evolutionary dynamics that were dominated by horizontal gene transfer. I then explore the optimality of a proposed precursor to the genetic code. The results show that the precursor code has only limited optimality, which is interpreted as evidence that the precursor emerged prior to translation, or else never existed. In the next part of the dissertation, I introduce a many-body formalism for reaction-diffusion systems described at the mesoscopic scale with master equations. I first apply this formalism to spatially-extended predator-prey ecosystems, resulting in the prediction that many-body correlations and fluctuations drive population cycles in time, called quasicycles. Most of these results were previously known, but were derived using the system size expansion [2, 3]. I next apply the analytical techniques developed in the study of quasi-cycles to a simple model of Turing patterns in a predator-prey ecosystem. This analysis shows that fluctuations drive the formation of a new kind of spatiotemporal pattern formation that I name "quasi-patterns." These quasi
Energy Technology Data Exchange (ETDEWEB)
Zakharov, A.Yu., E-mail: Anatoly.Zakharov@novsu.ru; Zakharov, M.A., E-mail: ma_zakharov@list.ru
2016-01-28
The exact equations of motion for microscopic density of classical many-body system with account of inter-particle retarded interactions is derived. It is shown that interactions retardation leads to irreversible behavior of many-body systems. - Highlights: • A new form of equation of motion of classical many-body system is proposed. • Interactions retardation as one of the mechanisms of many-body system irreversibility. • Irreversibility and determinism without probabilities. • The possible way to microscopic foundation of thermodynamics.
Many-Body Quantum Chaos and Entanglement in a Quantum Ratchet
Valdez, Marc Andrew; Shchedrin, Gavriil; Heimsoth, Martin; Creffield, Charles E.; Sols, Fernando; Carr, Lincoln D.
2018-06-01
We uncover signatures of quantum chaos in the many-body dynamics of a Bose-Einstein condensate-based quantum ratchet in a toroidal trap. We propose measures including entanglement, condensate depletion, and spreading over a fixed basis in many-body Hilbert space, which quantitatively identify the region in which quantum chaotic many-body dynamics occurs, where random matrix theory is limited or inaccessible. With these tools, we show that many-body quantum chaos is neither highly entangled nor delocalized in the Hilbert space, contrary to conventionally expected signatures of quantum chaos.
Spectrum of quantum transfer matrices via classical many-body systems
Energy Technology Data Exchange (ETDEWEB)
Gorsky, A. [ITEP,Bolshaya Cheremushkinskaya str. 25, 117218, Moscow (Russian Federation); MIPT,Inststitutskii per. 9, 141700, Dolgoprudny, Moscow region (Russian Federation); Zabrodin, A. [ITEP,Bolshaya Cheremushkinskaya str. 25, 117218, Moscow (Russian Federation); MIPT,Inststitutskii per. 9, 141700, Dolgoprudny, Moscow region (Russian Federation); Institute of Biochemical Physics,Kosygina str. 4, 119991, Moscow (Russian Federation); National Research University Higher School of Economics,Myasnitskaya str. 20, 101000, Moscow (Russian Federation); Zotov, A. [ITEP,Bolshaya Cheremushkinskaya str. 25, 117218, Moscow (Russian Federation); MIPT,Inststitutskii per. 9, 141700, Dolgoprudny, Moscow region (Russian Federation); Steklov Mathematical Institute, RAS,Gubkina str. 8, 119991, Moscow (Russian Federation)
2014-01-15
In this paper we clarify the relationship between inhomogeneous quantum spin chains and classical integrable many-body systems. It provides an alternative (to the nested Bethe ansatz) method for computation of spectra of the spin chains. Namely, the spectrum of the quantum transfer matrix for the inhomogeneous gl{sub n}-invariant XXX spin chain on N sites with twisted boundary conditions can be found in terms of velocities of particles in the rational N-body Ruijsenaars-Schneider model. The possible values of the velocities are to be found from intersection points of two Lagrangian submanifolds in the phase space of the classical model. One of them is the Lagrangian hyperplane corresponding to fixed coordinates of all N particles and the other one is an N-dimensional Lagrangian submanifold obtained by fixing levels of N classical Hamiltonians in involution. The latter are determined by eigenvalues of the twist matrix. To support this picture, we give a direct proof that the eigenvalues of the Lax matrix for the classical Ruijsenaars-Schneider model, where velocities of particles are substituted by eigenvalues of the spin chain Hamiltonians, calculated through the Bethe equations, coincide with eigenvalues of the twist matrix, with certain multiplicities. We also prove a similar statement for the gl{sub n} Gaudin model with N marked points (on the quantum side) and the Calogero-Moser system with N particles (on the classical side). The realization of the results obtained in terms of branes and supersymmetric gauge theories is also discussed.
Photoionization cross sections and Auger rates calculated by many-body perturbation theory
International Nuclear Information System (INIS)
Kelly, H.P.
1976-01-01
Methods for applying the many body perturbation theory to atomic calculations are discussed with particular emphasis on calculation of photoionization cross sections and Auger rates. Topics covered include: Rayleigh--Schroedinger theory; many body perturbation theory; calculations of photoionization cross sections; and Auger rates
Effective linear two-body method for many-body problems in atomic and nuclear physics
International Nuclear Information System (INIS)
Kim, Y.E.; Zubarev, A.L.
2000-01-01
We present an equivalent linear two-body method for the many body problem, which is based on an approximate reduction of the many-body Schroedinger equation by the use of a variational principle. The method is applied to several problems in atomic and nuclear physics. (author)
Three-body interactions in many-body effective field theory
International Nuclear Information System (INIS)
Furnstahl, R.J.
2004-01-01
This contribution is an advertisement for applying effective field theory (EFT) to many-body problems, including nuclei and cold atomic gases. Examples involving three-body interactions are used to illustrate how EFT's quantify and systematically eliminate model dependence, and how they make many-body calculations simpler and more powerful
Gray Code for Cayley Permutations
Directory of Open Access Journals (Sweden)
J.-L. Baril
2003-10-01
Full Text Available A length-n Cayley permutation p of a total ordered set S is a length-n sequence of elements from S, subject to the condition that if an element x appears in p then all elements y < x also appear in p . In this paper, we give a Gray code list for the set of length-n Cayley permutations. Two successive permutations in this list differ at most in two positions.
International Nuclear Information System (INIS)
Hirata, So
2003-01-01
We develop a symbolic manipulation program and program generator (Tensor Contraction Engine or TCE) that automatically derives the working equations of a well-defined model of second-quantized many-electron theories and synthesizes efficient parallel computer programs on the basis of these equations. Provided an ansatz of a many-electron theory model, TCE performs valid contractions of creation and annihilation operators according to Wick's theorem, consolidates identical terms, and reduces the expressions into the form of multiple tensor contractions acted by permutation operators. Subsequently, it determines the binary contraction order for each multiple tensor contraction with the minimal operation and memory cost, factorizes common binary contractions (defines intermediate tensors), and identifies reusable intermediates. The resulting ordered list of binary tensor contractions, additions, and index permutations is translated into an optimized program that is combined with the NWChem and UTChem computational chemistry software packages. The programs synthesized by TCE take advantage of spin symmetry, Abelian point-group symmetry, and index permutation symmetry at every stage of calculations to minimize the number of arithmetic operations and storage requirement, adjust the peak local memory usage by index range tiling, and support parallel I/O interfaces and dynamic load balancing for parallel executions. We demonstrate the utility of TCE through automatic derivation and implementation of parallel programs for various models of configuration-interaction theory (CISD, CISDT, CISDTQ), many-body perturbation theory[MBPT(2), MBPT(3), MBPT(4)], and coupled-cluster theory (LCCD, CCD, LCCSD, CCSD, QCISD, CCSDT, and CCSDTQ)
Ballistic near-field heat transport in dense many-body systems
Latella, Ivan; Biehs, Svend-Age; Messina, Riccardo; Rodriguez, Alejandro W.; Ben-Abdallah, Philippe
2018-01-01
Radiative heat transport mediated by near-field interactions is known to be superdiffusive in dilute, many-body systems. Here we use a generalized Landauer theory of radiative heat transfer in many-body planar systems to demonstrate a nonmonotonic transition from superdiffusive to ballistic transport in dense systems. We show that such a transition is associated to a change of the polarization of dominant modes. Our findings are complemented by a quantitative study of the relaxation dynamics of the system in the different regimes of heat transport. This result could have important consequences on thermal management at nanoscale of many-body systems.
Probing correlated quantum many-body systems at the single-particle level
International Nuclear Information System (INIS)
Endres, Manuel
2013-01-01
The detection of correlation and response functions plays a crucial role in the experimental characterization of quantum many-body systems. In this thesis, we present novel techniques for the measurement of such functions at the single-particle level. Specifically, we show the single-atom- and single-site-resolved detection of an ultracold quantum gas in an optical lattice. The quantum gas is described by the Bose-Hubbard model, which features a zero temperature phase transition from a superfluid to a Mott-insulating state, a paradigm example of a quantum phase transition. We used the aforementioned detection techniques to study correlation and response properties across the superfluid-Mott-insulator transition. The single-atom sensitivity of our method is achieved by fluorescence detection of individual atoms with a high signal-to-noise ratio. A high-resolution objective collects the fluorescence light and yields in situ 'snapshots' of the quantum gas that allow for a single-site-resolved reconstruction of the atomic distribution. This allowed us to measure two-site and non-local correlation-functions across the superfluid-Mott-insulator transition. Non-local correlation functions are based on the information of an extended region of the system and play an important role for the characterization of low-dimensional quantum phases. While non-local correlation functions were so far only theoretical tools, our results show that they are actually experimentally accessible. Furthermore, we used a new thermometry scheme, based on the counting of individual thermal excitations, to measure the response of the system to lattice modulation. Using this method, we studied the excitation spectrum of the system across the two-dimensional superfluid-Mott-insulator transition. In particular, we detected a 'Higgs' amplitude mode in the strongly-interacting superfluid close to the transition point where the system is described by an effectively Lorentz-invariant low-energy theory
Probing correlated quantum many-body systems at the single-particle level
Energy Technology Data Exchange (ETDEWEB)
Endres, Manuel
2013-02-27
The detection of correlation and response functions plays a crucial role in the experimental characterization of quantum many-body systems. In this thesis, we present novel techniques for the measurement of such functions at the single-particle level. Specifically, we show the single-atom- and single-site-resolved detection of an ultracold quantum gas in an optical lattice. The quantum gas is described by the Bose-Hubbard model, which features a zero temperature phase transition from a superfluid to a Mott-insulating state, a paradigm example of a quantum phase transition. We used the aforementioned detection techniques to study correlation and response properties across the superfluid-Mott-insulator transition. The single-atom sensitivity of our method is achieved by fluorescence detection of individual atoms with a high signal-to-noise ratio. A high-resolution objective collects the fluorescence light and yields in situ 'snapshots' of the quantum gas that allow for a single-site-resolved reconstruction of the atomic distribution. This allowed us to measure two-site and non-local correlation-functions across the superfluid-Mott-insulator transition. Non-local correlation functions are based on the information of an extended region of the system and play an important role for the characterization of low-dimensional quantum phases. While non-local correlation functions were so far only theoretical tools, our results show that they are actually experimentally accessible. Furthermore, we used a new thermometry scheme, based on the counting of individual thermal excitations, to measure the response of the system to lattice modulation. Using this method, we studied the excitation spectrum of the system across the two-dimensional superfluid-Mott-insulator transition. In particular, we detected a 'Higgs' amplitude mode in the strongly-interacting superfluid close to the transition point where the system is described by an effectively Lorentz-invariant
Visual recognition of permuted words
Rashid, Sheikh Faisal; Shafait, Faisal; Breuel, Thomas M.
2010-02-01
In current study we examine how letter permutation affects in visual recognition of words for two orthographically dissimilar languages, Urdu and German. We present the hypothesis that recognition or reading of permuted and non-permuted words are two distinct mental level processes, and that people use different strategies in handling permuted words as compared to normal words. A comparison between reading behavior of people in these languages is also presented. We present our study in context of dual route theories of reading and it is observed that the dual-route theory is consistent with explanation of our hypothesis of distinction in underlying cognitive behavior for reading permuted and non-permuted words. We conducted three experiments in lexical decision tasks to analyze how reading is degraded or affected by letter permutation. We performed analysis of variance (ANOVA), distribution free rank test, and t-test to determine the significance differences in response time latencies for two classes of data. Results showed that the recognition accuracy for permuted words is decreased 31% in case of Urdu and 11% in case of German language. We also found a considerable difference in reading behavior for cursive and alphabetic languages and it is observed that reading of Urdu is comparatively slower than reading of German due to characteristics of cursive script.
Symmetry analysis of many-body wave functions, with applications to the nuclear shell model
International Nuclear Information System (INIS)
Novoselsky, A.; Katriel, J.
1995-01-01
The weights of the different permutational symmetry components of a nonsymmetry-adapted many-particle wave function are evaluated in terms of the expectation values of the symmetric-group class sums. This facilitates the evaluation of the weights without the construction of a complete set of symmetry adapted functions. Subspace projection operators are introduced, to be used when prior knowledge about the symmetry-species composition of a wave function is available. The permutational weight analysis of a recursively angular-momentum coupled (shell model) wave function is presented as an illustration
Infinite permutations vs. infinite words
Directory of Open Access Journals (Sweden)
Anna E. Frid
2011-08-01
Full Text Available I am going to compare well-known properties of infinite words with those of infinite permutations, a new object studied since middle 2000s. Basically, it was Sergey Avgustinovich who invented this notion, although in an early study by Davis et al. permutations appear in a very similar framework as early as in 1977. I am going to tell about periodicity of permutations, their complexity according to several definitions and their automatic properties, that is, about usual parameters of words, now extended to permutations and behaving sometimes similarly to those for words, sometimes not. Another series of results concerns permutations generated by infinite words and their properties. Although this direction of research is young, many people, including two other speakers of this meeting, have participated in it, and I believe that several more topics for further study are really promising.
On the basis of molecular orbitals for relativistic bound systems of many bodies
International Nuclear Information System (INIS)
Cook, A.H.
1987-09-01
The quasi-relativistic Hamiltonian for bound states of many bodies proposed in previous articles (Cook, 1986, 1987a) is shown to provide a basis for the molecular orbital scheme of constructing wavefunctions and calculating eigenenergies. (author). 5 refs
A semiclassical approach to many-body interference in Fock-space
Energy Technology Data Exchange (ETDEWEB)
Engl, Thomas
2015-11-01
Many-body systems draw ever more physicists' attention. Such an increase of interest often comes along with the development of new theoretical methods. In this thesis, a non-perturbative semiclassical approach is developed, which allows to analytically study many-body interference effects both in bosonic and fermionic Fock space and is expected to be applicable to many research areas in physics ranging from Quantum Optics and Ultracold Atoms to Solid State Theory and maybe even High Energy Physics. After the derivation of the semiclassical approximation, which is valid in the limit of large total number of particles, first applications manifesting the presence of many-body interference effects are shown. Some of them are confirmed numerically thus verifying the semiclassical predictions. Among these results are coherent back-/forward-scattering in bosonic and fermionic Fock space as well as a many-body spin echo, to name only the two most important ones.
Heuristic method for determining outgoing waves in many-body wave functions
International Nuclear Information System (INIS)
Redish, E.F.; Tandy, P.C.; L'Huillier, M.
1975-12-01
A new and simple method is proposed for determining the kinds of outgoing waves present in a given many-body wave function. Whether any particular wave function contains ''hidden'' rearrangement components can be determined. 1 figure
Determinant method and quantum simulations of many-body effects in a single impurity Anderson model
International Nuclear Information System (INIS)
Gubernatis, J.E.; Olson, T.; Scalapino, D.J.; Sugar, R.L.
1985-01-01
A short description is presented of a quantum Monte Carlo technique, often referred to as the determinant method, that has proved useful for simulating many-body effects in systems of interacting fermions at finite temperatures. Preliminary results using this technique on a single impurity Anderson model are reported. Examples of such many-body effects as local moment formation, Kondo behavior, and mixed valence phenomena found in the simulations are shown. 10 refs., 3 figs
Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain
Imbrie, John Z
2016-01-01
We consider a weakly interacting quantum spin chain with random local interactions. We prove that many-body localization follows from a physically reasonable assumption that limits the extent of level attraction in the statistics of eigenvalues. In a KAM-style construction, a sequence of local unitary transformations is used to diagonalize the Hamiltonian by deforming the initial tensor product basis into a complete set of exact many-body eigenfunctions.
The many-body content of quantum gauge theories and its connection to mass generation mechanisms
International Nuclear Information System (INIS)
Natoli, C.R.; Palumbo, F.
1985-01-01
The aim of the paper is to get more knowledge about many-body systems and their properties, about many-body content of quantum gauge theories and its connection with mass generation mechanisms. The way to achieve this is to perform the galilean limit of the relativistic theory by sending the speed of light c to infinity. This limiting process exposes the low energy behaviour of the relativistic theory
Theory of many-body radiative heat transfer without the constraint of reciprocity
Zhu, Linxiao; Guo, Yu; Fan, Shanhui
2018-03-01
Using a self-consistent scattered field approach based on fluctuational electrodynamics, we develop compact formulas for radiative heat transfer in many-body systems without the constraint of reciprocity. The formulas allow for efficient numerical calculation for a system consisting of a large number of bodies, and are in principle exact. As a demonstration, for a nonreciprocal many-body system, we investigate persistent heat current at thermal equilibrium and directional heat transfer when the system is away from thermal equilibrium.
Many-body effects in X-ray photoemission spectroscopy and electronic properties of solids
International Nuclear Information System (INIS)
Kohiki, S.
1999-01-01
Photoemission from a solid is evidently a many-body process since the motion of each electron cannot be independent of the motions of other electrons. In this article we review the reported many-body effects in X-ray photoemission such as extra-atomic relaxation energy, charge transfer satellite and energy loss structure which are informative in relation to the characteristics of solids. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)
Genuine quantum correlations in quantum many-body systems: a review of recent progress.
De Chiara, Gabriele; Sanpera, Anna
2018-04-19
Quantum information theory has considerably helped in the understanding of quantum many-body systems. The role of quantum correlations and in particular, bipartite entanglement, has become crucial to characterise, classify and simulate quantum many body systems. Furthermore, the scaling of entanglement has inspired modifications to numerical techniques for the simulation of many-body systems leading to the, now established, area of tensor networks. However, the notions and methods brought by quantum information do not end with bipartite entanglement. There are other forms of correlations embedded in the ground, excited and thermal states of quantum many-body systems that also need to be explored and might be utilised as potential resources for quantum technologies. The aim of this work is to review the most recent developments regarding correlations in quantum many-body systems focussing on multipartite entanglement, quantum nonlocality, quantum discord, mutual information but also other non classical measures of correlations based on quantum coherence. Moreover, we also discuss applications of quantum metrology in quantum many-body systems. © 2018 IOP Publishing Ltd.
Nucleon many-body problem using quantum-mechanical few-body technique
International Nuclear Information System (INIS)
Horiuchi, Wataru
2016-01-01
A nucleus is treated as a quantum-mechanical many-body system consisting of protons and neutrons that interact with each other by nuclear force. This paper explains the variational calculation using the correlated basis function as a powerful technique for obtaining the precise solution of Schroedinger equation of many-body, and tries to understand the nucleon many-body system from the viewpoint of a few-body through the application cases of various nuclear systems. It describes the important correlation that characterizes the nucleon many-body system such as the mean field, cluster, and tensor of bound state, and shows that non-bound state is also describable. Since such precise theory is mantic, it is essential for explaining the nature of unknown unstable nuclei, and for determining the nuclear reaction rate under the environment of the stars difficult for experiment. The method is general and flexible, and can be applied to various quantum-mechanical many-body problems. For example, the multi-body calculation of atoms and molecules, hypernuclei, and hadron spectroscopy can be carried out only by changing the potential and particles. (A.O.)
Relativistic many-body perturbation-theory calculations based on Dirac-Fock-Breit wave functions
International Nuclear Information System (INIS)
Ishikawa, Y.; Quiney, H.M.
1993-01-01
A relativistic many-body perturbation theory based on the Dirac-Fock-Breit wave functions has been developed and implemented by employing analytic basis sets of Gaussian-type functions. The instantaneous Coulomb and low-frequency Breit interactions are treated using a unified formalism in both the construction of the Dirac-Fock-Breit self-consistent-field atomic potential and in the evaluation of many-body perturbation-theory diagrams. The relativistic many-body perturbation-theory calculations have been performed on the helium atom and ions of the helium isoelectronic sequence up to Z=50. The contribution of the low-frequency Breit interaction to the relativistic correlation energy is examined for the helium isoelectronic sequence
Probing quantum and thermal noise in an interacting many-body system
DEFF Research Database (Denmark)
Hofferberth, S.; Lesanovsky, Igor; Schumm, Thorsten
2008-01-01
of the shot-to-shot variations of interference-fringe contrast for pairs of independently created one-dimensional Bose condensates. Analysing different system sizes, we observe the crossover from thermal to quantum noise, reflected in a characteristic change in the distribution functions from poissonian......The probabilistic character of the measurement process is one of the most puzzling and fascinating aspects of quantum mechanics. In many-body systems quantum-mechanical noise reveals non-local correlations of the underlying many-body states. Here, we provide a complete experimental analysis....... Furthermore, our experiments constitute the first analysis of the full distribution of quantum noise in an interacting many-body system....
Moments of generalized Husimi distributions and complexity of many-body quantum states
International Nuclear Information System (INIS)
Sugita, Ayumu
2003-01-01
We consider generalized Husimi distributions for many-body systems, and show that their moments are good measures of complexity of many-body quantum states. Our construction of the Husimi distribution is based on the coherent state of the single-particle transformation group. Then the coherent states are independent-particle states, and, at the same time, the most localized states in the Husimi representation. Therefore delocalization of the Husimi distribution, which can be measured by the moments, is a sign of many-body correlation (entanglement). Since the delocalization of the Husimi distribution is also related to chaoticity of the dynamics, it suggests a relation between entanglement and chaos. Our definition of the Husimi distribution can be applied not only to systems of distinguishable particles, but also to those of identical particles, i.e., fermions and bosons. We derive an algebraic formula to evaluate the moments of the Husimi distribution
Paradeisos: A perfect hashing algorithm for many-body eigenvalue problems
Jia, C. J.; Wang, Y.; Mendl, C. B.; Moritz, B.; Devereaux, T. P.
2018-03-01
We describe an essentially perfect hashing algorithm for calculating the position of an element in an ordered list, appropriate for the construction and manipulation of many-body Hamiltonian, sparse matrices. Each element of the list corresponds to an integer value whose binary representation reflects the occupation of single-particle basis states for each element in the many-body Hilbert space. The algorithm replaces conventional methods, such as binary search, for locating the elements of the ordered list, eliminating the need to store the integer representation for each element, without increasing the computational complexity. Combined with the "checkerboard" decomposition of the Hamiltonian matrix for distribution over parallel computing environments, this leads to a substantial savings in aggregate memory. While the algorithm can be applied broadly to many-body, correlated problems, we demonstrate its utility in reducing total memory consumption for a series of fermionic single-band Hubbard model calculations on small clusters with progressively larger Hilbert space dimension.
Many-body calculations with deuteron based single-particle bases and their associated natural orbits
Puddu, G.
2018-06-01
We use the recently introduced single-particle states obtained from localized deuteron wave-functions as a basis for nuclear many-body calculations. We show that energies can be substantially lowered if the natural orbits (NOs) obtained from this basis are used. We use this modified basis for {}10{{B}}, {}16{{O}} and {}24{{Mg}} employing the bare NNLOopt nucleon–nucleon interaction. The lowering of the energies increases with the mass. Although in principle NOs require a full scale preliminary many-body calculation, we found that an approximate preliminary many-body calculation, with a marginal increase in the computational cost, is sufficient. The use of natural orbits based on an harmonic oscillator basis leads to a much smaller lowering of the energies for a comparable computational cost.
Symbolic Detection of Permutation and Parity Symmetries of Evolution Equations
Alghamdi, Moataz
2017-06-18
We introduce a symbolic computational approach to detecting all permutation and parity symmetries in any general evolution equation, and to generating associated invariant polynomials, from given monomials, under the action of these symmetries. Traditionally, discrete point symmetries of differential equations are systemically found by solving complicated nonlinear systems of partial differential equations; in the presence of Lie symmetries, the process can be simplified further. Here, we show how to find parity- and permutation-type discrete symmetries purely based on algebraic calculations. Furthermore, we show that such symmetries always form groups, thereby allowing for the generation of new group-invariant conserved quantities from known conserved quantities. This work also contains an implementation of the said results in Mathematica. In addition, it includes, as a motivation for this work, an investigation of the connection between variational symmetries, described by local Lie groups, and conserved quantities in Hamiltonian systems.
Introduction to modern methods of quantum many-body theory and their applications
Fantoni, Stefano; Krotscheck, Eckhard S
2002-01-01
This invaluable book contains pedagogical articles on the dominant nonstochastic methods of microscopic many-body theories - the methods of density functional theory, coupled cluster theory, and correlated basis functions - in their widest sense. Other articles introduce students to applications of these methods in front-line research, such as Bose-Einstein condensates, the nuclear many-body problem, and the dynamics of quantum liquids. These keynote articles are supplemented by experimental reviews on intimately connected topics that are of current relevance. The book addresses the striking l
Typical Relaxation of Isolated Many-Body Systems Which Do Not Thermalize
Balz, Ben N.; Reimann, Peter
2017-05-01
We consider isolated many-body quantum systems which do not thermalize; i.e., expectation values approach an (approximately) steady longtime limit which disagrees with the microcanonical prediction of equilibrium statistical mechanics. A general analytical theory is worked out for the typical temporal relaxation behavior in such cases. The main prerequisites are initial conditions which appreciably populate many energy levels and do not give rise to significant spatial inhomogeneities on macroscopic scales. The theory explains very well the experimental and numerical findings in a trapped-ion quantum simulator exhibiting many-body localization, in ultracold atomic gases, and in integrable hard-core boson and X X Z models.
Exact many-body dynamics with stochastic one-body density matrix evolution
International Nuclear Information System (INIS)
Lacroix, D.
2004-05-01
In this article, we discuss some properties of the exact treatment of the many-body problem with stochastic Schroedinger equation (SSE). Starting from the SSE theory, an equivalent reformulation is proposed in terms of quantum jumps in the density matrix space. The technical details of the derivation a stochastic version of the Liouville von Neumann equation are given. It is shown that the exact Many-Body problem could be replaced by an ensemble of one-body density evolution, where each density matrix evolves according to its own mean-field augmented by a one-body noise. (author)
Nonlinear field theories and non-Gaussian fluctuations for near-critical many-body systems
International Nuclear Information System (INIS)
Tuszynski, J.A.; Dixon, J.M.; Grundland, A.M.
1994-01-01
This review article outlines a number of efforts made over the past several decades to understand the physics of near critical many-body systems. Beginning with the phenomenological theories of Landau and Ginzburg the paper discusses the two main routes adopted in the past. The first approach is based on statistical calculations while the second investigates the underlying nonlinear field equations. In the last part of the paper we outline a generalisation of these methods which combines classical and quantum properties of the many-body systems studied. (orig.)
Time dependent mean field approximation to the many-body S-matrix
International Nuclear Information System (INIS)
Alhassid, Y.; Koonin, S.E.
1980-01-01
Time-dependent Hartree-Fock (TDHF) calculations are a good description of some inclusive properties of deep inelastic heavy-ion collisions. The first steps toward a mean-field theory that approximates specific elements of the many-body S matrix are presented. A many-body system with pairwise interactions excited by an external, time-dependent one-body field is considered. The methods are used to solve the forced Lipkin model. The moduli of elastic and excitation amplitudes are plotted. 3 figures
Local conservation laws and the structure of the many-body localized states.
Serbyn, Maksym; Papić, Z; Abanin, Dmitry A
2013-09-20
We construct a complete set of local integrals of motion that characterize the many-body localized (MBL) phase. Our approach relies on the assumption that local perturbations act locally on the eigenstates in the MBL phase, which is supported by numerical simulations of the random-field XXZ spin chain. We describe the structure of the eigenstates in the MBL phase and discuss the implications of local conservation laws for its nonequilibrium quantum dynamics. We argue that the many-body localization can be used to protect coherence in the system by suppressing relaxation between eigenstates with different local integrals of motion.
Relativistic many-body theory of atomic transitions: the relativistic equation-of-motion approach
International Nuclear Information System (INIS)
Huang, K.N.
1981-01-01
An equation-of-motion approach is used to develop the relativistic many-body theory of atomic transitions. The relativistic equations of motion for transition matrices are formulated using techniques of quantum field theory. To reduce the equation of motion to a tractable form which is appropriate for numerical calculations, a graphical method is employed to resolve the complication arising from the antisymmetrization and angular momentum coupling. The relativistic equation-of-motion method allows an ab initio treatment of correlation and relativistic effects in both closed- and open-shell many-body systems. A special case of the present formulation reduces to the relativistic random-phase approximation
Many-body-localization: strong disorder perturbative approach for the local integrals of motion
Monthus, Cécile
2018-05-01
For random quantum spin models, the strong disorder perturbative expansion of the local integrals of motion around the real-spin operators is revisited. The emphasis is on the links with other properties of the many-body-localized phase, in particular the memory in the dynamics of the local magnetizations and the statistics of matrix elements of local operators in the eigenstate basis. Finally, this approach is applied to analyze the many-body-localization transition in a toy model studied previously from the point of view of the entanglement entropy.
Jones, Alicia M; Atkinson, Joshua T; Silberg, Jonathan J
2017-01-01
Rearrangements that alter the order of a protein's sequence are used in the lab to study protein folding, improve activity, and build molecular switches. One of the simplest ways to rearrange a protein sequence is through random circular permutation, where native protein termini are linked together and new termini are created elsewhere through random backbone fission. Transposase mutagenesis has emerged as a simple way to generate libraries encoding different circularly permuted variants of proteins. With this approach, a synthetic transposon (called a permuteposon) is randomly inserted throughout a circularized gene to generate vectors that express different permuted variants of a protein. In this chapter, we outline the protocol for constructing combinatorial libraries of circularly permuted proteins using transposase mutagenesis, and we describe the different permuteposons that have been developed to facilitate library construction.
The proceedings of the 9th international conference on recent progress in many-body theories
International Nuclear Information System (INIS)
Neilson, D.; Bishop, R. F.
1998-01-01
This inaugural volume in this new World Scientific Publications series, 'Advances in Quantum Many-Body Theory' records the invited and contributed papers given at the Ninth International Conference on Recent Progress in Many-Body Theories. This conference was held in the School of Physics at The University of New South Wales in Sydney in July, 1997. The conference was also the seventh in the University's series of Gordon Godfrey International Workshop on Theoretical Physics. The style and format of the conference followed the accepted pattern for the series, focusing on the development, refinement, and important applications of many-body methods. A major aim of the series has been to foster an exchange of ideas among physicists working in such diverse areas as nuclear and subnuclear physics, quantum chemistry, complex systems, quantum field theory, strongly correlated electronic systems, magnetism, quantum fluids and condensed matter physics. A special feature of this ninth conference was a session devoted to theories for many-electron systems in zero dimensions (quantum dots), one dimension (quantum wires) and two dimensions (electron layers). These new systems are now firmly established as fertile sources of novel and challenging many-body phenomena
Understanding many-body physics in one dimension from the Lieb–Liniger model
International Nuclear Information System (INIS)
Jiang Yu-Zhu; Chen Yang-Yang; Guan Xi-Wen
2015-01-01
This article presents an elementary introduction on various aspects of the prototypical integrable model the Lieb–Liniger Bose gas ranging from the cooperative to the collective features of many-body phenomena. In 1963, Lieb and Liniger first solved this quantum field theory many-body problem using Bethe’s hypothesis, i.e., a particular form of wavefunction introduced by Bethe in solving the one-dimensional Heisenberg model in 1931. Despite the Lieb–Liniger model is arguably the simplest exactly solvable model, it exhibits rich quantum many-body physics in terms of the aspects of mathematical integrability and physical universality. Moreover, the Yang–Yang grand canonical ensemble description for the model provides us with a deep understanding of quantum statistics, thermodynamics, and quantum critical phenomena at the many-body physical level. Recently, such fundamental physics of this exactly solved model has been attracting growing interest in experiments. Since 2004, there have been more than 20 experimental papers that reported novel observations of different physical aspects of the Lieb–Liniger model in the laboratory. So far the observed results are in excellent agreement with results obtained using the analysis of this simplest exactly solved model. Those experimental observations reveal the unique beauty of integrability. (topical review)
Physics in one dimension: theoretical concepts for quantum many-body systems.
Schönhammer, K
2013-01-09
Various sophisticated approximation methods exist for the description of quantum many-body systems. It was realized early on that the theoretical description can simplify considerably in one-dimensional systems and various exact solutions exist. The focus in this introductory paper is on fermionic systems and the emergence of the Luttinger liquid concept.
Efficient molecular dynamics simulations with many-body potentials on graphics processing units
Fan, Zheyong; Chen, Wei; Vierimaa, Ville; Harju, Ari
2017-09-01
Graphics processing units have been extensively used to accelerate classical molecular dynamics simulations. However, there is much less progress on the acceleration of force evaluations for many-body potentials compared to pairwise ones. In the conventional force evaluation algorithm for many-body potentials, the force, virial stress, and heat current for a given atom are accumulated within different loops, which could result in write conflict between different threads in a CUDA kernel. In this work, we provide a new force evaluation algorithm, which is based on an explicit pairwise force expression for many-body potentials derived recently (Fan et al., 2015). In our algorithm, the force, virial stress, and heat current for a given atom can be accumulated within a single thread and is free of write conflicts. We discuss the formulations and algorithms and evaluate their performance. A new open-source code, GPUMD, is developed based on the proposed formulations. For the Tersoff many-body potential, the double precision performance of GPUMD using a Tesla K40 card is equivalent to that of the LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) molecular dynamics code running with about 100 CPU cores (Intel Xeon CPU X5670 @ 2.93 GHz).
Medders, Gregory R; Paesani, Francesco
2015-03-10
Vibrational spectroscopy is a powerful technique to probe the structure and dynamics of water. However, deriving an unambiguous molecular-level interpretation of the experimental spectral features remains a challenge due to the complexity of the underlying hydrogen-bonding network. In this contribution, we present an integrated theoretical and computational framework (named many-body molecular dynamics or MB-MD) that, by systematically removing uncertainties associated with existing approaches, enables a rigorous modeling of vibrational spectra of water from quantum dynamical simulations. Specifically, we extend approaches used to model the many-body expansion of interaction energies to develop many-body representations of the dipole moment and polarizability of water. The combination of these "first-principles" representations with centroid molecular dynamics simulations enables the simulation of infrared and Raman spectra of liquid water under ambient conditions that, without relying on any ad hoc parameters, are in good agreement with the corresponding experimental results. Importantly, since the many-body energy, dipole, and polarizability surfaces employed in the simulations are derived independently from accurate fits to correlated electronic structure data, MB-MD allows for a systematic analysis of the calculated spectra in terms of both electronic and dynamical contributions. The present analysis suggests that, while MB-MD correctly reproduces both the shifts and the shapes of the main spectroscopic features, an improved description of quantum dynamical effects possibly combined with a dissociable water potential may be necessary for a quantitative representation of the OH stretch band.
Many-body localization proximity effects in platforms of coupled spins and bosons
Marino, J.; Nandkishore, R. M.
2018-02-01
We discuss the onset of many-body localization in a one-dimensional system composed of a XXZ quantum spin chain and a Bose-Hubbard model linearly coupled together. We consider two complementary setups, depending whether spatial disorder is initially imprinted on spins or on bosons; in both cases, we explore the conditions for the disordered portion of the system to localize by proximity of the other clean half. Assuming that the dynamics of one of the two parts develops on shorter time scales than the other, we can adiabatically eliminate the fast degrees of freedom, and derive an effective Hamiltonian for the system's remainder using projection operator techniques. Performing a locator expansion on the strength of the many-body interaction term or on the hopping amplitude of the effective Hamiltonian thus derived, we present results on the stability of the many-body localized phases induced by proximity effect. We also briefly comment on the feasibility of the proposed model through modern quantum optics architectures, with the long-term perspective to realize experimentally, in composite open systems, Anderson or many-body localization proximity effects.
N=2 superconformal Newton-Hooke algebra and many-body mechanics
International Nuclear Information System (INIS)
Galajinsky, Anton
2009-01-01
A representation of the conformal Newton-Hooke algebra on a phase space of n particles in arbitrary dimension which interact with one another via a generic conformal potential and experience a universal cosmological repulsion or attraction is constructed. The minimal N=2 superconformal extension of the Newton-Hooke algebra and its dynamical realization in many-body mechanics are studied.
Construction of exact constants of motion and effective models for many-body localized systems
Goihl, M.; Gluza, M.; Krumnow, C.; Eisert, J.
2018-04-01
One of the defining features of many-body localization is the presence of many quasilocal conserved quantities. These constants of motion constitute a cornerstone to an intuitive understanding of much of the phenomenology of many-body localized systems arising from effective Hamiltonians. They may be seen as local magnetization operators smeared out by a quasilocal unitary. However, accurately identifying such constants of motion remains a challenging problem. Current numerical constructions often capture the conserved operators only approximately, thus restricting a conclusive understanding of many-body localization. In this work, we use methods from the theory of quantum many-body systems out of equilibrium to establish an alternative approach for finding a complete set of exact constants of motion which are in addition guaranteed to represent Pauli-z operators. By this we are able to construct and investigate the proposed effective Hamiltonian using exact diagonalization. Hence, our work provides an important tool expected to further boost inquiries into the breakdown of transport due to quenched disorder.
Many-body physics and the capacity of quantum channels with memory
International Nuclear Information System (INIS)
Plenio, M B; Virmani, S
2008-01-01
In most studies of the capacity of quantum channels, it is assumed that the errors in the use of each channel are independent. However, recent work has begun to investigate the effects of memory or correlations in the error, and has led to suggestions that there can be interesting non-analytic behaviour in the capacity of such channels. In a previous paper, we pursued this issue by connecting the study of channel capacities under correlated error to the study of critical behaviour in many-body physics. This connection enables the use of techniques from many-body physics to either completely solve or understand qualitatively a number of interesting models of correlated error with analogous behaviour to associated many-body systems. However, in order for this approach to work rigorously, there are a number of technical properties that need to be established for the lattice systems being considered. In this paper, we discuss these properties in detail, and establish them for some classes of many-body system
Relativistic Many-Body Theory A New Field-Theoretical Approach
Lindgren, Ingvar
2011-01-01
Relativistic Many-Body Theory treats — for the first time — the combination of relativistic atomic many-body theory with quantum-electrodynamics (QED) in a unified manner. This book can be regarded as a continuation of the book by Lindgren and Morrison, Atomic Many-Body Theory (Springer 1986), which deals with the non-relativistic theory of many-electron systems, describing several means of treating the electron correlation to essentially all orders of perturbation theory. The treatment of the present book is based upon quantum-field theory, and demonstrates that when the procedure is carried to all orders of perturbation theory, two-particle systems are fully compatible with the relativistically covariant Bethe-Salpeter equation. This procedure can be applied to arbitrary open-shell systems, in analogy with the standard many-body theory, and it is also applicable to systems with more than two particles. Presently existing theoretical procedures for treating atomic systems are, in several cases, insuffici...
On the many-body foundation of the nuclear field theory
International Nuclear Information System (INIS)
Bes, D.R.; Dussel, G.G.; Liotta, R.J.; Perazzo, R.P.J.; Broglia, R.A.
1976-01-01
The equivalence between the description of the many-body finite nuclear system in terms of Feynman diagrams involving only the fermion degrees of freedom and of Feynman diagrams involving fermion and phonon degrees of freedom is proved for intermediate states in the case of a general two-body residual interaction. (Auth.)
Enhancement and sign change of magnetic correlations in a driven quantum many-body system
Görg, Frederik; Messer, Michael; Sandholzer, Kilian; Jotzu, Gregor; Desbuquois, Rémi; Esslinger, Tilman
2018-01-01
Periodic driving can be used to control the properties of a many-body state coherently and to realize phases that are not accessible in static systems. For example, exposing materials to intense laser pulses makes it possible to induce metal-insulator transitions, to control magnetic order and to generate transient superconducting behaviour well above the static transition temperature. However, pinning down the mechanisms underlying these phenomena is often difficult because the response of a material to irradiation is governed by complex, many-body dynamics. For static systems, extensive calculations have been performed to explain phenomena such as high-temperature superconductivity. Theoretical analyses of driven many-body Hamiltonians are more challenging, but approaches have now been developed, motivated by recent observations. Here we report an experimental quantum simulation in a periodically modulated hexagonal lattice and show that antiferromagnetic correlations in a fermionic many-body system can be reduced, enhanced or even switched to ferromagnetic correlations (sign reversal). We demonstrate that the description of the many-body system using an effective Floquet-Hamiltonian with a renormalized tunnelling energy remains valid in the high-frequency regime by comparing the results to measurements in an equivalent static lattice. For near-resonant driving, the enhancement and sign reversal of correlations is explained by a microscopic model of the system in which the particle tunnelling and magnetic exchange energies can be controlled independently. In combination with the observed sufficiently long lifetimes of the correlations in this system, periodic driving thus provides an alternative way of investigating unconventional pairing in strongly correlated systems experimentally.
PREFACE: 17th International Conference on Recent Progress in Many-Body Theories (MBT17)
Reinholz, Heidi; Boronat, Jordi
2014-08-01
These are the proceedings of the XVII International Conference on Recent Progress in Many-Body Theories, which was held from 8-13 September 2013 in Rostock, Germany. The conference continued the triennial series initiated in Trieste in 1978 and was devoted to new developments in the field of many-body theories. The conference series encourages the exchange of ideas between physicists working in such diverse areas as nuclear physics, quantum chemistry, lattice Hamiltonians or quantum uids. Many-body theories are an integral part in different fields of theoretical physics such as condensed matter, nuclear matter and field theory. Phase transitions and macroscopic quantum effects such as magnetism, Bose-Einstein condensation, super uidity or superconductivity have been investigated within ultra-cold gases, finite systems or various nanomaterials. The conference series on Recent Progress in Many-Body Theories is devoted to foster the interaction and to cross-fertilize between different fields and to discuss future lines of research. The topics of the 17th meeting were Cluster Physics Cold Gases High Energy Density Matter and Intense Lasers Magnetism New Developments in Many-Body Techniques Nuclear Many-Body and Relativistic Theories Quantum Fluids and Solids Quantum Phase Transitions Topological Insulators and Low Dimensional Systems. 109 participants from 20 countries participated. 44 talks and 61 posters werde presented. As a particular highlight of the conference, The Eugene Feenberg Memorial Medal for outstanding results in the field of many-body theory and The Hermann Kümmel Early Achievement Award in Many-Body Physics for young scientists in that field were awarded. The Feenberg Medal went jointly to Patrick Lee (MIT, USA) for his fundamental contributions to condensed-matter theory, especially in regard to the quantum Hall effect, to universal conductance uctuations, and to the Kondo effect in quantum dots, and Douglas Scalapino (UC Santa Barbara, USA) for his
Highly Enhanced Many-Body Interactions in Anisotropic 2D Semiconductors.
Sharma, Ankur; Yan, Han; Zhang, Linglong; Sun, Xueqian; Liu, Boqing; Lu, Yuerui
2018-05-15
Atomically thin two-dimensional (2D) semiconductors have presented a plethora of opportunities for future optoelectronic devices and photonics applications, made possible by the strong light matter interactions at the 2D quantum limit. Many body interactions between fundamental particles in 2D semiconductors are strongly enhanced compared with those in bulk semiconductors because of the reduced dimensionality and, thus, reduced dielectric screening. These enhanced many body interactions lead to the formation of robust quasi-particles, such as excitons, trions, and biexcitons, which are extremely important for the optoelectronics device applications of 2D semiconductors, such as light emitting diodes, lasers, and optical modulators, etc. Recently, the emerging anisotropic 2D semiconductors, such as black phosphorus (termed as phosphorene) and phosphorene-like 2D materials, such as ReSe 2 , 2D-perovskites, SnS, etc., show strong anisotropic optical and electrical properties, which are different from conventional isotropic 2D semiconductors, such as transition metal dichalcogenide (TMD) monolayers. This anisotropy leads to the formation of quasi-one-dimensional (quasi-1D) excitons and trions in a 2D system, which results in even stronger many body interactions in anisotropic 2D materials, arising from the further reduced dimensionality of the quasi-particles and thus reduced dielectric screening. Many body interactions have been heavily investigated in TMD monolayers in past years, but not in anisotropic 2D materials yet. The quasi-particles in anisotropic 2D materials have fractional dimensionality which makes them perfect candidates to serve as a platform to study fundamental particle interactions in fractional dimensional space. In this Account, we present our recent progress related to 2D phosphorene, a 2D system with quasi-1D excitons and trions. Phosphorene, because of its unique anisotropic properties, provides a unique 2D platform for investigating the
How should we understand non-equilibrium many-body steady states?
Maghrebi, Mohammad; Gorshkov, Alexey
: Many-body systems with both coherent dynamics and dissipation constitute a rich class of models which are nevertheless much less explored than their dissipationless counterparts. The advent of numerous experimental platforms that simulate such dynamics poses an immediate challenge to systematically understand and classify these models. In particular, nontrivial many-body states emerge as steady states under non-equilibrium dynamics. In this talk, I use a field-theoretic approach based on the Keldysh formalism to study nonequilibrium phases and phase transitions in such models. I show that an effective temperature generically emerges as a result of dissipation, and the universal behavior including the dynamics near the steady state is described by a thermodynamic universality class. In the end, I will also discuss possibilities that go beyond the paradigm of an effective thermodynamic behavior.
Auger recombination in Dirac materials: A tangle of many-body effects
Alymov, Georgy; Vyurkov, Vladimir; Ryzhii, Victor; Satou, Akira; Svintsov, Dmitry
2018-05-01
The peculiar electron dispersion in Dirac materials makes lowest-order Auger processes prohibited or marginally prohibited by energy and momentum conservation laws. Thus, Auger recombination (AR) in these materials is very sensitive to many-body effects. We incorporate them at the level of the G W approximation into the nonequilibrium Green's functions approach to AR and study the role of dynamic screening, spectrum broadening, and renormalization in the case of weakly pumped undoped graphene. We find that incorrect treatment of many-body effects can lead to an order-of-magnitude error in the recombination rate. We show that the AR time depends weakly (sublinearly) on the background dielectric constant, which limits the possibility to control recombination by the choice of substrate. However, the AR time can be considerably prolonged by placing graphene under a metal gate or by introducing a band gap. With carrier cooling taken into account, our results comply with experiments on photoexcited graphene.
In-Medium Similarity Renormalization Group Approach to the Nuclear Many-Body Problem
Hergert, Heiko; Bogner, Scott K.; Lietz, Justin G.; Morris, Titus D.; Novario, Samuel J.; Parzuchowski, Nathan M.; Yuan, Fei
We present a pedagogical discussion of Similarity Renormalization Group (SRG) methods, in particular the In-Medium SRG (IMSRG) approach for solving the nuclear many-body problem. These methods use continuous unitary transformations to evolve the nuclear Hamiltonian to a desired shape. The IMSRG, in particular, is used to decouple the ground state from all excitations and solve the many-body Schrödinger equation. We discuss the IMSRG formalism as well as its numerical implementation, and use the method to study the pairing model and infinite neutron matter. We compare our results with those of Coupled cluster theory (Chap. 8), Configuration-Interaction Monte Carlo (Chap. 9), and the Self-Consistent Green's Function approach discussed in Chap. 11 The chapter concludes with an expanded overview of current research directions, and a look ahead at upcoming developments.
Many-body optimization using an ab initio monte carlo method.
Haubein, Ned C; McMillan, Scott A; Broadbelt, Linda J
2003-01-01
Advances in computing power have made it possible to study solvated molecules using ab initio quantum chemistry. Inclusion of discrete solvent molecules is required to determine geometric information about solute/solvent clusters. Monte Carlo methods are well suited to finding minima in many-body systems, and ab initio methods are applicable to the widest range of systems. A first principles Monte Carlo (FPMC) method was developed to find minima in many-body systems, and emphasis was placed on implementing moves that increase the likelihood of finding minimum energy structures. Partial optimization and molecular interchange moves aid in finding minima and overcome the incomplete sampling that is unavoidable when using ab initio methods. FPMC was validated by studying the boron trifluoride-water system, and then the method was used to examine the methyl carbenium ion in water to demonstrate its application to solvation problems.
Bell Correlations in a Many-Body System with Finite Statistics
Wagner, Sebastian; Schmied, Roman; Fadel, Matteo; Treutlein, Philipp; Sangouard, Nicolas; Bancal, Jean-Daniel
2017-10-01
A recent experiment reported the first violation of a Bell correlation witness in a many-body system [Science 352, 441 (2016)]. Following discussions in this Letter, we address here the question of the statistics required to witness Bell correlated states, i.e., states violating a Bell inequality, in such experiments. We start by deriving multipartite Bell inequalities involving an arbitrary number of measurement settings, two outcomes per party and one- and two-body correlators only. Based on these inequalities, we then build up improved witnesses able to detect Bell correlated states in many-body systems using two collective measurements only. These witnesses can potentially detect Bell correlations in states with an arbitrarily low amount of spin squeezing. We then establish an upper bound on the statistics needed to convincingly conclude that a measured state is Bell correlated.
Lattice Methods and the Nuclear Few- and Many-Body Problem
Lee, Dean
This chapter builds upon the review of lattice methods and effective field theory of the previous chapter. We begin with a brief overview of lattice calculations using chiral effective field theory and some recent applications. We then describe several methods for computing scattering on the lattice. After that we focus on the main goal, explaining the theory and algorithms relevant to lattice simulations of nuclear few- and many-body systems. We discuss the exact equivalence of four different lattice formalisms, the Grassmann path integral, transfer matrix operator, Grassmann path integral with auxiliary fields, and transfer matrix operator with auxiliary fields. Along with our analysis we include several coding examples and a number of exercises for the calculations of few- and many-body systems at leading order in chiral effective field theory.
Coupled-channel equations and off-shell transformations in many-body scattering
International Nuclear Information System (INIS)
Cattapan, G.; Vanzani, V.
1977-01-01
The general structure and the basic features of several many-body coupled-channel integral equations, obtained by means of the channel coupling array device, are studied in a systematic way. Particular attention is paid to the employment of symmetric transition operators. The connection between different formulations has been clarified and the role played by some off-shell transformations for many-body transition operators has been discussed. Specific choices of the coupling scheme are considered and the corresponding coupled equations are compared with similar equations previously derived. Several sets of linear relations between transition operators have also been presented and used in a three-body context to derive uncoupled integral equations with connected kernel
Relativistic many-body theory of atomic transitions. The relativistic equation-of-motion approach
International Nuclear Information System (INIS)
Huang, K.
1982-01-01
An equation-of-motion approach is used to develop the relativistic many-body theory of atomic transitions. The relativistic equations of motion for transition matrices are formulated with the use of techniques of quantum-field theory. To reduce the equations of motion to a tractable form which is appropriate for numerical calculations, a graphical method to resolve the complication arising from the antisymmetrization and angular-momentum coupling is employed. The relativistic equation-of-motion method allows an ab initio treatment of correlation and relativistic effects in both closed- and open-shell many-body systems. A special case of the present formulation reduces to the relativistic random-phase approximation
Many-body effects in the mesoscopic x-ray edge problem
International Nuclear Information System (INIS)
Hentschel, Martina; Roeder, Georg; Ullmo, Denis
2007-01-01
Many-body phenomena, a key interest in the investigation of bulk solid state systems, are studied here in the context of the x-ray edge problem for mesoscopic systems. We investigate the many-body effects associated with the sudden perturbation following the x-ray exciton of a core electron into the conduction band. For small systems with dimensions at the nanoscale we find considerable deviations from the well-understood metallic case where Anderson orthogonality catastrophe and the Mahan-Nozieres-DeDominicis response cause characteristic deviations of the photoabsorption cross section from the naive expectation. Whereas the K-edge is typically rounded in metallic systems, we find a slightly peaked K-edge in generic mesoscopic systems with chaotic-coherent electron dynamics. Thus the behavior of the photoabsorption cross section at threshold depends on the system size and is different for the metallic and the mesoscopic case. (author)
Diagrammatic many-body perturbation expansion for atoms and molecules. Pt. 6
International Nuclear Information System (INIS)
Moncrieff, D.; Baker, D.J.; Wilson, S.
1989-01-01
The efficient evaluation of the second-order expression in the many-body perturbation theory expansion for the correlation energy on vector processing and parallel processing computers is discussed. It is argued that the linked diagram theorem not only leads to the well known theoretical advantages of the many-body perturbation theory approach which allows the calculation of correlation energies for large (i.e. extended molecules or species containing heavy atoms) systems but also decouples the many-electron problem allowing efficient implementation on parallel processing machines. Furthermore, the computation associated with each of the resulting subproblems is very well suited to vector processing machines. Timing tests are reported for the CRAY 1 and CDC Cyber 205 vector processors, for a 1 processor implementation on the CRAY X-MP/48 and the ETA-10E, and for a 4 processor implementation on the Cray X-MP/48. (orig.)
Morphology of Laplacian growth processes and statistics of equivalent many-body systems
International Nuclear Information System (INIS)
Blumenfeld, R.
1994-01-01
The authors proposes a theory for the nonlinear evolution of two dimensional interfaces in Laplacian fields. The growing region is conformally mapped onto the unit disk, generating an equivalent many-body system whose dynamics and statistics are studied. The process is shown to be Hamiltonian, with the Hamiltonian being the imaginary part of the complex electrostatic potential. Surface effects are introduced through the Hamiltonian as an external field. An extension to a continuous density of particles is presented. The results are used to study the morphology of the interface using statistical mechanics for the many-body system. The distribution of the curvature and the moments of the growth probability along the interface are calculated exactly from the distribution of the particles. In the dilute limit, the distribution of the curvature is shown to develop algebraic tails, which may, for the first time, explain the origin of fractality in diffusion controlled processes
Method for the Direct Solve of the Many-Body Schrödinger Wave Equation
Jerke, Jonathan; Tymczak, C. J.; Poirier, Bill
We report on theoretical and computational developments towards a computationally efficient direct solve of the many-body Schrödinger wave equation for electronic systems. This methodology relies on two recent developments pioneered by the authors: 1) the development of a Cardinal Sine basis for electronic structure calculations; and 2) the development of a highly efficient and compact representation of multidimensional functions using the Canonical tensor rank representation developed by Belykin et. al. which we have adapted to electronic structure problems. We then show several relevant examples of the utility and accuracy of this methodology, scaling with system size, and relevant convergence issues of the methodology. Method for the Direct Solve of the Many-Body Schrödinger Wave Equation.
The closed time-path Green function formalism in many-body theory
International Nuclear Information System (INIS)
Guang-zhao Zhou; Zhao-bin Su; Bai-lin Hao; Lu Yu.
1983-09-01
The closed time-path Green function formalism, developed by our group during recent years, is briefly reviewed. The generating functional technique, the coupled equations for the order parameter and the elementary excitations as well as the systematic loop expansion are outlined. The applications to critical dynamics, quenched random systems, nonlinear response theory, superconductivity, laser system and quasi-one-dimensional conductors are described. The theoretical approach developed can be applied to both equilibrium and non-equilibrium many-body systems. (author)
Many-body theory of charge transfer in hyperthermal atomic scattering
International Nuclear Information System (INIS)
Marston, J.B.; Andersson, D.R.; Behringer, E.R.; Cooper, B.H.; DiRubio, C.A.; Kimmel, G.A.; Richardson, C.
1993-01-01
We use the Newns-Anderson Hamiltonian to describe many-body electronic processes that occur when hyperthermal alkali atoms scatter off metallic surfaces. Following Brako and Newns, we expand the electronic many-body wave function in the number of particle-hole pairs (we keep terms up to and including a single particle-hole pair). We extend their earlier work by including level crossings, excited neutrals, and negative ions. The full set of equations of motion is integrated numerically, without further approximations, to obtain the many-body amplitudes as a function of time. The velocity and work-function dependence of final-state quantities such as the distribution of ion charges and excited atomic occupancies are compared with experiment. In particular, experiments that scatter alkali ions off clean Cu(001) surfaces in the energy range 5--1600 eV constrain the theory quantitatively. The neutralization probability of Na + ions shows a minimum at intermediate velocity in agreement with the theory. This behavior contrasts with that of K + , which shows virtually no neutralization, and with Li + , which exhibits a monotonically increasing neutral fraction with decreasing velocity. Particle-hole excitations are left behind in the metal during a fraction of the collision events; this dissipated energy is predicted to be quite small (on the order of tenths of an electron volt). Indeed, classical trajectory simulations of the surface dynamics account well for the observed energy loss, and thus provide some justification for our truncation of the equations of motion at the single particle-hole pair level. Li + scattering experiments off low work-function surfaces provide qualitative information on the importance of many-body effects. At sufficiently low work function, the negative ions predicted to occur are in fact observed
One-dimensional classical many-body system having a normal thermal conductivity
International Nuclear Information System (INIS)
Casati, G.; Ford, J.; Vivaldi, F.; Visscher, W.M.
1984-01-01
By numerically computing orbits for a chaotic, one-dimensional, many-body system placed between two thermal reservoirs, we verify directly that its energy transport obeys the Fourier heat law and we determine its thermal conductivity K. The same value of K is independently obtained by use of the Green-Kubo formalism. These numerical studies verify that chaos is the essential ingredient of diffusive energy transport, and they validate the Green-Kubo formalism
Many-body localization-delocalization transition in the quantum Sherrington-Kirkpatrick model
Mukherjee, Sudip; Nag, Sabyasachi; Garg, Arti
2018-04-01
We analyze the many-body localization- (MBL) to-delocalization transition in the Sherrington-Kirkpatrick (SK) model of Ising spin glass in the presence of a transverse field Γ . Based on energy-resolved analysis, which is of relevance for a closed quantum system, we show that the quantum SK model has many-body mobility edges separating the MBL phase, which is nonergodic and nonthermal, from the delocalized phase, which is ergodic and thermal. The range of the delocalized regime increases with an increase in the strength of Γ , and eventually for Γ larger than ΓCP the entire many-body spectrum is delocalized. We show that the Renyi entropy is almost independent of the system size in the MBL phase while the delocalized phase shows extensive Renyi entropy. We further obtain the spin-glass transition curve in the energy density ɛ -Γ plane from the collapse of the eigenstate spin susceptibility. We demonstrate that in most of the parameter regime, the spin-glass transition occurs close to the MBL transition, indicating that the spin-glass phase is nonergodic and nonthermal while the paramagnetic phase is delocalized and thermal.
Spin-dependent electron many-body effects in GaAs
Nemec, P.; Kerachian, Y.; van Driel, H. M.; Smirl, Arthur L.
2005-12-01
Time- and polarization-resolved differential transmission measurements employing same and oppositely circularly polarized 150fs optical pulses are used to investigate spin characteristics of conduction band electrons in bulk GaAs at 295K . Electrons and holes with densities in the 2×1016cm-3-1018cm-3 range are generated and probed with pulses whose center wavelength is between 865 and 775nm . The transmissivity results can be explained in terms of the spin sensitivity of both phase-space filling and many-body effects (band-gap renormalization and screening of the Coulomb enhancement factor). For excitation and probing at 865nm , just above the band-gap edge, the transmissivity changes mainly reflect spin-dependent phase-space filling which is dominated by the electron Fermi factors. However, for 775nm probing, the influence of many-body effects on the induced transmission change are comparable with those from reduced phase space filling, exposing the spin dependence of the many-body effects. If one does not take account of these spin-dependent effects one can misinterpret both the magnitude and time evolution of the electron spin polarization. For suitable measurements we find that the electron spin relaxation time is 130ps .
Many-body localization dynamics from a one-particle perspective
Energy Technology Data Exchange (ETDEWEB)
Lezama Mergold Love, Talia; Bera, Soumya; Bardarson, Jens Hjorleifur [Max Planck Institute for the Physics of Complex Systems, Dresden (Germany)
2016-07-01
Systems exhibiting many-body localization (Anderson insulators in the presence of interactions) present a novel class of nonergodic phases of matter. The study of entanglement, in terms of both exact eigenstates and its time evolution after quenches, has been useful to reveal the salient signatures of these systems. Similarly to the entanglement entropy of exact eigenstates, the one-particle density matrix can be used as a tool to characterize the many-body localization transition with its eigenvalues showing a Fermi-liquid like step discontinuity in the localized phase. However, this analysis distinguishes the Fock-space structure of the eigenstates from the real space. Here, we present numerical evidence for dynamical signatures of the many-body localized phase for a closed fermionic system, using the one-particle density matrix and its time evolution after a global quench. We discuss and compare our results with the well-known logarithmic spreading of entanglement (a dynamical signature of this phase, absent in the Anderson insulator).
Fifth International Conference on Recent Progress in Many-Body Theories
Pajanne, E; Bishop, R; Recent Progress in MANY-BODY THEORIES
1988-01-01
The present volume contains the texts of the invited talks delivered at the Fifth International Conference on Recent Progress in Many-Body Theories held in Oulu, Finland during the period 3-8 August 1987. The general format and style of the meeting followed closely those which had evolved from the earlier conferences in the series: Trieste 1978, Oaxtepec 1981, Altenberg 1983 and San Francisco 1985. Thus, the conferences in this series are in tended, as far as is practicable, to cover in a broad and balanced fashion both the entire spectrum of theoretical tools developed to tackle the quan tum many-body problem, and their major fields of· application. One of the major aims of the series is to foster the exchange of ideas and techniques among physicists working in such diverse areas of application of many-body theories as nucleon-nucleon interactions, nuclear physics, astronomy, atomic and molecular physics, quantum chemistry, quantum fluids and plasmas, and solid-state and condensed matter physics. A spec...
Calculation of the hyperfine interaction using an effective-operator form of many-body theory
International Nuclear Information System (INIS)
Garpman, S.; Lindgren, I.; Lindgren, J.; Morrison, J.
1975-01-01
The effective-operator form of many-body theory is reviewed and applied to the calculation of the hyperfine structure. Numerical results are given for the 2p, 3p, and 4p excited states of Li and the 3p state of Na. This is the first complete calculation of the hyperfine structure using an effective-operator form of perturbation theory. As in the Brueckner-Goldstone form of many-body theory, the various terms in the perturbation expansion are represented by Feynman diagrams which correspond to basic physical processes. The angular part of the perturbation diagrams are evaluated by taking advantage of the formal analogy between the Feynman diagrams and the angular-momentum diagrams, introduced by Jucys et al. The radial part of the diagrams is calculated by solving one- and two-particle equations for the particular linear combination of excited states that contribute to the Feynman diagrams. In this way all second- and third-order effects are accurately evaluated without explicitly constructing the excited orbitals. For the 2p state of Li our results are in agreement with the calculations of Nesbet and of Hameed and Foley. However, our quadrupole calculation disagrees with the work of Das and co-workers. The many-body results for Li and Na are compared with semiempirical methods for evaluating the quadrupole moment from the hyperfine interaction, and a new quadrupole moment of 23 Na is given
Functional integral representation of the nuclear many-body grand partition function
International Nuclear Information System (INIS)
Kerman, A.K.; Troudet, T.
1984-01-01
A local functional integral formulation of the nuclear many-body problem is proposed which is a generalization of the method previously developed. Its most interesting feature is that it allows an expansion of the many-body evolution operator around any arbitrary mean-field which takes into account the pairing correlations between the nucleons. This is explicitly illustrated for the nuclear many-body grand partition function for which special attention is paid to the static temperature-dependent Hartree-Fock-Bogolyubov (H.F.B.) approximation. Indeed, the temperature-dependent H.F.B. configuration appears to be the optimal choice from a variational point of view among all the possible independent quasi-particle motion approximations. An analytic approximation of the energy level density rho (E,A) is given using explicitly the arbitrariness in the choice of the mean-field and a possible numerical application is proposed. Finally, a new compact formulation of our functional integral that might be useful for future Monte Carlo calculations is proposed
Many-body quantum chaos: Recent developments and applications to nuclei
International Nuclear Information System (INIS)
Gomez, J.M.G.; Kar, K.; Kota, V.K.B.; Molina, R.A.; Relano, A.; Retamosa, J.
2011-01-01
In the last decade, there has been an increasing interest in the analysis of energy level spectra and wave functions of nuclei, particles, atoms and other quantum many-body systems by means of statistical methods and random matrix ensembles. The concept of quantum chaos plays a central role for understanding the universal properties of the energy spectrum of quantum systems. Since these properties concern the whole spectrum, statistical methods become an essential tool. Besides random matrix theory, new theoretical developments making use of information theory, time series analysis, and the merging of thermodynamics and the semiclassical approximation are emphasized. Applications of these methods to quantum systems, especially to atomic nuclei, are reviewed. We focus on recent developments like the study of 'imperfect spectra' to estimate the degree of symmetry breaking or the fraction of missing levels, the existence of chaos remnants in nuclear masses, the onset of chaos in nuclei, and advances in the comprehension of the Hamiltonian structure in many-body systems. Finally, some applications of statistical spectroscopy methods generated by many-body chaos and two-body random matrix ensembles are described, with emphasis on Gamow-Teller strength sums and beta decay rates for stellar evolution and supernovae.
Many-body dynamics with cold atoms and molecules in optical lattices
International Nuclear Information System (INIS)
Schachenmayer, J.
2012-01-01
Systems of cold atoms or molecules, trapped in a periodic potential formed from standing waves of laser light, provide an experimental possibility to study strongly correlated many-body lattice models, which are traditionally used in condensed matter physics. Due to the relatively weak energy scales in these ''optical lattices'' (next-neighbor tunneling energies are typically on the order of tens of Hertz), the time-scales of the dynamics in these systems is relatively slow and can be observed in experiments. Furthermore, the microscopic parameters of the models can be very well controlled by lattice laser intensities and external fields. Thus, optical lattices provide an excellent framework to study many-body quantum non-equilibrium dynamics, which on the theoretical level is the topic of this thesis. This thesis contains a study of many-body dynamics in optical lattices for both idealized isolated models and realistic models with imperfections. It is centered around four main topics: The first two topics are studies of coherent many-body dynamics. This contains explicitly: (i) an analysis of the possibility to dynamically prepare crystalline states of Rydberg atoms or polar molecules by adiabatically tuning laser parameters; and (ii) a study of the collapses and revivals of the momentum-distribution of a Bose-Einstein condensate with a fixed number of atoms, which is suddenly loaded into a deep optical lattice. The third main topic is entanglement and specifically the dynamical growth of entanglement between portions of an optical lattice in quench experiments. A method to create and measure large-scale entanglement is presented in this thesis. The fourth main topic addresses classical noise. Specifically, a system of atoms in an optical lattice, which is created from lasers with intensity fluctuations, is analyzed in this work. The noisy evolution of many-body correlation functions is studied and a method to cancel this noise in a realistic experimental setup is
Many-body forces and stability of the alkaline-earth tetramers
International Nuclear Information System (INIS)
Diaz-Torrejon, C.C.; Kaplan, Ilya G.
2011-01-01
Graphical abstract: Many-body forces effect. In a three-particle system, the two-body interaction energies depend upon coordinates of all three particles. The comparative study of the interaction energy and its many-body decomposition for alkaline-earths tetramers Be 4 , Mg 4 , and Ca 4 at the all-electron CCSD(T)/aug-cc-pVQZ level is performed. For study of dependence of the binding energy and the orbital population on the cluster size the corresponding dimers and trimers were also calculated at the same level of theory. In comparison with weakly bound dimers, the binding energy in trimers and, especially, in tetramers drastically increases; e.g., E b /N in Be 3 is 7 times larger and in Be 4 is 18.4 times larger than in Be 2 . This sharp increase is explained as a manifestation of many-body forces. The trimers and tetramers are stabilized by the three-body forces, whereas the two- and four-body forces are repulsive. The attractive contribution to the three-body forces has a three-atom electron exchange origin. The natural bond orbital (NBO) population analysis reveals a relatively large np-population in trimers and tetramers. The population of the valence np-orbitals leads to the sp-hybridization providing the covalent bonding. Research highlights: → The alkaline-earths trimers and tetramers are stabilized by the three-body forces. → Two- and four-body forces are repulsive for trimers and tetramers. → The attractive contribution to the three-body forces has a three-atom electron exchange origin. → The population of the np-orbitals leads to the sp-hybridization providing the covalent bonding. - Abstract: The comparative study of the interaction energy and its many-body decomposition for Be 4 , Mg 4 , and Ca 4 at the all-electron CCSD(T)/aug-cc-pVQZ level is performed. For study of dependence of the binding energy and the orbital population on the cluster size the corresponding dimers and trimers were also calculated at the same level of theory. In
Exploring one-particle orbitals in large many-body localized systems
Villalonga, Benjamin; Yu, Xiongjie; Luitz, David J.; Clark, Bryan K.
2018-03-01
Strong disorder in interacting quantum systems can give rise to the phenomenon of many-body localization (MBL), which defies thermalization due to the formation of an extensive number of quasilocal integrals of motion. The one-particle operator content of these integrals of motion is related to the one-particle orbitals (OPOs) of the one-particle density matrix and shows a strong signature across the MBL transition as recently pointed out by Bera et al. [Phys. Rev. Lett. 115, 046603 (2015), 10.1103/PhysRevLett.115.046603; Ann. Phys. 529, 1600356 (2017), 10.1002/andp.201600356]. We study the properties of the OPOs of many-body eigenstates of an MBL system in one dimension. Using shift-and-invert MPS, a matrix product state method to target highly excited many-body eigenstates introduced previously [Phys. Rev. Lett. 118, 017201 (2017), 10.1103/PhysRevLett.118.017201], we are able to obtain accurate results for large systems of sizes up to L =64 . We find that the OPOs drawn from eigenstates at different energy densities have high overlap and their occupations are correlated with the energy of the eigenstates. Moreover, the standard deviation of the inverse participation ratio of these orbitals is maximal at the nose of the mobility edge. Also, the OPOs decay exponentially in real space, with a correlation length that increases at low disorder. In addition, we find that the probability distribution of the strength of the large-range coupling constants of the number operators generated by the OPOs approach a log-uniform distribution at strong disorder.
Simulating local measurements on a quantum many-body system with stochastic matrix product states
DEFF Research Database (Denmark)
Gammelmark, Søren; Mølmer, Klaus
2010-01-01
We demonstrate how to simulate both discrete and continuous stochastic evolutions of a quantum many-body system subject to measurements using matrix product states. A particular, but generally applicable, measurement model is analyzed and a simple representation in terms of matrix product operators...... is found. The technique is exemplified by numerical simulations of the antiferromagnetic Heisenberg spin-chain model subject to various instances of the measurement model. In particular, we focus on local measurements with small support and nonlocal measurements, which induce long-range correlations....
Self-consistent RPA based on a many-body vacuum
International Nuclear Information System (INIS)
Jemaï, M.; Schuck, P.
2011-01-01
Self-Consistent RPA is extended in a way so that it is compatible with a variational ansatz for the ground-state wave function as a fermionic many-body vacuum. Employing the usual equation-of-motion technique, we arrive at extended RPA equations of the Self-Consistent RPA structure. In principle the Pauli principle is, therefore, fully respected. However, the correlation functions entering the RPA matrix can only be obtained from a systematic expansion in powers of some combinations of RPA amplitudes. We demonstrate for a model case that this expansion may converge rapidly.
Workshop on Kadanoff-Baym Equations : Progress and Perspectives for Many-Body Physics
2000-01-01
Equilibrium and nonequilibrium properties of correlated many-body systems are of growing interest in many fields of physics, including condensed matter, dense plasmas, nuclear matter and particles. The most powerful and general method which applies equally to all these areas is given by quantum field theory.Written by the leading experts and understandable to non-specialists, this book provides an overview on the basic ideas and concepts of the method of nonequilibrium Green's functions. It is complemented by modern applications of the method to a variety of topics, such as optics and transpor
First-principles many-body theory for ultra-cold atoms
International Nuclear Information System (INIS)
Drummond, Peter D.; Hu Hui; Liu Xiaji
2010-01-01
Recent breakthroughs in the creation of ultra-cold atoms in the laboratory have ushered in unprecedented changes in physical science. These enormous changes in the coldest temperatures available in the laboratory mean that many novel experiments are possible. There is unprecedented control and simplicity in these novel systems, meaning that quantum many-body theory is now facing severe challenges in quantitatively understanding these new results. We discuss some of the new experiments and recently developed theoretical techniques required to predict the results obtained.
Theoretical approaches to many-body perturbation theory and the challenges
International Nuclear Information System (INIS)
Barrett, Bruce R
2005-01-01
A brief review of the history of many-body perturbation theory (MBPT) and its applications in nuclear physics is given. Problems regarding its application to nuclear-structure calculations are discussed and analysed. It is concluded that the usefulness of nuclear MBPT in terms of an expansion in the nuclear reaction matrix G for the calculation of effective interactions in shell-model investigations is severely challenged and restricted by the problems and uncertainties connected with this approach. New methods based on unitary transformation approaches have proven to be more accurate and reliable, particularly for light nuclei
The Lanczos algorithm for extensive many-body systems in the thermodynamic limit
International Nuclear Information System (INIS)
Witte, N.S.; Bessis, D.
1999-01-01
We establish rigorously the scaling properties of the Lanczos process applied to an arbitrary extensive Many-Body System which is carried to convergence n → ∞ and the thermodynamic limit N → ∞ taken. In this limit the solution for the limiting Lanczos coefficients are found exactly and generally through two equivalent sets of equations, given initial knowledge of the exact cumulant generating function. The measure and the Orthogonal Polynomial System associated with the Lanczos process in this regime are also given explicitly. Some important representations of these Lanczos functions are provided, including Taylor series expansions, and the theorems controlling their general properties are proven. (authors)
Energy Distributions from Three-Body Decaying Many-Body Resonances
International Nuclear Information System (INIS)
Alvarez-Rodriguez, R.; Jensen, A. S.; Fedorov, D. V.; Fynbo, H. O. U.; Garrido, E.
2007-01-01
We compute energy distributions of three particles emerging from decaying many-body resonances. We reproduce the measured energy distributions from decays of two archetypal states chosen as the lowest 0 + and 1 + resonances in 12 C populated in β decays. These states are dominated by sequential, through the 8 Be ground state, and direct decays, respectively. These decay mechanisms are reflected in the ''dynamic'' evolution from small, cluster or shell-model states, to large distances, where the coordinate or momentum space continuum wave functions are accurately computed
Real-space decoupling transformation for quantum many-body systems.
Evenbly, G; Vidal, G
2014-06-06
We propose a real-space renormalization group method to explicitly decouple into independent components a many-body system that, as in the phenomenon of spin-charge separation, exhibits separation of degrees of freedom at low energies. Our approach produces a branching holographic description of such systems that opens the path to the efficient simulation of the most entangled phases of quantum matter, such as those whose ground state violates a boundary law for entanglement entropy. As in the coarse-graining transformation of Vidal [Phys. Rev. Lett. 99, 220405 (2007).
Gritsev, Vladimir; Demler, Eugene; Lukin, Mikhail; Polkovnikov, Anatoli
2007-11-16
We study the problem of rapid change of the interaction parameter (quench) in a many-body low-dimensional system. It is shown that, measuring the correlation functions after the quench, the information about a spectrum of collective excitations in a system can be obtained. This observation is supported by analysis of several integrable models and we argue that it is valid for nonintegrable models as well. Our conclusions are supplemented by performing exact numerical simulations on finite systems. We propose that measuring the power spectrum in a dynamically split 1D Bose-Einsten condensate into two coupled condensates can be used as an experimental test of our predictions.
Exploring excited eigenstates of many-body systems using the functional renormalization group
Klöckner, Christian; Kennes, Dante Marvin; Karrasch, Christoph
2018-05-01
We introduce approximate, functional renormalization group based schemes to obtain correlation functions in pure excited eigenstates of large fermionic many-body systems at arbitrary energies. The algorithms are thoroughly benchmarked and their strengths and shortcomings are documented using a one-dimensional interacting tight-binding chain as a prototypical testbed. We study two "toy applications" from the world of Luttinger liquid physics: the survival of power laws in lowly excited states as well as the spectral function of high-energy "block" excitations, which feature several single-particle Fermi edges.
The use of many-body expansions and geometry optimizations in fragment-based methods.
Fedorov, Dmitri G; Asada, Naoya; Nakanishi, Isao; Kitaura, Kazuo
2014-09-16
Conspectus Chemists routinely work with complex molecular systems: solutions, biochemical molecules, and amorphous and composite materials provide some typical examples. The questions one often asks are what are the driving forces for a chemical phenomenon? How reasonable are our views of chemical systems in terms of subunits, such as functional groups and individual molecules? How can one quantify the difference in physicochemical properties of functional units found in a different chemical environment? Are various effects on functional units in molecular systems additive? Can they be represented by pairwise potentials? Are there effects that cannot be represented in a simple picture of pairwise interactions? How can we obtain quantitative values for these effects? Many of these questions can be formulated in the language of many-body effects. They quantify the properties of subunits (fragments), referred to as one-body properties, pairwise interactions (two-body properties), couplings of two-body interactions described by three-body properties, and so on. By introducing the notion of fragments in the framework of quantum chemistry, one obtains two immense benefits: (a) chemists can finally relate to quantum chemistry, which now speaks their language, by discussing chemically interesting subunits and their interactions and (b) calculations become much faster due to a reduced computational scaling. For instance, the somewhat academic sounding question of the importance of three-body effects in water clusters is actually another way of asking how two hydrogen bonds affect each other, when they involve three water molecules. One aspect of this is the many-body charge transfer (CT), because the charge transfers in the two hydrogen bonds are coupled to each other (not independent). In this work, we provide a generalized view on the use of many-body expansions in fragment-based methods, focusing on the general aspects of the property expansion and a contraction of a
Many-body perturbation theory using the density-functional concept: beyond the GW approximation.
Bruneval, Fabien; Sottile, Francesco; Olevano, Valerio; Del Sole, Rodolfo; Reining, Lucia
2005-05-13
We propose an alternative formulation of many-body perturbation theory that uses the density-functional concept. Instead of the usual four-point integral equation for the polarizability, we obtain a two-point one, which leads to excellent optical absorption and energy-loss spectra. The corresponding three-point vertex function and self-energy are then simply calculated via an integration, for any level of approximation. Moreover, we show the direct impact of this formulation on the time-dependent density-functional theory. Numerical results for the band gap of bulk silicon and solid argon illustrate corrections beyond the GW approximation for the self-energy.
Many-body perturbation theory using the density-functional concept: beyond the GW approximation
Bruneval, Fabien; Sottile, Francesco; Olevano, Valerio; Del Sole, Rodolfo; Reining, Lucia
2005-01-01
We propose an alternative formulation of Many-Body Perturbation Theory that uses the density-functional concept. Instead of the usual four-point integral equation for the polarizability, we obtain a two-point one, that leads to excellent optical absorption and energy loss spectra. The corresponding three-point vertex function and self-energy are then simply calculated via an integration, for any level of approximation. Moreover, we show the direct impact of this formulation on the time-depend...
Ultracold atoms in optical lattices simulating quantum many-body systems
Lewenstein, Maciej; Ahufinger, Verònica
2012-01-01
Quantum computers, though not yet available on the market, will revolutionize the future of information processing. Quantum computers for special purposes like quantum simulators are already within reach. The physics of ultracold atoms, ions and molecules offer unprecedented possibilities of control of quantum many body systems and novel possibilities of applications to quantum information processing and quantum metrology. Particularly fascinating is the possibility of usingultracold atoms in lattices to simulate condensed matter or even high energy physics.This book provides a complete and co
Proceedings of the fifth symposium on simulation of hadronic many-body system
Energy Technology Data Exchange (ETDEWEB)
Chiba, Satoshi; Maruyama, Toshiki [eds.
1998-07-01
The fifth symposium on Simulation of Hadronic Many-Body System, organized by the Research Group for Hadron Transport Theory, Advanced Science Research Center, was held at Tokai Research Establishment of JAERI on March 3 and 4, 1998. The symposium was devoted for discussion and presentation of research results on light- and heavy-ion induced nuclear reactions in terms of microscopic simulation method, while wide variety of other topics were also presented such as nuclear structure, properties of nuclear matter and high-energy multi-fragmentation experiments. The 17 of the presented papers are indexed individually. (J.P.N.)
On nonequilibrium many-body systems. 1: The nonequilibrium statistical operator method
International Nuclear Information System (INIS)
Algarte, A.C.S.; Vasconcellos, A.R.; Luzzi, R.; Sampaio, A.J.C.
1985-01-01
The theoretical aspects involved in the treatment of many-body systems strongly departed from equilibrium are discussed. The nonequilibrium statistical operator (NSO) method is considered in detail. Using Jaynes' maximum entropy formalism complemented with an ad hoc hypothesis a nonequilibrium statistical operator is obtained. This approach introduces irreversibility from the outset and we recover statistical operators like those of Green-Mori and Zubarev as particular cases. The connection with Generalized Thermodynamics and the construction of nonlinear transport equations are briefly described. (Author) [pt
Off-shell effects and consistency of many-body treatments of dense matter
International Nuclear Information System (INIS)
Krippa, Boris; Birse, Michael C.; McGovern, Judith A.; Walet, Niels R.
2003-01-01
Effective field theory requires all observables to be independent of the representation used for the quantum field operators. It means that off-shell properties of the interactions should not lead to any observable effects. We analyze this issue in the context of many-body approaches to nuclear matter, where it should be possible to shift the contributions of lowest order in purely off-shell two-body interactions into three-body forces. We show that none of the commonly used truncations of the two-body scattering amplitude such as the ladder, Brueckner-Hartree-Fock, or parquet approximations respect this requirement
Two novel classes of solvable many-body problems of goldfish type with constraints
Energy Technology Data Exchange (ETDEWEB)
Calogero, F [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , 00185 Rome (Italy); Gomez-Ullate, D [Departamento de Fisica Teorica II, Universidad Complutense, 28040 Madrid (Spain)
2007-05-18
Two novel classes of many-body models with nonlinear interactions 'of goldfish type' are introduced. They are solvable provided the initial data satisfy a single constraint (in one case; in the other, two constraints), i.e., for such initial data the solution of their initial-value problem can be achieved via algebraic operations, such as finding the eigenvalues of given matrices or equivalently the zeros of known polynomials. Entirely isochronous versions of some of these models are also exhibited, i.e., versions of these models whose nonsingular solutions are all completely periodic with the same period.
Semiclassical expansion of quantum characteristics for many-body potential scattering problem
International Nuclear Information System (INIS)
Krivoruchenko, M.I.; Fuchs, C.; Faessler, A.
2007-01-01
In quantum mechanics, systems can be described in phase space in terms of the Wigner function and the star-product operation. Quantum characteristics, which appear in the Heisenberg picture as the Weyl's symbols of operators of canonical coordinates and momenta, can be used to solve the evolution equations for symbols of other operators acting in the Hilbert space. To any fixed order in the Planck's constant, many-body potential scattering problem simplifies to a statistical-mechanical problem of computing an ensemble of quantum characteristics and their derivatives with respect to the initial canonical coordinates and momenta. The reduction to a system of ordinary differential equations pertains rigorously at any fixed order in ℎ. We present semiclassical expansion of quantum characteristics for many-body scattering problem and provide tools for calculation of average values of time-dependent physical observables and cross sections. The method of quantum characteristics admits the consistent incorporation of specific quantum effects, such as non-locality and coherence in propagation of particles, into the semiclassical transport models. We formulate the principle of stationary action for quantum Hamilton's equations and give quantum-mechanical extensions of the Liouville theorem on conservation of the phase-space volume and the Poincare theorem on conservation of 2p-forms. The lowest order quantum corrections to the Kepler periodic orbits are constructed. These corrections show the resonance behavior. (Abstract Copyright [2007], Wiley Periodicals, Inc.)
Quasiparticle engineering and entanglement propagation in a quantum many-body system.
Jurcevic, P; Lanyon, B P; Hauke, P; Hempel, C; Zoller, P; Blatt, R; Roos, C F
2014-07-10
The key to explaining and controlling a range of quantum phenomena is to study how information propagates around many-body systems. Quantum dynamics can be described by particle-like carriers of information that emerge in the collective behaviour of the underlying system, the so-called quasiparticles. These elementary excitations are predicted to distribute quantum information in a fashion determined by the system's interactions. Here we report quasiparticle dynamics observed in a quantum many-body system of trapped atomic ions. First, we observe the entanglement distributed by quasiparticles as they trace out light-cone-like wavefronts. Second, using the ability to tune the interaction range in our system, we observe information propagation in an experimental regime where the effective-light-cone picture does not apply. Our results will enable experimental studies of a range of quantum phenomena, including transport, thermalization, localization and entanglement growth, and represent a first step towards a new quantum-optic regime of engineered quasiparticles with tunable nonlinear interactions.
Relativistic many-body theory a new field-theoretical approach
Lindgren, Ingvar
2016-01-01
This revised second edition of the author’s classic text offers readers a comprehensively updated review of relativistic atomic many-body theory, covering the many developments in the field since the publication of the original title. In particular, a new final section extends the scope to cover the evaluation of QED effects for dynamical processes. The treatment of the book is based upon quantum-field theory, and demonstrates that when the procedure is carried to all orders of perturbation theory, two-particle systems are fully compatible with the relativistically covariant Bethe-Salpeter equation. This procedure can be applied to arbitrary open-shell systems, in analogy with the standard many-body theory, and it is also applicable to systems with more than two particles. Presently existing theoretical procedures for treating atomic systems are, in several cases, insufficient to explain the accurate experimental data recently obtained, particularly for highly charged ions. The main text is divided into...
Model many-body Stoner Hamiltonian for binary FeCr alloys
Nguyen-Manh, D.; Dudarev, S. L.
2009-09-01
We derive a model tight-binding many-body d -electron Stoner Hamiltonian for FeCr binary alloys and investigate the sensitivity of its mean-field solutions to the choice of hopping integrals and the Stoner exchange parameters. By applying the local charge-neutrality condition within a self-consistent treatment we show that the negative enthalpy-of-mixing anomaly characterizing the alloy in the low chromium concentration limit is due entirely to the presence of the on-site exchange Stoner terms and that the occurrence of this anomaly is not specifically related to the choice of hopping integrals describing conventional chemical bonding between atoms in the alloy. The Bain transformation pathway computed, using the proposed model Hamiltonian, for the Fe15Cr alloy configuration is in excellent agreement with ab initio total-energy calculations. Our investigation also shows how the parameters of a tight-binding many-body model Hamiltonian for a magnetic alloy can be derived from the comparison of its mean-field solutions with other, more accurate, mean-field approximations (e.g., density-functional calculations), hence stimulating the development of large-scale computational algorithms for modeling radiation damage effects in magnetic alloys and steels.
Many-body localization transition: Schmidt gap, entanglement length, and scaling
Gray, Johnnie; Bose, Sougato; Bayat, Abolfazl
2018-05-01
Many-body localization has become an important phenomenon for illuminating a potential rift between nonequilibrium quantum systems and statistical mechanics. However, the nature of the transition between ergodic and localized phases in models displaying many-body localization is not yet well understood. Assuming that this is a continuous transition, analytic results show that the length scale should diverge with a critical exponent ν ≥2 in one-dimensional systems. Interestingly, this is in stark contrast with all exact numerical studies which find ν ˜1 . We introduce the Schmidt gap, new in this context, which scales near the transition with an exponent ν >2 compatible with the analytical bound. We attribute this to an insensitivity to certain finite-size fluctuations, which remain significant in other quantities at the sizes accessible to exact numerical methods. Additionally, we find that a physical manifestation of the diverging length scale is apparent in the entanglement length computed using the logarithmic negativity between disjoint blocks.
Dynamics of many-body localization in the presence of particle loss
van Nieuwenburg, EPL; Yago Malo, J.; Daley, AJ; Fischer, MH
2018-01-01
At long times, residual couplings to the environment become relevant even in the most isolated experiments, a crucial difficulty for the study of fundamental aspects of many-body dynamics. A particular example is many-body localization in a cold-atom setting, where incoherent photon scattering introduces both dephasing and particle loss. Whereas dephasing has been studied in detail and is known to destroy localization already on the level of non-interacting particles, the effect of particle loss is less well understood. A difficulty arises due to the ‘non-local’ nature of the loss process, complicating standard numerical tools using matrix product decomposition. Utilizing symmetries of the Lindbladian dynamics, we investigate the particle loss on both the dynamics of observables, as well as the structure of the density matrix and the individual states. We find that particle loss in the presence of interactions leads to dissipation and a strong suppression of the (operator space) entanglement entropy. Our approach allows for the study of the interplay of dephasing and loss for pure and mixed initial states to long times, which is important for future experiments using controlled coupling of the environment.
Many-body effects in transport through a quantum-dot cavity system
Dinu, I. V.; Moldoveanu, V.; Gartner, P.
2018-05-01
We theoretically describe electric transport through an optically active quantum dot embedded in a single-mode cavity, and coupled to source-drain particle reservoirs. The populations of various many-body configurations (e.g., excitons, trions, biexciton) and the photon-number occupancies are calculated from a master equation which is derived in the basis of dressed states. These take into account both the Coulomb and the light-matter interaction. The former is essential in the description of the transport, while for the latter we identify situations in which it can be neglected in the expression of tunneling rates. The fermionic nature of the particle reservoirs plays an important role in the argument. The master equation is numerically solved for the s -shell many-body configurations of disk-shaped quantum dots. If the cavity is tuned to the biexciton-exciton transition, the most efficient optical processes take place in a three-level Λ system. The alternative exciton-ground-state route is inhibited as nonresonant due to the biexciton binding energy. The steady-state current is analyzed as a function of the photon frequency and the coupling to the leads. An unexpected feature appears in its dependence on the cavity loss rate, which turns out to be nonmonotonic.
Many-Body Effects on the Thermodynamics of Fluids, Mixtures, and Nanoconfined Fluids.
Desgranges, Caroline; Delhommelle, Jerome
2015-11-10
Using expanded Wang-Landau simulations, we show that taking into account the many-body interactions results in sharp changes in the grand-canonical partition functions of single-component systems, binary mixtures, and nanoconfined fluids. The many-body contribution, modeled with a 3-body Axilrod-Teller-Muto term, results in shifts toward higher chemical potentials of the phase transitions from low-density phases to high-density phases and accounts for deviations of more than, e.g., 20% of the value of the partition function for a single-component liquid. Using the statistical mechanics formalism, we analyze how this contribution has a strong impact on some properties (e.g., pressure, coexisting densities, and enthalpy) and a moderate impact on others (e.g., Gibbs or Helmholtz free energies). We also characterize the effect of the 3-body terms on adsorption isotherms and adsorption thermodynamic properties, thereby providing a full picture of the effect of the 3-body contribution on the thermodynamics of nanoconfined fluids.
PREFACE: Advanced many-body and statistical methods in mesoscopic systems
Anghel, Dragos Victor; Sabin Delion, Doru; Sorin Paraoanu, Gheorghe
2012-02-01
It has increasingly been realized in recent times that the borders separating various subfields of physics are largely artificial. This is the case for nanoscale physics, physics of lower-dimensional systems and nuclear physics, where the advanced techniques of many-body theory developed in recent times could provide a unifying framework for these disciplines under the general name of mesoscopic physics. Other fields, such as quantum optics and quantum information, are increasingly using related methods. The 6-day conference 'Advanced many-body and statistical methods in mesoscopic systems' that took place in Constanta, Romania, between 27 June and 2 July 2011 was, we believe, a successful attempt at bridging an impressive list of topical research areas: foundations of quantum physics, equilibrium and non-equilibrium quantum statistics/fractional statistics, quantum transport, phases and phase transitions in mesoscopic systems/superfluidity and superconductivity, quantum electromechanical systems, quantum dissipation, dephasing, noise and decoherence, quantum information, spin systems and their dynamics, fundamental symmetries in mesoscopic systems, phase transitions, exactly solvable methods for mesoscopic systems, various extension of the random phase approximation, open quantum systems, clustering, decay and fission modes and systematic versus random behaviour of nuclear spectra. This event brought together participants from seventeen countries and five continents. Each of the participants brought considerable expertise in his/her field of research and, at the same time, was exposed to the newest results and methods coming from the other, seemingly remote, disciplines. The talks touched on subjects that are at the forefront of topical research areas and we hope that the resulting cross-fertilization of ideas will lead to new, interesting results from which everybody will benefit. We are grateful for the financial and organizational support from IFIN-HH, Ovidius
On Permuting Cut with Contraction
Borisavljevic, Mirjana; Dosen, Kosta; Petric, Zoran
1999-01-01
The paper presents a cut-elimination procedure for intuitionistic propositional logic in which cut is eliminated directly, without introducing the multiple-cut rule mix, and in which pushing cut above contraction is one of the reduction steps. The presentation of this procedure is preceded by an analysis of Gentzen's mix-elimination procedure, made in the perspective of permuting cut with contraction. It is also shown that in the absence of implication, pushing cut above contraction doesn't p...
Sorting permutations by prefix and suffix rearrangements.
Lintzmayer, Carla Negri; Fertin, Guillaume; Dias, Zanoni
2017-02-01
Some interesting combinatorial problems have been motivated by genome rearrangements, which are mutations that affect large portions of a genome. When we represent genomes as permutations, the goal is to transform a given permutation into the identity permutation with the minimum number of rearrangements. When they affect segments from the beginning (respectively end) of the permutation, they are called prefix (respectively suffix) rearrangements. This paper presents results for rearrangement problems that involve prefix and suffix versions of reversals and transpositions considering unsigned and signed permutations. We give 2-approximation and ([Formula: see text])-approximation algorithms for these problems, where [Formula: see text] is a constant divided by the number of breakpoints (pairs of consecutive elements that should not be consecutive in the identity permutation) in the input permutation. We also give bounds for the diameters concerning these problems and provide ways of improving the practical results of our algorithms.
Evidence of tensor correlations in the nuclear many-body system using a modern NN potential
International Nuclear Information System (INIS)
Fiase, J.O.; Nkoma, J.S.; Sharmaand, L.K.; Hosaka, A.
2003-01-01
In this paper we show evidence of the importance of tensor correlations in the nuclear many-body system by calculating the effective two-body nuclear matrix elements in the frame work of the Lowest-Order Constrained Variational (LOCV) technique with two-body correlation functions using the Reid93 potential. We have achieved this by switching on and off the strength of the tensor correlations, α k . We have found that in order to obtain reasonable agreement with earlier calculations based on the G-matrix theory, we must turn on the strength of the tensor correlations especially in the triplet even (TE) and tensor even (TNE) channels to take the value of approximately, 0.05. As an application, we have estimated the value of the Landau - Migdal parameter, g' NN which we found to be g' NN = 0.65. This compares favorably with the G-matrix calculated value of g' NN = 0.54. (author)
Density-density functionals and effective potentials in many-body electronic structure calculations
International Nuclear Information System (INIS)
Reboredo, Fernando A.; Kent, Paul R.
2008-01-01
We demonstrate the existence of different density-density functionals designed to retain selected properties of the many-body ground state in a non-interacting solution starting from the standard density functional theory ground state. We focus on diffusion quantum Monte Carlo applications that require trial wave functions with optimal Fermion nodes. The theory is extensible and can be used to understand current practices in several electronic structure methods within a generalized density functional framework. The theory justifies and stimulates the search of optimal empirical density functionals and effective potentials for accurate calculations of the properties of real materials, but also cautions on the limits of their applicability. The concepts are tested and validated with a near-analytic model.
Towards predictive many-body calculations of phonon-limited carrier mobilities in semiconductors
Poncé, Samuel; Margine, Elena R.; Giustino, Feliciano
2018-03-01
We probe the accuracy limit of ab initio calculations of carrier mobilities in semiconductors, within the framework of the Boltzmann transport equation. By focusing on the paradigmatic case of silicon, we show that fully predictive calculations of electron and hole mobilities require many-body quasiparticle corrections to band structures and electron-phonon matrix elements, the inclusion of spin-orbit coupling, and an extremely fine sampling of inelastic scattering processes in momentum space. By considering all these factors we obtain excellent agreement with experiment, and we identify the band effective masses as the most critical parameters to achieve predictive accuracy. Our findings set a blueprint for future calculations of carrier mobilities, and pave the way to engineering transport properties in semiconductors by design.
The electronic structure of molecules by a many-body approach. Pt. 1
International Nuclear Information System (INIS)
Niessen, W. von; Cederbaum, L.S.; Kraemer, W.P.
1976-01-01
The ionization potentials of benzene are studied by an ab initio many-body approach which includes the effects of electron correlation and reorganization beyond the one-particle approximation. The calculations confirm the assignment of the photoelectron spectrum experimentally proposed by Jonsson and Lindholm: 1esub(1g)(π), 2esub(2g), 1asub(2u)(π), 2esub(1u), 1bsub(2u), 1bsub(1u), 2asub(1g), 1esub(2g) in order of increasing binding energy. To definitely establish the ordering of the ionization potentials in the second band, which has been very controversial, the corresponding vibrational structure has been calculated. A number of one-electron properties are calculated in the one-particle approximation and compared to experimental work and other theoretical calculations. (orig.) [de
Probing the electronic structure of liquid water with many-body perturbation theory
Pham, Tuan Anh; Zhang, Cui; Schwegler, Eric; Galli, Giulia
2014-03-01
We present a first-principles investigation of the electronic structure of liquid water based on many-body perturbation theory (MBPT), within the G0W0 approximation. The liquid quasiparticle band gap and the position of its valence band maximum and conduction band minimum with respect to vacuum were computed and it is shown that the use of MBPT is crucial to obtain results that are in good agreement with experiment. We found that the level of theory chosen to generate molecular dynamics trajectories may substantially affect the electronic structure of the liquid, in particular, the relative position of its band edges and redox potentials. Our results represent an essential step in establishing a predictive framework for computing the relative position of water redox potentials and the band edges of semiconductors and insulators. Work supported by DOE/BES (Grant No. DE-SC0008938). Work at LLNL was performed under Contract DE-AC52-07NA27344.
Identifying the closeness of eigenstates in quantum many-body systems
International Nuclear Information System (INIS)
Li Hai-bin; Yang Yang; Wang Pei; Wang Xiao-guang
2017-01-01
We propose a quantity called modulus fidelity to measure the closeness of two quantum pure states. We use it to investigate the closeness of eigenstates in one-dimensional hard-core bosons. When the system is integrable, eigenstates close to their neighbor or not, which leads to a large fluctuation in the distribution of modulus fidelity. When the system becomes chaos, the fluctuation is reduced dramatically, which indicates all eigenstates become close to each other. It is also found that two kind of closeness, i.e., closeness of eigenstates and closeness of eigenvalues, are not correlated at integrability but correlated at chaos. We also propose that the closeness of eigenstates is the underlying mechanism of eigenstate thermalization hypothesis (ETH) which explains the thermalization in quantum many-body systems. (paper)
New formalism for determining excitation spectra of many-body systems
International Nuclear Information System (INIS)
Saito, S.; Zhang, S.B.; Louie, S.G.; Cohen, M.L.
1990-01-01
We present a new general formalism for determining the excitation spectrum of interacting many-body systems. The basic assumption is that the number of the excitations is equal to the number of sites. Within this approximation, it is shown that the density-density response functions with two different pure-imaginary energies determine the excitation spectrum. The method is applied to the valence electrons of sodium clusters of differing sizes in the time-dependent local-density approximation (TDLDA). A jellium-sphere background model is used for the ion cores. The excitation spectra obtained in this way represent well the excitation spectra given by the full TDLDA calculation along the real energy axis. Important collective modes are reproduced very well
Many-body dynamics of driven-dissipative Rydberg cavity polaritons
Pistorius, Tim; Fan, Jingtao; Weimer, Hendrik
2017-04-01
The usage of photons as long-range information carriers has greatly increased the interest in systems with nonlinear optical properties in recent years. The nonlinearity is easily achievable in Rydberg mediums through the strong van der Waals interaction which makes them one of the best candidates for such a system. Here, we propose a way to analyze the steady state solutions of a Rydberg medium in a cavity through the combination of the variational principle for open quantum systems and the P-distribution of the density matrix. To get a better understanding of the many-body-dynamics a transformation into the polariton picture is performed and investigated. Volkswagen Foundation, Deutsche Forschungsgemeinschaft.
Ab Initio Many-Body Calculations Of Nucleon-Nucleus Scattering
Energy Technology Data Exchange (ETDEWEB)
Quaglioni, S; Navratil, P
2008-12-17
We develop a new ab initio many-body approach capable of describing simultaneously both bound and scattering states in light nuclei, by combining the resonating-group method with the use of realistic interactions, and a microscopic and consistent description of the nucleon clusters. This approach preserves translational symmetry and Pauli principle. We outline technical details and present phase shift results for neutron scattering on {sup 3}H, {sup 4}He and {sup 10}Be and proton scattering on {sup 3,4}He, using realistic nucleon-nucleon (NN) potentials. Our A = 4 scattering results are compared to earlier ab initio calculations. We find that the CD-Bonn NN potential in particular provides an excellent description of nucleon-{sup 4}He S-wave phase shifts. We demonstrate that a proper treatment of the coupling to the n-{sup 10}Be continuum is successful in explaining the parity-inverted ground state in {sup 11}Be.
Stochastic evaluation of second-order many-body perturbation energies.
Willow, Soohaeng Yoo; Kim, Kwang S; Hirata, So
2012-11-28
With the aid of the Laplace transform, the canonical expression of the second-order many-body perturbation correction to an electronic energy is converted into the sum of two 13-dimensional integrals, the 12-dimensional parts of which are evaluated by Monte Carlo integration. Weight functions are identified that are analytically normalizable, are finite and non-negative everywhere, and share the same singularities as the integrands. They thus generate appropriate distributions of four-electron walkers via the Metropolis algorithm, yielding correlation energies of small molecules within a few mE(h) of the correct values after 10(8) Monte Carlo steps. This algorithm does away with the integral transformation as the hotspot of the usual algorithms, has a far superior size dependence of cost, does not suffer from the sign problem of some quantum Monte Carlo methods, and potentially easily parallelizable and extensible to other more complex electron-correlation theories.
Many-body Tunneling and Nonequilibrium Dynamics of Doublons in Strongly Correlated Quantum Dots.
Hou, WenJie; Wang, YuanDong; Wei, JianHua; Zhu, ZhenGang; Yan, YiJing
2017-05-30
Quantum tunneling dominates coherent transport at low temperatures in many systems of great interest. In this work we report a many-body tunneling (MBT), by nonperturbatively solving the Anderson multi-impurity model, and identify it a fundamental tunneling process on top of the well-acknowledged sequential tunneling and cotunneling. We show that the MBT involves the dynamics of doublons in strongly correlated systems. Proportional to the numbers of dynamical doublons, the MBT can dominate the off-resonant transport in the strongly correlated regime. A T 3/2 -dependence of the MBT current on temperature is uncovered and can be identified as a fingerprint of the MBT in experiments. We also prove that the MBT can support the coherent long-range tunneling of doublons, which is well consistent with recent experiments on ultracold atoms. As a fundamental physical process, the MBT is expected to play important roles in general quantum systems.
Excitons and Cooper pairs two composite bosons in many-body physics
Combescot, Monique
2015-01-01
This book bridges a gap between two major communities of Condensed Matter Physics, Semiconductors and Superconductors, that have thrived independently. Through an original perspective that their key particles, excitons and Cooper pairs, are composite bosons, the authors raise fundamental questions of current interest: how does the Pauli exclusion principle wield its power on the fermionic components of bosonic particles at a microscopic level and how this affects the macroscopic physics? What can we learn from Wannier and Frenkel excitons and from Cooper pairs that helps us understand "bosonic condensation" of composite bosons and its difference from Bose-Einstein condensation of elementary bosons? The authors start from solid mathematical and physical foundation to derive excitons and Cooper pairs. They further introduce Shiva diagrams as a graphic support to grasp the many-body physics induced by fermion exchange - a novel mechanism not visualized by standard Feynman diagrams. Advanced undergraduate or grad...
Collective many-body dynamics in the vicinity of nuclear driplines
International Nuclear Information System (INIS)
Volya, Alexander; Zelevinsky, Vladimir
2007-01-01
The Continuum Shell Model is a powerful theoretical tool for analysis of many-body dynamics embedded in the continuum. Here we formulate the method and use an example of a realistic shell model calculation for oxygen isotopes to demonstrate the seamless transition from bound states to resonances and cross sections in continuum within the same framework. The coupled dynamics of intrinsic states and continuum is traced further to the regime of continuum dominance that implies the decay width collectivization and onset of super-radiance. The coexistence and interplay of internal collective motion, such as giant resonances, and decay are of particular interest. Schematic and realistic calculations illustrate changes in the strength distribution and the natural appearance of the so-called pygmy mode
Many-Body Energy Decomposition with Basis Set Superposition Error Corrections.
Mayer, István; Bakó, Imre
2017-05-09
The problem of performing many-body decompositions of energy is considered in the case when BSSE corrections are also performed. It is discussed that the two different schemes that have been proposed go back to the two different interpretations of the original Boys-Bernardi counterpoise correction scheme. It is argued that from the physical point of view the "hierarchical" scheme of Valiron and Mayer should be preferred and not the scheme recently discussed by Ouyang and Bettens, because it permits the energy of the individual monomers and all the two-body, three-body, etc. energy components to be free of unphysical dependence on the arrangement (basis functions) of other subsystems in the cluster.
On the acceleration of convergence of many-body perturbation theory. Pt. 2
International Nuclear Information System (INIS)
Dietz, K.; Schmidt, C.; Warken, M.; Hess, B.A.
1992-07-01
We employ the method developed in a previous paper to small systems-Be, LiH, H 2 -where full CI-calculations are available for monitoring convergence of many-body perturbation theory. It is shown that divergent series, in particular for excited states, can be transformed into fast converging ones. In essence our method consists in performing infinite subsummations of perturbation series in order to improve convergence: coupling constants are redefined such that singularities are incorporated in a non-perturbative manner and remaining correlations can be expanded in a larger domain of the complex coupling constant plane. It is in this way that the notion of 'improved convergence' has a well defined meaning. (orig.)
Regimes of heating and dynamical response in driven many-body localized systems
Gopalakrishnan, Sarang; Knap, Michael; Demler, Eugene
2016-09-01
We explore the response of many-body localized (MBL) systems to periodic driving of arbitrary amplitude, focusing on the rate at which they exchange energy with the drive. To this end, we introduce an infinite-temperature generalization of the effective "heating rate" in terms of the spread of a random walk in energy space. We compute this heating rate numerically and estimate it analytically in various regimes. When the drive amplitude is much smaller than the frequency, this effective heating rate is given by linear response theory with a coefficient that is proportional to the optical conductivity; in the opposite limit, the response is nonlinear and the heating rate is a nontrivial power law of time. We discuss the mechanisms underlying this crossover in the MBL phase. We comment on implications for the subdiffusive thermal phase near the MBL transition, and for response in imperfectly isolated MBL systems.
Many-body strategies for multiqubit gates: Quantum control through Krawtchouk-chain dynamics
Groenland, Koen; Schoutens, Kareljan
2018-04-01
We propose a strategy for engineering multiqubit quantum gates. As a first step, it employs an eigengate to map states in the computational basis to eigenstates of a suitable many-body Hamiltonian. The second step employs resonant driving to enforce a transition between a single pair of eigenstates, leaving all others unchanged. The procedure is completed by mapping back to the computational basis. We demonstrate the strategy for the case of a linear array with an even number N of qubits, with specific X X +Y Y couplings between nearest neighbors. For this so-called Krawtchouk chain, a two-body driving term leads to the iSWAPN gate, which we numerically test for N =4 and 6.
Graphene-induced band gap renormalization in polythiophene: a many-body perturbation study
Marsusi, F.; Fedorov, I. A.; Gerivani, S.
2018-01-01
Density functional theory and many-body perturbation theory at the G0W0 level are employed to study the electronic properties of polythiophene (PT) adsorbed on the graphene surface. Analysis of the charge density difference shows that substrate-adsorbate interaction leads to a strong physisorption and interfacial electric dipole moment formation. The electrostatic potential displays a -0.19 eV shift in the graphene work function from its initial value of 4.53 eV, as the result of the interaction. The LDA band gap of the polymer does not show any change. However, the band structure exhibits weak orbital hybridizations resulting from slight overlapping between the polymer and graphene states wave functions. The interfacial polarization effects on the band gap and levels alignment are investigated at the G0W0 level and show a notable reduction of PT band gap compared to that of the isolated chain.
Coefficient of reversibility and two particular cases of deterministic many body systems
International Nuclear Information System (INIS)
Grossu, Ioan Valeriu; Besliu, Calin; Jipa, Alexandru
2004-01-01
We discuss the importance of a new measure of chaos in study of nonlinear dynamic systems, the - coefficient of reversibility-. This is defined as the probability of returning in the same point of phasic space. Is very interesting to compare this coefficient with other measures like fractal dimension or Liapunov exponent. We have also studied two very interesting many body systems, both having any number of particles but a deterministic evolution. One system is composed by n particles initially at rest, having the same mass and interacting through harmonic bi-particle forces, other is composed by two types of particles (with mass m 1 and mass m 2 ) initially at rest and interacting too through harmonic bi-particle forces
Electronic and optical properties of phosphorene-like arsenic phosphorus: a many-body study
Shu, Huabing; Guo, Jiyuan
2018-03-01
By employing density functional and many-body perturbation theories, we explore the geometrics, quasiparticle band structure, and optical response of two-dimensional arsenic phosphorus (α-AsxP1-x). Calculations indicate that the α-AsxP1-x exhibits excellent stability at high temperature. The quasi-particle bandgap of α-AsxP1-x is highly tunable in a broad range of 1.54-2.14 eV depending on the composition. The optical absorption of α-AsxP1-x can cover the visible and ultraviolet regions, and is highly anisotropic. More interestingly, it is tunable to optical absorption of α-AsxP1-x when the composition continuously increased. Also, they have sizable exciton binding energies. These findings suggest that α-AsxP1-x holds great potentials for applications in high-performance electronics and optoelectronics.
Seniority in quantum many-body systems. I. Identical particles in a single shell
Energy Technology Data Exchange (ETDEWEB)
Van Isacker, P., E-mail: isacker@ganil.fr [Grand Accélérateur National d’Ions Lourds, CEA/DSM–CNRS/IN2P3, BP 55027, F-14076 Caen Cedex 5 (France); Heinze, S. [Institut für Kernphysik der Universität zu Köln, 50937 Köln (Germany)
2014-10-15
A discussion of the seniority quantum number in many-body systems is presented. The analysis is carried out for bosons and fermions simultaneously but is restricted to identical particles occupying a single shell. The emphasis of the paper is on the possibility of partial conservation of seniority which turns out to be a peculiar property of spin-9/2 fermions but prevalent in systems of interacting bosons of any spin. Partial conservation of seniority is at the basis of the existence of seniority isomers, frequently observed in semi-magic nuclei, and also gives rise to peculiar selection rules in one-nucleon transfer reactions. - Highlights: • Unified derivation of conditions for the total and partial conservation of seniority. • General analysis of the partial conservation of seniority in boson systems. • Why partial conservation of seniority is crucial for seniority isomers in nuclei. • The effect of partial conservation of seniority on one-nucleon transfer intensities.
From optics to superconductivity. Many body effects in transition metal dichalcogenides
Energy Technology Data Exchange (ETDEWEB)
Roesner, Malte; Schoenhoff, Gunnar; Wehling, Tim [Institute for Theoretical Physics, University of Bremen (Germany); Bremen Center for Computational Material Sciences, University of Bremen (Germany); Steinhoff, Alexander; Jahnke, Frank; Gies, Christopher [Institute for Theoretical Physics, University of Bremen (Germany); Haas, Stephan [Department of Physics and Astronomy, University of Southern California, Los Angeles, CA (United States)
2015-07-01
We discuss many body effects in MoS{sub 2} ranging from optical properties to the emergence superconductivity (SC) and charge density wave phases (CDW). Combining ab-initio theory and semiconductor Bloch equations we show that excited carriers cause a redshift of the excitonic ground-state absorption line, while higher excitonic lines disappear successively due to a huge Coulomb-induced band gap shrinkage of more than 500 meV and concomitant exciton binding-energy reductions. Upon strong charge doping, we observe a succession of semiconducting, metallic, SC, and CDW regimes. Both, the SC and the CDW instabilities trace back to a Kohn anomaly and related softening of Brillouin zone boundary phonons.
A mesoscopic simulation of static and dynamic wetting using many-body dissipative particle dynamics
Ghorbani, Najmeh; Pishevar, Ahmadreza
2018-01-01
A many-body dissipative particle dynamics simulation is applied here to pave the way for investigating the behavior of mesoscale droplets after impact on horizontal solid substrates. First, hydrophobic and hydrophilic substrates are simulated through tuning the solid-liquid interfacial interaction parameters of an innovative conservative force model. The static contact angles are calculated on homogeneous and several patterned surfaces and compared with the predicted values by the Cassie's law in order to verify the model. The results properly evaluate the amount of increase in surface superhydrophobicity as a result of surface patterning. Then drop impact phenomenon is studied by calculating the spreading factor and dimensionless height versus dimensionless time and the comparisons made between the results and the experimental values for three different static contact angles. The results show the capability of the procedure in calculating the amount of maximum spreading factor, which is a significant concept in ink-jet printing and coating process.
Seniority in quantum many-body systems. I. Identical particles in a single shell
International Nuclear Information System (INIS)
Van Isacker, P.; Heinze, S.
2014-01-01
A discussion of the seniority quantum number in many-body systems is presented. The analysis is carried out for bosons and fermions simultaneously but is restricted to identical particles occupying a single shell. The emphasis of the paper is on the possibility of partial conservation of seniority which turns out to be a peculiar property of spin-9/2 fermions but prevalent in systems of interacting bosons of any spin. Partial conservation of seniority is at the basis of the existence of seniority isomers, frequently observed in semi-magic nuclei, and also gives rise to peculiar selection rules in one-nucleon transfer reactions. - Highlights: • Unified derivation of conditions for the total and partial conservation of seniority. • General analysis of the partial conservation of seniority in boson systems. • Why partial conservation of seniority is crucial for seniority isomers in nuclei. • The effect of partial conservation of seniority on one-nucleon transfer intensities
International Nuclear Information System (INIS)
Kuwahara, Tomotaka; Mori, Takashi; Saito, Keiji
2016-01-01
This work explores a fundamental dynamical structure for a wide range of many-body quantum systems under periodic driving. Generically, in the thermodynamic limit, such systems are known to heat up to infinite temperature states in the long-time limit irrespective of dynamical details, which kills all the specific properties of the system. In the present study, instead of considering infinitely long-time scale, we aim to provide a general framework to understand the long but finite time behavior, namely the transient dynamics. In our analysis, we focus on the Floquet–Magnus (FM) expansion that gives a formal expression of the effective Hamiltonian on the system. Although in general the full series expansion is not convergent in the thermodynamics limit, we give a clear relationship between the FM expansion and the transient dynamics. More precisely, we rigorously show that a truncated version of the FM expansion accurately describes the exact dynamics for a certain time-scale. Our theory reveals an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed. We discuss several dynamical phenomena, such as the effect of small integrability breaking, efficient numerical simulation of periodically driven systems, dynamical localization and thermalization. Especially on thermalization, we discuss a generic scenario on the prethermalization phenomenon in periodically driven systems. -- Highlights: •A general framework to describe transient dynamics for periodically driven systems. •The theory is applicable to generic quantum many-body systems including long-range interacting systems. •Physical meaning of the truncation of the Floquet–Magnus expansion is rigorously established. •New mechanism of the prethermalization is proposed. •Revealing an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed.
Directory of Open Access Journals (Sweden)
L. Fusco
2014-08-01
Full Text Available We analyze the nature of the statistics of the work done on or by a quantum many-body system brought out of equilibrium. We show that, for the sudden quench and for an initial state that commutes with the initial Hamiltonian, it is possible to retrieve the whole nonequilibrium thermodynamics via single projective measurements of observables. We highlight, in a physically clear way, the qualitative implications for the statistics of work coming from considering processes described by operators that either commute or do not commute with the unperturbed Hamiltonian of a given system. We consider a quantum many-body system and derive an expression that allows us to give a physical interpretation, for a thermal initial state, to all of the cumulants of the work in the case of quenched operators commuting with the unperturbed Hamiltonian. In the commuting case, the observables that we need to measure have an intuitive physical meaning. Conversely, in the noncommuting case, we show that, although it is possible to operate fully within the single-measurement framework irrespectively of the size of the quench, some difficulties are faced in providing a clear-cut physical interpretation to the cumulants. This circumstance makes the study of the physics of the system nontrivial and highlights the nonintuitive phenomenology of the emergence of thermodynamics from the fully quantum microscopic description. We illustrate our ideas with the example of the Ising model in a transverse field showing the interesting behavior of the high-order statistical moments of the work distribution for a generic thermal state and linking them to the critical nature of the model itself.
Energy Technology Data Exchange (ETDEWEB)
Kuwahara, Tomotaka, E-mail: tomotaka.phys@gmail.com [Department of Physics, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033 (Japan); WPI, Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577 (Japan); Mori, Takashi [Department of Physics, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033 (Japan); Saito, Keiji [Department of Physics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522 (Japan)
2016-04-15
This work explores a fundamental dynamical structure for a wide range of many-body quantum systems under periodic driving. Generically, in the thermodynamic limit, such systems are known to heat up to infinite temperature states in the long-time limit irrespective of dynamical details, which kills all the specific properties of the system. In the present study, instead of considering infinitely long-time scale, we aim to provide a general framework to understand the long but finite time behavior, namely the transient dynamics. In our analysis, we focus on the Floquet–Magnus (FM) expansion that gives a formal expression of the effective Hamiltonian on the system. Although in general the full series expansion is not convergent in the thermodynamics limit, we give a clear relationship between the FM expansion and the transient dynamics. More precisely, we rigorously show that a truncated version of the FM expansion accurately describes the exact dynamics for a certain time-scale. Our theory reveals an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed. We discuss several dynamical phenomena, such as the effect of small integrability breaking, efficient numerical simulation of periodically driven systems, dynamical localization and thermalization. Especially on thermalization, we discuss a generic scenario on the prethermalization phenomenon in periodically driven systems. -- Highlights: •A general framework to describe transient dynamics for periodically driven systems. •The theory is applicable to generic quantum many-body systems including long-range interacting systems. •Physical meaning of the truncation of the Floquet–Magnus expansion is rigorously established. •New mechanism of the prethermalization is proposed. •Revealing an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed.
Many-body theory of electrical, thermal and optical response of molecular heterojunctions
Bergfield, Justin Phillip
In this work, we develop a many-body theory of electronic transport through single molecule junctions based on nonequilibrium Green's functions (NEGFs). The central quantity of this theory is the Coulomb self-energy matrix of the junction SigmaC. SigmaC is evaluated exactly in the sequential-tunneling limit, and the correction due to finite lead-molecule tunneling is evaluated using a conserving approximation based on diagrammatic perturbation theory on the Keldysh contour. In this way, tunneling processes are included to infinite order, meaning that any approximation utilized is a truncation in the physical processes considered rather than in the order of those processes. Our theory reproduces the key features of both the Coulomb blockade and coherent transport regimes simultaneously in a single unified theory. Nonperturbative effects of intramolecular correlations are included, which are necessary to accurately describe the highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gap, essential for a quantitative theory of transport. This work covers four major topics related to transport in single-molecule junctions. First, we use our many-body theory to calculate the nonlinear electrical response of the archetypal Au-1,4-benzenedithiol-Au junction and find irregularly shaped 'molecular diamonds' which have been experimentally observed in some larger molecules but which are inaccessible to existing theoretical approaches. Next, we extend our theory to include heat transport and develop an exact expression for the heat current in an interacting nanostructure. Using this result, we discover that quantum coherence can strongly enhance the thermoelectric response of a device, a result with a number of technological applications. We then develop the formalism to include multi-orbital lead-molecule contacts and multi-channel leads, both of which strongly affect the observable transport. Lastly, we include a dynamic screening correction to
International Nuclear Information System (INIS)
Hartono, Albert; Lu, Qingda; Henretty, Thomas; Krishnamoorthy, Sriram; Zhang, Huaijian; Baumgartner, Gerald; Bernholdt, David E.; Nooijen, Marcel; Pitzer, Russell M.; Ramanujam, J.; Sadayappan, Ponnuswamy
2009-01-01
Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the coupled cluster method. This paper addresses two complementary aspects of performance optimization of such tensor contraction expressions. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions. The identification of common subexpressions among a set of tensor contraction expressions can result in a reduction of the total number of operations required to evaluate the tensor contractions. The first part of the paper describes an effective algorithm for operation minimization with common subexpression identification and demonstrates its effectiveness on tensor contraction expressions for coupled cluster equations. The second part of the paper highlights the importance of data layout transformation in the optimization of tensor contraction computations on modern processors. A number of considerations such as minimization of cache misses and utilization of multimedia vector instructions are discussed. A library for efficient index permutation of multi-dimensional tensors is described and experimental performance data is provided that demonstrates its effectiveness.
International Nuclear Information System (INIS)
Krishnamoorthy, Sriram; Bernholdt, David E.; Pitzer, R.M.; Sadayappan, Ponnuswamy
2009-01-01
Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the coupled cluster method. This paper addresses two complementary aspects of performance optimization of such tensor contraction expressions. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions. The identification of common subexpressions among a set of tensor contraction expressions can result in a reduction of the total number of operations required to evaluate the tensor contractions. The first part of the paper describes an effective algorithm for operation minimization with common subexpression identification and demonstrates its effectiveness on tensor contraction expressions for coupled cluster equations. The second part of the paper highlights the importance of data layout transformation in the optimization of tensor contraction computations on modern processors. A number of considerations, such as minimization of cache misses and utilization of multimedia vector instructions, are discussed. A library for efficient index permutation of multidimensional tensors is described, and experimental performance data is provided that demonstrates its effectiveness.
Importance-truncated no-core shell model for fermionic many-body systems
Energy Technology Data Exchange (ETDEWEB)
Spies, Helena
2017-03-15
The exact solution of quantum mechanical many-body problems is only possible for few particles. Therefore, numerical methods were developed in the fields of quantum physics and quantum chemistry for larger particle numbers. Configuration Interaction (CI) methods or the No-Core Shell Model (NCSM) allow ab initio calculations for light and intermediate-mass nuclei, without resorting to phenomenology. An extension of the NCSM is the Importance-Truncated No-Core Shell Model, which uses an a priori selection of the most important basis states. The importance truncation was first developed and applied in quantum chemistry in the 1970s and latter successfully applied to models of light and intermediate mass nuclei. Other numerical methods for calculations for ultra-cold fermionic many-body systems are the Fixed-Node Diffusion Monte Carlo method (FN-DMC) and the stochastic variational approach with Correlated Gaussian basis functions (CG). There are also such method as the Coupled-Cluster method, Green's Function Monte Carlo (GFMC) method, et cetera, used for calculation of many-body systems. In this thesis, we adopt the IT-NCSM for the calculation of ultra-cold Fermi gases at unitarity. Ultracold gases are dilute, strongly correlated systems, in which the average interparticle distance is much larger than the range of the interaction. Therefore, the detailed radial dependence of the potential is not resolved, and the potential can be replaced by an effective contact interaction. At low energy, s-wave scattering dominates and the interaction can be described by the s-wave scattering length. If the scattering length is small and negative, Cooper-pairs are formed in the Bardeen-Cooper-Schrieffer (BCS) regime. If the scattering length is small and positive, these Cooper-pairs become strongly bound molecules in a Bose-Einstein-Condensate (BEC). In between (for large scattering lengths) is the unitary limit with universal properties. Calculations of the energy spectra
Bally, B.; Duguet, T.
2018-02-01
Background: State-of-the-art multi-reference energy density functional calculations require the computation of norm overlaps between different Bogoliubov quasiparticle many-body states. It is only recently that the efficient and unambiguous calculation of such norm kernels has become available under the form of Pfaffians [L. M. Robledo, Phys. Rev. C 79, 021302 (2009), 10.1103/PhysRevC.79.021302]. Recently developed particle-number-restored Bogoliubov coupled-cluster (PNR-BCC) and particle-number-restored Bogoliubov many-body perturbation (PNR-BMBPT) ab initio theories [T. Duguet and A. Signoracci, J. Phys. G 44, 015103 (2017), 10.1088/0954-3899/44/1/015103] make use of generalized norm kernels incorporating explicit many-body correlations. In PNR-BCC and PNR-BMBPT, the Bogoliubov states involved in the norm kernels differ specifically via a global gauge rotation. Purpose: The goal of this work is threefold. We wish (i) to propose and implement an alternative to the Pfaffian method to compute unambiguously the norm overlap between arbitrary Bogoliubov quasiparticle states, (ii) to extend the first point to explicitly correlated norm kernels, and (iii) to scrutinize the analytical content of the correlated norm kernels employed in PNR-BMBPT. Point (i) constitutes the purpose of the present paper while points (ii) and (iii) are addressed in a forthcoming paper. Methods: We generalize the method used in another work [T. Duguet and A. Signoracci, J. Phys. G 44, 015103 (2017), 10.1088/0954-3899/44/1/015103] in such a way that it is applicable to kernels involving arbitrary pairs of Bogoliubov states. The formalism is presently explicated in detail in the case of the uncorrelated overlap between arbitrary Bogoliubov states. The power of the method is numerically illustrated and benchmarked against known results on the basis of toy models of increasing complexity. Results: The norm overlap between arbitrary Bogoliubov product states is obtained under a closed
Many-body and spin-orbit aspects of the alternating current phenomena
Glenn, Rachel M.
The thesis reports on research in the general field of light interaction with matter. According to the topics addressed, it can be naturally divided into two parts: Part I, many-body aspects of the Rabi oscillations which a two-level systems undergoes under a strong resonant drive; and Part II, absorption of the ac field between the spectrum branches of two-dimensional fermions that are split by the combined action of Zeeman and spin-orbit (SO) fields. The focus of Part I is the following many-body effects that modify the conventional Rabi oscillations: Chapter 1, coupling of a two-level system to a single vibrational mode of the environment. Chapter 2, correlated Rabi oscillations in two electron-hole systems coupled by tunneling with strong electron-hole attraction. In Chapter 1, a new effect of Rabi-vibronic resonance is uncovered. If the frequency of the Rabi oscillations, OR, is close to the frequency o0 of the vibrational mode, the oscillations acquire a collective character. It is demonstrated that the actual frequency of the collective oscillations exhibits a bistable behavior as a function of OR - o0. The main finding in Chapter 2 is, that the Fourier spectrum of the Rabi oscillations in two coupled electron-hole systems undergoes a strong transformation with increasing O R. For OR smaller than the tunneling frequency, the spectrum is dominated by a low-frequency (Rabi oscillations are restored only as OR exceeds the electron-hole attraction strength. The highlight of Part II is a finding that, while the spectrum of absorption between either Zeeman-split branches or SO-split branches is close to a delta-peak, in the presence of both, it transforms into a broad line with singular behavior at the edges. In particular, when the magnitudes of Zeeman and SO are equal, absorption of very low (much smaller than the splitting) frequencies become possible. The shape of the absorption spectrum is highly anisotropic with respect to the exciting field. This peculiar
Daily, Kevin Michael
Underlying the many-body effects of ultracold atomic gases are the few-body dynamics and interparticle interactions. Moreover, the study of few-body systems on their own has accelerated due to confining few atoms in each well of a deep optical lattice or in a single microtrap. This thesis studies the microscopic properties of few-body systems under external spherically symmetric harmonic confinement and how the few-body properties translate to the many-body system. Bosonic and fermionic few-body systems are considered and the dependence of the energetics and other quantities are investigated as functions of the s-wave scattering length, the mass ratio and the temperature. It is found that the condensate fraction of a weakly-interacting trapped Bose gas depletes quadratically with the s-wave scattering length. The next order term in the depletion depends not only, as might be expected naively, on the s-wave scattering length and the effective range but additionally on a two-body parameter that is not needed to reproduce the energy of weakly-interacting trapped Bose gases. This finding has important implications for effective field theory treatments of the system. Weakly-interacting atomic and molecular two-component Fermi gases with equal masses are described using perturbative approaches. The energy shifts are tabulated and interpreted, and a measure of the molecular condensate fraction is developed. We develop a measure of the molecular condensate fraction using the two-body density matrix and we develop a model of the spherical component of the momentum distribution that agrees well with stochastic variational calculations. We establish the existence of intersystem degeneracies for equal mass two-component Fermi gases with zero-range interactions, where the eigen energies of the spin-imbalanced system are degenerate with a subset of the eigen energies of the more spin-balanced system and the same total number of fermions. For unequal mass two-component Fermi
Quantum Simulation with Circuit-QED Lattices: from Elementary Building Blocks to Many-Body Theory
Zhu, Guanyu
Recent experimental and theoretical progress in superconducting circuits and circuit QED (quantum electrodynamics) has helped to develop high-precision techniques to control, manipulate, and detect individual mesoscopic quantum systems. A promising direction is hence to scale up from individual building blocks to form larger-scale quantum many-body systems. Although realizing a scalable fault-tolerant quantum computer still faces major barriers of decoherence and quantum error correction, it is feasible to realize scalable quantum simulators with state-of-the-art technology. From the technological point of view, this could serve as an intermediate stage towards the final goal of a large-scale quantum computer, and could help accumulating experience with the control of quantum systems with a large number of degrees of freedom. From the physical point of view, this opens up a new regime where condensed matter systems can be simulated and studied, here in the context of strongly correlated photons and two-level systems. In this thesis, we mainly focus on two aspects of circuit-QED based quantum simulation. First, we discuss the elementary building blocks of the quantum simulator, in particular a fluxonium circuit coupled to a superconducting resonator. We show the interesting properties of the fluxonium circuit as a qubit, including the unusual structure of its charge matrix elements. We also employ perturbation theory to derive the effective Hamiltonian of the coupled system in the dispersive regime, where qubit and the photon frequencies are detuned. The observables predicted with our theory, including dispersive shifts and Kerr nonlinearity, are compared with data from experiments, such as homodyne transmission and two-tone spectroscopy. These studies also relate to the problem of detection in a circuit-QED quantum simulator. Second, we study many-body physics of circuit-QED lattices, serving as quantum simulators. In particular, we focus on two different
Rare events in many-body systems: reactive paths and reaction constants for structural transitions
International Nuclear Information System (INIS)
Picciani, M.
2012-01-01
This PhD thesis deals with the study of fundamental physics phenomena, with applications to nuclear materials of interest. We have developed methods for the study of rare events related to thermally activated structural transitions in many body systems. The first method involves the numerical simulation of the probability current associated with reactive paths. After deriving the evolution equations for the probability current, a Diffusion Monte Carlo algorithm is implemented in order to sample this current. This technique, called Transition Current Sampling was applied to the study of structural transitions in a cluster of 38 atoms with Lennard-Jones potential (LJ-38). A second algorithm, called Transition Path Sampling with local Lyapunov bias (LyTPS), was then developed. LyTPS calculates reaction rates at finite temperature by following the transition state theory. A statistical bias based on the maximum local Lyapunov exponents is introduced to accelerate the sampling of reactive trajectories. To extract the value of the equilibrium reaction constants obtained from LyTPS, we use the Multistate Bennett Acceptance Ratio. We again validate this method on the LJ-38 cluster. LyTPS is then used to calculate migration constants for vacancies and divacancies in the α-Iron, and the associated migration entropy. These constants are used as input parameter for codes modeling the kinetic evolution after irradiation (First Passage Kinetic Monte Carlo) to reproduce numerically resistivity recovery experiments in α-Iron. (author) [fr
Many-body excitations and deexcitations in trapped ultracold bosonic clouds
Theisen, Marcus; Streltsov, Alexej I.
2016-11-01
We employ the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method to study excited states of interacting Bose-Einstein condensates confined by harmonic and double-well trap potentials. Two approaches to access excitations, one static and the other dynamic, are investigated and contrasted. In static simulations the low-lying excitations are computed by utilizing a linear-response theory constructed on top of a static MCTDHB solution (LR-MCTDHB). Complimentarily, we propose two dynamic protocols that address excitations by propagating the MCTDHB wave function. In particular, we investigate dipolelike oscillations induced by shifting the origin of the confining potential and breathinglike excitations by quenching the frequency of a parabolic part of the trap. To contrast static predictions and dynamic results we compute the time evolution and regard the respective Fourier transform of several local and nonlocal observables. Namely, we study the expectation value of the position operator , its variance Var [x (t )] , and a local density computed at selected positions. We find that the variance is the most sensitive and informative quantity: Along with excitations it contains information about deexcitations even in a linear regime of the induced dynamics. The dynamic protocols are found to access the many-body excitations predicted by the static LR-MCTDHB approach.
Relativistic many-body calculations of magnetic dipole transitions in Be-like ions
International Nuclear Information System (INIS)
Safronova, U.I.; Johnson, W.R.; Derevianko, A.
1999-01-01
Reduced matrix elements and transition rates are calculated for all magnetic dipole (M1) transitions within 2l2l' configurations and for some 2l3l'-2l2l' transitions in Be-like ions with nuclear charges ranging from Z = 4 to 100. Many-body perturbation theory (MBPT), including the Breit interaction, is used to evaluate retarded M1 matrix elements. The calculations start with a (1s) 2 Dirac-Fock potential and include all possible n = 2 configurations, leading to 4 odd-parity and 6 even-parity states, and some n = 3 configurations. First-order perturbation theory is used to obtain intermediate coupling coefficients. Second-order MBPT is used to determine the matrix elements, which are evaluated for all 11 M1 transitions within 2l2l' configurations and for 35 M1 transitions between 2l3l' and 2l2l' states. The transition energies used in the calculation of oscillator strengths and transition rates are obtained from second-order MBPT. The importance of negative-energy contributions to M1 transition amplitudes is discussed. (orig.)
Simulation of Quantum Many-Body Dynamics for Generic Strongly-Interacting Systems
Meyer, Gregory; Machado, Francisco; Yao, Norman
2017-04-01
Recent experimental advances have enabled the bottom-up assembly of complex, strongly interacting quantum many-body systems from individual atoms, ions, molecules and photons. These advances open the door to studying dynamics in isolated quantum systems as well as the possibility of realizing novel out-of-equilibrium phases of matter. Numerical studies provide insight into these systems; however, computational time and memory usage limit common numerical methods such as exact diagonalization to relatively small Hilbert spaces of dimension 215 . Here we present progress toward a new software package for dynamical time evolution of large generic quantum systems on massively parallel computing architectures. By projecting large sparse Hamiltonians into a much smaller Krylov subspace, we are able to compute the evolution of strongly interacting systems with Hilbert space dimension nearing 230. We discuss and benchmark different design implementations, such as matrix-free methods and GPU based calculations, using both pre-thermal time crystals and the Sachdev-Ye-Kitaev model as examples. We also include a simple symbolic language to describe generic Hamiltonians, allowing simulation of diverse quantum systems without any modification of the underlying C and Fortran code.
Mazziotti, David A.; Erdahl, Robert M.
2001-04-01
For the description of ground-state correlation phenomena an accurate mapping of many-body quantum mechanics onto four particles is developed. The energy for a quantum system with no more than two-particle interactions may be expressed in terms of a two-particle reduced density matrix (2-RDM), but variational optimization of the 2-RDM requires that it corresponds to an N-particle wave function. We derive N-representability conditions on the 2-RDM that guarantee the validity of the uncertainty relations for all operators with two-particle interactions. One of these conditions is shown to be necessary and sufficient to make the RDM solutions of the dispersion condition equivalent to those from the contracted Schrödinger equation (CSE) [Mazziotti, Phys. Rev. A 57, 4219 (1998)]. In general, the CSE is a stronger N-representability condition than the dispersion condition because the CSE implies the dispersion condition as well as additional N-representability constraints from the Hellmann-Feynman theorem. Energy minimization subject to the representability constraints is performed for a boson model with 10, 30, and 75 particles. Even when traditional wave-function methods fail at large perturbations, the present method yields correlation energies within 2%.
Exact self-energy of the many-body problem from conserving approximations
International Nuclear Information System (INIS)
Takada, Y.
1995-01-01
A procedure is proposed to obtain the exact self-energy in the many-body problem. This algorithm is based on the formal analysis to reach the exact theory by repeated applications of an operator F to an arbitrarily chosen input self-energy represented as a functional of the dressed Green's function. The operator F is so defined that the microscopic conservation law for particle number is satisfied. The rigorous self-energy is obtained by the solution of an eigenfunction of F. Particular attention is paid to the relation between the present procedure and the Baym-Kadanoff framework of conserving approximations. By simplifying the procedure in F with use of the generalized Ward identity, we suggest a practical method to implement this algorithm rather easily in actual systems. In order to suggest future directions to improve on this practical method, the recently developed mean-field theory for the Hubbard model in the limit of high spatial dimensions is also discussed in the context of our theory
Loop corrections and other many-body effects in relativistic field theories
International Nuclear Information System (INIS)
Ainsworth, T.L.; Brown, G.E.; Prakash, M.; Weise, W.
1988-01-01
Incorporation of effective masses into negative energy states (nucleon loop corrections) gives rise to repulsive many-body forces, as has been known for some time. Rather than renormalizing away the three- and four-body terms, we introduce medium corrections into the effective σ-exchange, which roughly cancel the nucleon loop terms for densities ρ ≅ ρ nm , where ρ nm is nuclear matter density. Going to higher densities, the repulsive contributions tend to saturate whereas the attractive ones keep on growing in magnitude. The latter is achieved through use of a density-dependent effective mass for the σ-particle, m σ = m σ (ρ), such that m σ (ρ) decreases with increasing density. Such a behavior is seen e.g. in the Nambu-Jona-Lasinio model. It is argued that a smooth transition to chiral restoration implies a similar behavior. The resulting nuclear equation of state is, because of the self-consistency in the problem, immensely insensitive to changes in the mass or coupling constant of the σ-particle. (orig.)
Comment on "Many-body localization in Ising models with random long-range interactions"
Maksymov, Andrii O.; Rahman, Noah; Kapit, Eliot; Burin, Alexander L.
2017-11-01
This Comment is dedicated to the investigation of many-body localization in a quantum Ising model with long-range power-law interactions r-α, relevant for a variety of systems ranging from electrons in Anderson insulators to spin excitations in chains of cold atoms. It has earlier been argued [arXiv:cond-mat/0611387 (2005); Phys. Rev. B 91, 094202 (2015), 10.1103/PhysRevB.91.094202] that this model obeys the dimensional constraint suggesting the delocalization of all finite-temperature states in the thermodynamic limit for α ≤2 d in a d -dimensional system. This expectation conflicts with the recent numerical studies of the specific interacting spin model of Li et al. [Phys. Rev. A 94, 063625 (2016), 10.1103/PhysRevA.94.063625]. To resolve this controversy we reexamine the model of Li et al. [Phys. Rev. A 94, 063625 (2016), 10.1103/PhysRevA.94.063625] and demonstrate that the infinite-temperature states there obey the dimensional constraint. The earlier developed scaling theory for the critical system size required for delocalization is extended to small exponents 0 ≤α ≤d . The disagreements between the two works are explained by the nonstandard selection of investigated states in the ordered phase in the work of Li et al. [Phys. Rev. A 94, 063625 (2016)type="doi" specific-use="suppress-display">10.1103/PhysRevA.94.063625].
Algorithm for simulation of quantum many-body dynamics using dynamical coarse-graining
International Nuclear Information System (INIS)
Khasin, M.; Kosloff, R.
2010-01-01
An algorithm for simulation of quantum many-body dynamics having su(2) spectrum-generating algebra is developed. The algorithm is based on the idea of dynamical coarse-graining. The original unitary dynamics of the target observables--the elements of the spectrum-generating algebra--is simulated by a surrogate open-system dynamics, which can be interpreted as weak measurement of the target observables, performed on the evolving system. The open-system state can be represented by a mixture of pure states, localized in the phase space. The localization reduces the scaling of the computational resources with the Hilbert-space dimension n by factor n 3/2 (ln n) -1 compared to conventional sparse-matrix methods. The guidelines for the choice of parameters for the simulation are presented and the scaling of the computational resources with the Hilbert-space dimension of the system is estimated. The algorithm is applied to the simulation of the dynamics of systems of 2x10 4 and 2x10 6 cold atoms in a double-well trap, described by the two-site Bose-Hubbard model.
Local Convertibility and the Quantum Simulation of Edge States in Many-Body Systems
Directory of Open Access Journals (Sweden)
Fabio Franchini
2014-11-01
Full Text Available In some many-body systems, certain ground-state entanglement (Rényi entropies increase even as the correlation length decreases. This entanglement nonmonotonicity is a potential indicator of nonclassicality. In this work, we demonstrate that such a phenomenon, known as lack of local convertibility, is due to the edge-state (deconstruction occurring in the system. To this end, we employ the example of the Ising chain, displaying an order-disorder quantum phase transition. Employing both analytical and numerical methods, we compute entanglement entropies for various system bipartitions (A|B and consider ground states with and without Majorana edge states. We find that the thermal ground states, enjoying the Hamiltonian symmetries, show lack of local convertibility if either A or B is smaller than, or of the order of, the correlation length. In contrast, the ordered (symmetry-breaking ground state is always locally convertible. The edge-state behavior explains all these results and could disclose a paradigm to understand local convertibility in other quantum phases of matter. The connection we establish between convertibility and nonlocal, quantum correlations provides a clear criterion of which features a universal quantum simulator should possess to outperform a classical machine.
Many-body dynamics of holes in a driven, dissipative spin chain of Rydberg superatoms
Letscher, Fabian; Petrosyan, David; Fleischhauer, Michael
2017-11-01
Strong, long-range interactions between atoms in high-lying Rydberg states can suppress multiple Rydberg excitations within a micron-sized trapping volume and yield sizable Rydberg level shifts at larger distances. Ensembles of atoms in optical microtraps then form Rydberg superatoms with collectively enhanced transition rates to the singly excited state. These superatoms can represent mesoscopic, strongly interacting spins. We study a regular array of such effective spins driven by a laser field tuned to compensate the interaction-induced level shifts between neighboring superatoms. During the initial transient, a few excited superatoms seed a cascade of resonantly facilitated excitation of large clusters of superatoms. Due to spontaneous decay, the system then relaxes to the steady state having nearly universal Rydberg excitation density {ρ }{{R}}=2/3. This state is characterized by highly non-trivial equilibrium dynamics of quasi-particles—excitation holes in the lattice of Rydberg excited superatoms. We derive an effective many-body model that accounts for hole mobility as well as continuous creation and annihilation of holes upon collisions with each other. We find that holes exhibit a nearly incompressible liquid phase with highly sub-Poissonian number statistics and finite-range density-density correlations.
Experimental quantum simulations of many-body physics with trapped ions.
Schneider, Ch; Porras, Diego; Schaetz, Tobias
2012-02-01
Direct experimental access to some of the most intriguing quantum phenomena is not granted due to the lack of precise control of the relevant parameters in their naturally intricate environment. Their simulation on conventional computers is impossible, since quantum behaviour arising with superposition states or entanglement is not efficiently translatable into the classical language. However, one could gain deeper insight into complex quantum dynamics by experimentally simulating the quantum behaviour of interest in another quantum system, where the relevant parameters and interactions can be controlled and robust effects detected sufficiently well. Systems of trapped ions provide unique control of both the internal (electronic) and external (motional) degrees of freedom. The mutual Coulomb interaction between the ions allows for large interaction strengths at comparatively large mutual ion distances enabling individual control and readout. Systems of trapped ions therefore exhibit a prominent system in several physical disciplines, for example, quantum information processing or metrology. Here, we will give an overview of different trapping techniques of ions as well as implementations for coherent manipulation of their quantum states and discuss the related theoretical basics. We then report on the experimental and theoretical progress in simulating quantum many-body physics with trapped ions and present current approaches for scaling up to more ions and more-dimensional systems.
Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems
International Nuclear Information System (INIS)
Guan, X-W; Batchelor, M T
2011-01-01
We demonstrate that the thermodynamics of one-dimensional Lieb-Liniger bosons can be accurately calculated in analytic fashion using the polylog function in the framework of the thermodynamic Bethe ansatz. The approach does away with the need to numerically solve the thermodynamic Bethe ansatz (Yang-Yang) equation. The expression for the equation of state allows the exploration of Tomonaga-Luttinger liquid physics and quantum criticality in an archetypical quantum system. In particular, the low-temperature phase diagram is obtained, along with the scaling functions for the density and compressibility. It has been shown recently by Guan and Ho (arXiv:1010.1301) that such scaling can be used to map out the criticality of ultracold fermionic atoms in experiments. We show here how to map out quantum criticality for Lieb-Liniger bosons. More generally, the polylog function formalism can be applied to a wide range of Bethe ansatz integrable quantum many-body systems which are currently of theoretical and experimental interest, such as strongly interacting multi-component fermions, spinor bosons and mixtures of bosons and fermions. (fast track communication)
Many-body dispersion effects in the binding of adsorbates on metal surfaces
Energy Technology Data Exchange (ETDEWEB)
Maurer, Reinhard J. [Department of Chemistry, Yale University, New Haven, Connecticut 06520 (United States); Ruiz, Victor G.; Tkatchenko, Alexandre [Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin (Germany)
2015-09-14
A correct description of electronic exchange and correlation effects for molecules in contact with extended (metal) surfaces is a challenging task for first-principles modeling. In this work, we demonstrate the importance of collective van der Waals dispersion effects beyond the pairwise approximation for organic–inorganic systems on the example of atoms, molecules, and nanostructures adsorbed on metals. We use the recently developed many-body dispersion (MBD) approach in the context of density-functional theory [Tkatchenko et al., Phys. Rev. Lett. 108, 236402 (2012) and Ambrosetti et al., J. Chem. Phys. 140, 18A508 (2014)] and assess its ability to correctly describe the binding of adsorbates on metal surfaces. We briefly review the MBD method and highlight its similarities to quantum-chemical approaches to electron correlation in a quasiparticle picture. In particular, we study the binding properties of xenon, 3,4,9,10-perylene-tetracarboxylic acid, and a graphene sheet adsorbed on the Ag(111) surface. Accounting for MBD effects, we are able to describe changes in the anisotropic polarizability tensor, improve the description of adsorbate vibrations, and correctly capture the adsorbate–surface interaction screening. Comparison to other methods and experiment reveals that inclusion of MBD effects improves adsorption energies and geometries, by reducing the overbinding typically found in pairwise additive dispersion-correction approaches.
Evidence for many-body interactions in the structure of molten alkali chlorides
International Nuclear Information System (INIS)
Malescio, G.P.; Tosi, M.P.
1985-02-01
An inversion of the measured partial structure factors of molten sodium chloride is attempted in order to assess some qualitative features of interionic forces in the melt. We start from a calculation of liquid structure and thermodynamic properties by means of a refined theory based on interionic pair potentials determined from properties of the solid phase. This yields very good agreement with the measured values of the internal energy and the compressibility of the liquid, whereas discrepancies with the observed structure are mainly localized in the region of interionic distances outside the minimum of the cation-anion potential. These discrepancies, when interpreted in terms of effective pair potentials in the melt through inversion of the structural data, strongly suggest the presence of many-body effects, insofar as such effective pair potentials oscillate with the local liquid structure and are inconsistent with the measured thermodynamic quantities. A similar analysis of data on molten rubidium and cesium chloride, though harder to carry out quantitatively, supports the above conclusion. (author)
Comparison of many bodied and binary collision cascade models up to 1 keV
International Nuclear Information System (INIS)
Schwartz, D.M.; Schiffgens, J.D.; Doran, D.G.; Odette, G.R.; Ariyasu, R.G.
1976-01-01
A quasi-dynamical code ADDES has been developed to model displacement cascades in copper for primary knockon atom energies up to several keV. ADDES is like a dynamical code in that it employs a many body treatment, yet similar to a binary collision code in that it incorporates the basic assumption that energy transfers below several eV can be ignored in describing cascade evolution. This paper is primarily concerned with (1) a continuing effort to validate the assumptions and specific parameters in the code by the comparison of ADDES results with experiment and with results from a dynamical code, and (2) comparisons of ADDES results with those from a binary collision code. The directional dependence of the displacement threshold is in reasonable agreement with the measurements of Jung et al. The behavior of focused replacement sequences is very similar to that obtained with the dynamical codes GRAPE and COMENT. Qualitative agreement was found between ADDES and COMENT for a higher energy (500 eV) defocused event while differences, still under study, are apparent in a 250 eV high index event. Comparisons of ADDES with the binary collision code MARLOWE show surprisingly good agreement in the 250 to 1000 eV range for both number and separation of Frenkel pairs. A preliminary observation, perhaps significant to displacement calculations utilizing the concept of a mean displacement energy, is the dissipation of 300 to 400 eV in a replacement sequence producing a single interstitial
Hartree–Fock many-body perturbation theory for nuclear ground-states
Directory of Open Access Journals (Sweden)
Alexander Tichai
2016-05-01
Full Text Available We investigate the order-by-order convergence behavior of many-body perturbation theory (MBPT as a simple and efficient tool to approximate the ground-state energy of closed-shell nuclei. To address the convergence properties directly, we explore perturbative corrections up to 30th order and highlight the role of the partitioning for convergence. The use of a simple Hartree–Fock solution for the unperturbed basis leads to a convergent MBPT series for soft interactions, in contrast to the divergent MBPT series obtained with a harmonic oscillator basis. For larger model spaces and heavier nuclei, where a direct high-order MBPT calculation is not feasible, we perform third-order calculations and compare to advanced ab initio coupled-cluster results for the same interactions and model spaces. We demonstrate that third-order MBPT provides ground-state energies for nuclei up into the tin isotopic chain in excellent agreement with the best available coupled-cluster calculations at a fraction of the computational cost.
Hartree–Fock many-body perturbation theory for nuclear ground-states
Energy Technology Data Exchange (ETDEWEB)
Tichai, Alexander, E-mail: alexander.tichai@physik.tu-darmstadt.de [Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt (Germany); Langhammer, Joachim [Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt (Germany); Binder, Sven [Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996 (United States); Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States); Roth, Robert, E-mail: robert.roth@physik.tu-darmstadt.de [Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt (Germany)
2016-05-10
We investigate the order-by-order convergence behavior of many-body perturbation theory (MBPT) as a simple and efficient tool to approximate the ground-state energy of closed-shell nuclei. To address the convergence properties directly, we explore perturbative corrections up to 30th order and highlight the role of the partitioning for convergence. The use of a simple Hartree–Fock solution for the unperturbed basis leads to a convergent MBPT series for soft interactions, in contrast to the divergent MBPT series obtained with a harmonic oscillator basis. For larger model spaces and heavier nuclei, where a direct high-order MBPT calculation is not feasible, we perform third-order calculations and compare to advanced ab initio coupled-cluster results for the same interactions and model spaces. We demonstrate that third-order MBPT provides ground-state energies for nuclei up into the tin isotopic chain in excellent agreement with the best available coupled-cluster calculations at a fraction of the computational cost.
Rotation of quantum impurities in the presence of a many-body environment
Lemeshko, Mikhail; Schmidt, Richard
2015-05-01
Pioneered by the seminal works of Wigner and Racah, the quantum theory of angular momentum evolved into a powerful machinery, commonly used to classify the states of isolated quantum systems and perturbations to their structure due to electromagnetic or crystalline fields. In ``realistic'' experiments, however, quantum systems are almost inevitably coupled to a many-particle environment and a field of elementary excitations associated with it, which is capable of fundamentally altering the physics of the system. We present the first systematic treatment of quantum rotation coupled to a many-particle environment. By using a series of canonical transformations on a generic microscopic Hamiltonian, we single out the conserved quantities of the problem. Using a variational ansatz accounting for an infinite number of many-body excitations, we characterize the spectrum of angular momentum eigenstates and identify the regions of instability, accompanied by emission of angular Cerenkov radiation. The developed technique can be applied to a wide range of systems described by the angular momentum algebra, from Rydberg atoms immersed into BEC's, to cold molecules solvated in helium droplets, to ultracold molecular ions.
Maximizing kinetic energy transfer in one-dimensional many-body collisions
International Nuclear Information System (INIS)
Ricardo, Bernard; Lee, Paul
2015-01-01
The main problem discussed in this paper involves a simple one-dimensional two-body collision, in which the problem can be extended into a chain of one-dimensional many-body collisions. The result is quite interesting, as it provides us with a thorough mathematical understanding that will help in designing a chain system for maximum energy transfer for a range of collision types. In this paper, we will show that there is a way to improve the kinetic energy transfer between two masses, and the idea can be applied recursively. However, this method only works for a certain range of collision types, which is indicated by a range of coefficients of restitution. Although the concept of momentum, elastic and inelastic collision, as well as Newton’s laws, are taught in junior college physics, especially in Singapore schools, students in this level are not expected to be able to do this problem quantitatively, as it requires rigorous mathematics, including calculus. Nevertheless, this paper provides nice analytical steps that address some common misconceptions in students’ way of thinking about one-dimensional collisions. (paper)
The transformation of elementary particle physics into many-body physics
International Nuclear Information System (INIS)
Hove, L. van
1986-01-01
The author illustrates the domains of particle physics where the theoretical problems and methods have much in common with many-body and condensed-matter physics. The multitude of diverse physical systems accessible to experimentation in condensed-matter physics, and the numerous concepts developed for their theoretical understanding provide a rich store of ideas and analogies to the particle physicist. This can help him to overcome the great handicap that in his own discipline the experimental facts are very hard to come by and are often extremely incomplete. On the other hand, particle physics brought us such truly fundamental advances as non-Abelian gauge theories, electroweak unification with the heavy weak bosons, and quantum chromodynamics with the confinement principle for the field quanta. As our understanding of these novel schemes deepens, possibly with further progress toward unification, one can expect that they will slowly have an impact on the rest of physics, just as the concepts and techniques of Abelian field theories have gradually invaded most of condensed-matter physics. (Auth.)
Kuwahara, Tomotaka; Mori, Takashi; Saito, Keiji
2016-04-01
This work explores a fundamental dynamical structure for a wide range of many-body quantum systems under periodic driving. Generically, in the thermodynamic limit, such systems are known to heat up to infinite temperature states in the long-time limit irrespective of dynamical details, which kills all the specific properties of the system. In the present study, instead of considering infinitely long-time scale, we aim to provide a general framework to understand the long but finite time behavior, namely the transient dynamics. In our analysis, we focus on the Floquet-Magnus (FM) expansion that gives a formal expression of the effective Hamiltonian on the system. Although in general the full series expansion is not convergent in the thermodynamics limit, we give a clear relationship between the FM expansion and the transient dynamics. More precisely, we rigorously show that a truncated version of the FM expansion accurately describes the exact dynamics for a certain time-scale. Our theory reveals an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed. We discuss several dynamical phenomena, such as the effect of small integrability breaking, efficient numerical simulation of periodically driven systems, dynamical localization and thermalization. Especially on thermalization, we discuss a generic scenario on the prethermalization phenomenon in periodically driven systems.
Density functional approach to many-body effects in the optical response of atoms
International Nuclear Information System (INIS)
Zangwill, A.
1981-01-01
The purpose of this work is to present a new method for calculating the optical response of finite electronic system which is accurate, computationally simple, and lends itself to a ready physical interpretation of the results. This work is concerned with the so-called many-body effects which render an independent particle calculation inappropriate for comparison with experimental photoabsorption and photoemission cross sections. Polarization effects are included which describe the response of the system to an external probe and self-energy effects, which describe the dynamics and decay of a single particle state. This work, which essentially reintroduces the residual Coulomb interactions among the electrons, is confined to atoms. The method is a time-dependent local density approximation (TDLDA) and represents a natural generalization of the usual local density approximation to the ground state properties of a many electron system. Using standard first-order time-dependent perturbation theory, a self-consistent mean field theory is derived for an effective field which replaces the external field in the dipole matrix elements of the Golden Rule for photoabsorption. This effective field includes a contribution from an induced classical Coulomb field as well as an induced exchange-correlation field. This work successfully demonstrates the applicability of time-dependent generalization of the local density approximation to the practical calculation of the photo-response of atoms. For the rare gases, barium, cerium and copper are obtained cross sections in quantitative agreement with recent experiments
Maximizing kinetic energy transfer in one-dimensional many-body collisions
Ricardo, Bernard; Lee, Paul
2015-03-01
The main problem discussed in this paper involves a simple one-dimensional two-body collision, in which the problem can be extended into a chain of one-dimensional many-body collisions. The result is quite interesting, as it provides us with a thorough mathematical understanding that will help in designing a chain system for maximum energy transfer for a range of collision types. In this paper, we will show that there is a way to improve the kinetic energy transfer between two masses, and the idea can be applied recursively. However, this method only works for a certain range of collision types, which is indicated by a range of coefficients of restitution. Although the concept of momentum, elastic and inelastic collision, as well as Newton’s laws, are taught in junior college physics, especially in Singapore schools, students in this level are not expected to be able to do this problem quantitatively, as it requires rigorous mathematics, including calculus. Nevertheless, this paper provides nice analytical steps that address some common misconceptions in students’ way of thinking about one-dimensional collisions.
International Nuclear Information System (INIS)
Hansen, Katja; Biegler, Franziska; Ramakrishnan, Raghunathan; Pronobis, Wiktor; Lilienfeld, O. Anatole von; Müller, Klaus-Robert; Tkatchenko, Alexandre
2015-01-01
Simultaneously accurate and efficient prediction of molecular properties throughout chemical compound space is a critical ingredient toward rational compound design in chemical and pharmaceutical industries. Aiming toward this goal, we develop and apply a systematic hierarchy of efficient empirical methods to estimate atomization and total energies of molecules. These methods range from a simple sum over atoms, to addition of bond energies, to pairwise interatomic force fields, reaching to the more sophisticated machine learning approaches that are capable of describing collective interactions between many atoms or bonds. In the case of equilibrium molecular geometries, even simple pairwise force fields demonstrate prediction accuracy comparable to benchmark energies calculated using density functional theory with hybrid exchange-correlation functionals; however, accounting for the collective many-body interactions proves to be essential for approaching the 'holy grail' of chemical accuracy of 1 kcal/mol for both equilibrium and out-of-equilibrium geometries. This remarkable accuracy is achieved by a vectorized representation of molecules (so-called Bag of Bonds model) that exhibits strong nonlocality in chemical space. The same representation allows us to predict accurate electronic properties of molecules, such as their polarizability and molecular frontier orbital energies
Patterns in Permutations and Words
Kitaev, Sergey
2011-01-01
There has been considerable interest recently in the subject of patterns in permutations and words, a new branch of combinatorics with its roots in the works of Rotem, Rogers, and Knuth in the 1970s. Consideration of the patterns in question has been extremely interesting from the combinatorial point of view, and it has proved to be a useful language in a variety of seemingly unrelated problems, including the theory of Kazhdan--Lusztig polynomials, singularities of Schubert varieties, interval orders, Chebyshev polynomials, models in statistical mechanics, and various sorting algorithms, inclu
Tensor Permutation Matrices in Finite Dimensions
Christian, Rakotonirina
2005-01-01
We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows us to construct a tensor permutation matrix, which is a generalisation of tensor commutation matrix, has been established. The expression of an element of a tensor commutation matrix has been generalised in the case of any element of a tensor permutation ma...
Quantum many-body dynamics of ultracold atoms in optical lattices
Energy Technology Data Exchange (ETDEWEB)
Kessler, Stefan
2014-04-15
Ultracold atoms can be trapped in periodic intensity patterns of light created by counterpropagating laser beams, so-called optical lattices. In contrast to its natural counterpart, electrons in a solid state crystal, this man-made setup is very clean and highly isolated from environmental degrees of freedom. Moreover, to a large extent, the experimenter has dynamical control over the relevant system parameters: the interaction between atoms, the tunneling amplitude between lattice sites, and even the dimensionality of the lattice. These advantages render this system a unique platform for the simulation of quantum many-body dynamics for various lattice Hamiltonians as has been demonstrated in several experiments by now. The most significant step in recent times has arguably been the introduction of single-site detection of individual atoms in optical lattices. This technique, based on fluorescence microscopy, opens a new doorway for the study of quantum many-body states: the detection of the microscopic atom configuration. In this thesis, we theoretically explore the dynamics of ultracold atoms in optical lattices for various setups realized in present-day experiments. Our main focus lies on aspects that become experimentally accessible by (realistic extensions of) the novel single-site measurement technique. The first part deals with the expansion of initially confined atoms in a homogeneous lattice, which is one way to create atomic motion in experiments. We analyze the buildup of spatial correlations during the expansion of a finitely extended band insulating state in one dimension. The numerical simulation reveals the creation of remote spin-entangled fermions in the strongly interacting regime. We discuss the experimental observation of such spin-entangled pairs by means of a single-site measurement. Furthermore, we suggest studying the impact of observations on the expansion dynamics for the extreme case of a projective measurement in the spatial occupation
Beautiful Models: 70 Years of Exactly Solved Quantum Many-Body Problems
International Nuclear Information System (INIS)
Batchelor, M T
2005-01-01
A key element of theoretical physics is the conceptualisation of physical phenomena in terms of models, which are then investigated by the tools at hand. For quantum many-body systems, some models can be exactly solved, i.e., their physical properties can be calculated in an exact fashion. There is often a deep underlying reason why this can be done-the theory of integrability-which manifests itself in many guises. In Beautiful models, Bill Sutherland looks at exactly solved models in quantum many-body systems, a well established field dating back to Bethe's 1931 exact solution of the spin-1/2 Heisenberg chain. This field is enjoying a renaissance due to the ongoing and striking experimental advances in low-dimensional quantum physics, which includes the manufacture of quasi one-dimensional quantum gases. Apart from the intrinsic beauty of the subject material, Beautiful Models is written by a pioneering master of the field. Sutherland has aimed to provide a broad textbook style introduction to the subject for graduate students and interested non-experts. An important point here is the 'language' of the book. In Sutherland's words, the subject of exactly solved models 'belongs to the realm of mathematical physics-too mathematical to be 'respectable' physics, yet not rigorous enough to be 'real' mathematics. ...there are perennial attempts to translate this body of work into either respectable physics or real mathematics; this is not that sort of book.' Rather, Sutherland discusses the models and their solutions in terms of their 'intrinisic' language, which is largely as found in the physics literature. The book begins with a helpful overview of the contents and then moves on to the foundation material, which is the chapter on integrability and non-diffraction. As is shown, these two concepts go hand in hand. The topics covered in later chapters include models with δ-function potentials, the Heisenberg spin chain, the Hubbard model, exchange models, the Calogero
Beautiful Models: 70 Years of Exactly Solved Quantum Many-Body Problems
Energy Technology Data Exchange (ETDEWEB)
Batchelor, M T [Department of Theoretical Physics, RSPSE and Department of Mathematics, MSI, Australian National University, Canberra ACT 0200 (Australia)
2005-04-08
A key element of theoretical physics is the conceptualisation of physical phenomena in terms of models, which are then investigated by the tools at hand. For quantum many-body systems, some models can be exactly solved, i.e., their physical properties can be calculated in an exact fashion. There is often a deep underlying reason why this can be done-the theory of integrability-which manifests itself in many guises. In Beautiful models, Bill Sutherland looks at exactly solved models in quantum many-body systems, a well established field dating back to Bethe's 1931 exact solution of the spin-1/2 Heisenberg chain. This field is enjoying a renaissance due to the ongoing and striking experimental advances in low-dimensional quantum physics, which includes the manufacture of quasi one-dimensional quantum gases. Apart from the intrinsic beauty of the subject material, Beautiful Models is written by a pioneering master of the field. Sutherland has aimed to provide a broad textbook style introduction to the subject for graduate students and interested non-experts. An important point here is the 'language' of the book. In Sutherland's words, the subject of exactly solved models 'belongs to the realm of mathematical physics-too mathematical to be 'respectable' physics, yet not rigorous enough to be 'real' mathematics. ...there are perennial attempts to translate this body of work into either respectable physics or real mathematics; this is not that sort of book.' Rather, Sutherland discusses the models and their solutions in terms of their 'intrinisic' language, which is largely as found in the physics literature. The book begins with a helpful overview of the contents and then moves on to the foundation material, which is the chapter on integrability and non-diffraction. As is shown, these two concepts go hand in hand. The topics covered in later chapters include models with {delta}-function potentials, the
Quantum Many-Body Dynamics with Driven Bose Condensates: Kibble-Zurek Mechanism and Bose Fireworks
Clark, Logan William
In recent years there has been an explosion of interest in the field of quantum many-body physics. Understanding the complex and often unintuitive behavior of systems containing interacting quantum constituents is not only fascinating but also crucial for developing the next generation of quantum technology, including better materials, sensors, and computers. Yet understanding such systems remains a challenge, particularly when considering the dynamics which occur when they are excited far from equilibrium. Ultracold atomic gases provide an ideal system with which to study dynamics by enabling clean, well-controlled experiments at length- and time-scales which allow us to observe the dynamics directly. This thesis describes experiments on the many-body dynamics of ultracold, bosonic cesium atoms. Our apparatus epitomizes the versatility of ultracold atoms by providing extensive control over the quantum gas. In particular, we will discuss our use of a digital micromirror device to project arbitrary, dynamic external potentials onto the gas; our development of a powerful new scheme for optically controlling Feshbach resonances to enable spatiotemporal control of the interactions between atoms; and our use of near-resonant shaking lattices to modify the kinetic energy of atoms. Taking advantage of this flexible apparatus, we have been able to test a longstanding conjecture based on the Kibble-Zurek mechanism, which says that the dynamics of a system crossing a quantum phase transition should obey a universal scaling symmetry of space and time. After accounting for this scaling symmetry, critical dynamics would be essentially independent of the rate at which a system crossed a phase transition. We tested the universal scaling of critical dynamics by using near-resonant shaking to drive Bose-Einstein condensates across an effectively ferromagnetic quantum phase transition. After crossing the phase transition, condensates divide themselves spatially into domains with
PREFACE: Many-body correlations from dilute to dense nuclear systems
Otsuka, Takaharu; Urban, Michael; Yamada, Taiichi
2011-09-01
The International EFES-IN2P3 conference on "Many body correlations from dilute to dense nuclear systems" was held at the Institut Henri Poincaré (IHP), Paris, France, from 15-18 February 2011, on the occasion of the retirement of our colleague Peter Schuck. Correlations play a decisive role in various many-body systems such as nuclear systems, condensed matter and quantum gases. Important examples include: pairing correlations (Cooper pairs) which give rise to nuclear superfluidity (analogous to superconductivity in condensed matter); particle-hole (RPA) correlations in the description of the ground state beyond mean-field theory; clusters; and α-particle correlations in certain nuclei. Also, the nucleons themselves can be viewed as clusters of three quarks. During the past few years, researchers have started to study how the character of these correlations changes with the variation of the density. For instance, the Cooper pairs in dense matter can transform into a Bose-Einstein condensate (BEC) of true bound states at low density (this is the BCS-BEC crossover studied in ultracold Fermi gases). Similar effects play a role in neutron matter at low density, e.g., in the "neutron skin" of exotic nuclei. The α-cluster correlation becomes particularly important at lower density, such as in the excited states of some nuclei (e.g., the α-condensate-like structure in the Hoyle state of 12C) or in the formation of compact stars. In addition to nuclear physics, topics from astrophysics (neutron stars), condensed matter, and quantum gases were discussed in 48 talks and 19 posters, allowing the almost 90 participants from different communities to exchange their ideas, experiences and methods. The conference dinner took place at the Musée d'Orsay, and all the participants enjoyed the very pleasant atmosphere. One session of the conference was dedicated to the celebration of Peter's retirement. We would like to take this opportunity to wish Peter all the best and we hope
Quantum many-body dynamics of ultracold atoms in optical lattices
International Nuclear Information System (INIS)
Kessler, Stefan
2014-01-01
Ultracold atoms can be trapped in periodic intensity patterns of light created by counterpropagating laser beams, so-called optical lattices. In contrast to its natural counterpart, electrons in a solid state crystal, this man-made setup is very clean and highly isolated from environmental degrees of freedom. Moreover, to a large extent, the experimenter has dynamical control over the relevant system parameters: the interaction between atoms, the tunneling amplitude between lattice sites, and even the dimensionality of the lattice. These advantages render this system a unique platform for the simulation of quantum many-body dynamics for various lattice Hamiltonians as has been demonstrated in several experiments by now. The most significant step in recent times has arguably been the introduction of single-site detection of individual atoms in optical lattices. This technique, based on fluorescence microscopy, opens a new doorway for the study of quantum many-body states: the detection of the microscopic atom configuration. In this thesis, we theoretically explore the dynamics of ultracold atoms in optical lattices for various setups realized in present-day experiments. Our main focus lies on aspects that become experimentally accessible by (realistic extensions of) the novel single-site measurement technique. The first part deals with the expansion of initially confined atoms in a homogeneous lattice, which is one way to create atomic motion in experiments. We analyze the buildup of spatial correlations during the expansion of a finitely extended band insulating state in one dimension. The numerical simulation reveals the creation of remote spin-entangled fermions in the strongly interacting regime. We discuss the experimental observation of such spin-entangled pairs by means of a single-site measurement. Furthermore, we suggest studying the impact of observations on the expansion dynamics for the extreme case of a projective measurement in the spatial occupation
Quantum scaling in many-body systems an approach to quantum phase transitions
Continentino, Mucio
2017-01-01
Quantum phase transitions are strongly relevant in a number of fields, ranging from condensed matter to cold atom physics and quantum field theory. This book, now in its second edition, approaches the problem of quantum phase transitions from a new and unifying perspective. Topics addressed include the concepts of scale and time invariance and their significance for quantum criticality, as well as brand new chapters on superfluid and superconductor quantum critical points, and quantum first order transitions. The renormalisation group in real and momentum space is also established as the proper language to describe the behaviour of systems close to a quantum phase transition. These phenomena introduce a number of theoretical challenges which are of major importance for driving new experiments. Being strongly motivated and oriented towards understanding experimental results, this is an excellent text for graduates, as well as theorists, experimentalists and those with an interest in quantum criticality.
Spontaneous Symmetry Breaking and Nambu–Goldstone Bosons in Quantum Many-Body Systems
Directory of Open Access Journals (Sweden)
Tomáš Brauner
2010-04-01
Full Text Available Spontaneous symmetry breaking is a general principle that constitutes the underlying concept of a vast number of physical phenomena ranging from ferromagnetism and superconductivity in condensed matter physics to the Higgs mechanism in the standard model of elementary particles. I focus on manifestations of spontaneously broken symmetries in systems that are not Lorentz invariant, which include both nonrelativistic systems as well as relativistic systems at nonzero density, providing a self-contained review of the properties of spontaneously broken symmetries specific to such theories. Topics covered include: (i Introduction to the mathematics of spontaneous symmetry breaking and the Goldstone theorem. (ii Minimization of Higgs-type potentials for higher-dimensional representations. (iii Counting rules for Nambu–Goldstone bosons and their dispersion relations. (iv Construction of effective Lagrangians. Specific examples in both relativistic and nonrelativistic physics are worked out in detail.
Long-distance entanglement in many-body atomic and optical systems
Energy Technology Data Exchange (ETDEWEB)
Giampaolo, Salvatore M; Illuminati, Fabrizio [Dipartimento di Matematica e Informatica, Universita degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano, SA (Italy)], E-mail: illuminati@sa.infn.it
2010-02-15
We discuss the phenomenon of long-distance entanglement (LDE) in the ground state of quantum spin models, its use in high-fidelity and robust quantum communication, and its realization in many-body systems of ultracold atoms in optical lattices and in arrays of coupled optical cavities. We investigate XX quantum spin models on one-dimensional lattices with open ends and different patterns of site-dependent interaction couplings, singling out two general settings: patterns that allow for perfect LDE in the ground state of the system, namely such that the end-to-end entanglement remains finite in the thermodynamic limit, and patterns of quasi-long-distance entanglement (QLDE) in the ground state of the system, namely such that the end-to-end entanglement vanishes with a very slow power-law decay as the length of the spin chain is increased. We discuss physical realizations of these models in ensembles of ultracold bosonic atoms loaded in optical lattices. We show how, using either suitably engineered super-lattice structures or exploiting the presence of edge impurities in lattices with single periodicity, it is possible to realize models endowed with nonvanishing LDE or QLDE. We then study how to realize models that optimize the robustness of QLDE at finite temperature and in the presence of imperfections using suitably engineered arrays of coupled optical cavities. For both cases the numerical estimates of the end-to-end entanglement in the actual physical systems are thoroughly compared with the analytical results obtained for the spin model systems. We finally introduce LDE-based schemes of long-distance quantum teleportation in linear arrays of coupled cavities, and show that they allow for high-fidelity and high success rates even at moderately high temperatures.
Long-distance entanglement in many-body atomic and optical systems
International Nuclear Information System (INIS)
Giampaolo, Salvatore M; Illuminati, Fabrizio
2010-01-01
We discuss the phenomenon of long-distance entanglement (LDE) in the ground state of quantum spin models, its use in high-fidelity and robust quantum communication, and its realization in many-body systems of ultracold atoms in optical lattices and in arrays of coupled optical cavities. We investigate XX quantum spin models on one-dimensional lattices with open ends and different patterns of site-dependent interaction couplings, singling out two general settings: patterns that allow for perfect LDE in the ground state of the system, namely such that the end-to-end entanglement remains finite in the thermodynamic limit, and patterns of quasi-long-distance entanglement (QLDE) in the ground state of the system, namely such that the end-to-end entanglement vanishes with a very slow power-law decay as the length of the spin chain is increased. We discuss physical realizations of these models in ensembles of ultracold bosonic atoms loaded in optical lattices. We show how, using either suitably engineered super-lattice structures or exploiting the presence of edge impurities in lattices with single periodicity, it is possible to realize models endowed with nonvanishing LDE or QLDE. We then study how to realize models that optimize the robustness of QLDE at finite temperature and in the presence of imperfections using suitably engineered arrays of coupled optical cavities. For both cases the numerical estimates of the end-to-end entanglement in the actual physical systems are thoroughly compared with the analytical results obtained for the spin model systems. We finally introduce LDE-based schemes of long-distance quantum teleportation in linear arrays of coupled cavities, and show that they allow for high-fidelity and high success rates even at moderately high temperatures.
Many-body pairing in a two-dimensional Fermi gas
Energy Technology Data Exchange (ETDEWEB)
Neidig, Mathias
2017-05-24
This thesis reports on experiments conducted in a single layer, quasi two-dimensional, two-component ultracold Fermi gas in the strongly interacting regime. Ultracold gases can be used to simulate key aspects of more complicated systems like for example cuprates which show high-T{sub c} superconductivity. The momentum distribution of a sample of bosonic dimers in a quasi-2D square lattice geometry was measured to obtain the coherence properties. For shallow lattices, sharp peaks in the momentum distribution, indicating coherence, were observed at zero momentum as well as at positive and negative lattice momenta along each axis. For deeper lattices, heating impeded the ability to prepare a Mott-insulator. A spatially resolved radio-frequency spectroscopy was employed for a quasi-2D Fermi gas in the normal phase throughout the BEC-BCS crossover. The interaction induced energy shifts were measured in the strongly interacting region where they can be on the order of the Fermi energy and thus the local resolution is crucial. Furthermore, the onset of pairing in the strongly interacting region was measured as a function of temperature and it was shown that the fraction of free atoms decreases faster than expected from thermal non-interacting theory. At last, the pairing gap was measured using an imbalanced sample. On the BEC side it was found to be in very good agreement with two-body physics as expected. In the strongly interacting regime, however, a deviation from two-body physics indicates that here many-body effects play a role and thus further studies are required.
Hallez, Yannick; Meireles, Martine
2016-10-11
Electrostatic interactions play a key role in hollow shell suspensions as they determine their structure, stability, thermodynamics, and rheology and also the loading capacity of small charged species for nanoreservoir applications. In this work, fast, reliable modeling strategies aimed at predicting the electrostatics of hollow shells for one, two, and many colloids are proposed and validated. The electrostatic potential inside and outside a hollow shell with a finite thickness and a specific permittivity is determined analytically in the Debye-Hückel (DH) limit. An expression for the interaction potential between two such hollow shells is then derived and validated numerically. It follows a classical Yukawa form with an effective charge depending on the shell geometry, permittivity, and inner and outer surface charge densities. The predictions of the Ornstein-Zernike (OZ) equation with this pair potential to determine equations of state are then evaluated by comparison to results obtained with a Brownian dynamics algorithm coupled to the resolution of the linearized Poisson-Boltzmann and Laplace equations (PB-BD simulations). The OZ equation based on the DLVO-like potential performs very well in the dilute regime as expected, but also quite well, and more surprisingly, in the concentrated regime in which full spheres exhibit significant many-body effects. These effects are shown to vanish for shells with small thickness and high permittivity. For highly charged hollow shells, we propose and validate a charge renormalization procedure. Finally, using PB-BD simulations, we show that the cell model predicts the ion distribution inside and outside hollow shells accurately in both electrostatically dilute and concentrated suspensions. We then determine the shell loading capacity as a function of salt concentration, volume fraction, and surface charge density for nanoreservoir applications such as drug delivery, sensing, or smart coatings.
Many-body calculation of the coincidence L3 photoelectron spectroscopy main line of Ni metal
International Nuclear Information System (INIS)
Ohno, Masahide
2008-01-01
The partial singles L 3 photoelectron spectroscopy (PES) main line of Ni metal correlated with Auger electrons emitted by the localized L 3 -VV Auger decay is calculated by a many-body theory. The partial singles L 3 PES main line of Ni metal almost coincides in both line shape and peak kinetic energy (KE) with the singles one. The former main line peak shows a KE shift of only 0.01 eV toward the lower KE and a very small asymmetric line shape change compared to the singles one. The asymmetric line shape change and the peak KE shift of the partial singles L 3 main line are very small. However, they are due to the variation with photoelectron KE in the branching ratio of the partial Auger decay width in the partial singles L 3 PES main line by the photoelectron KE dependent imaginary part of the shakeup self-energy. The L 3 PES main line of Ni metal measured in coincidence with the L 3 -VV ( 1 G) Auger electron spectroscopy (AES) main line peak is the partial singles one modulated by a spectral function R a of a fixed energy Auger electron analyzer so that it should show only a symmetric line narrowing by R a compared to the singles one. The L 3 PES main line peak of Ni metal measured in coincidence with the delocalized band-like L 3 -VV AES peak or not completely split-off (or not completely localized) L 3 -VV ( 3 F) AES peak, will show an asymmetric line narrowing and a KE shift compared to the singles one. Thus, the L 3 PES main line of Ni metal in coincidence with various parts of the L 3 -VV AES spectrum depends on which part of the L 3 -VV AES spectrum a fixed energy Auger electron analyzer is set. The experimental verification is in need
The many-body level density; Densite de niveaux du probleme a n-corps
Energy Technology Data Exchange (ETDEWEB)
Roccia, J
2007-09-15
We investigate the many-body level density {rho}{sub MB} for fermion and boson gases. We establish its behavior as a function of the temperature and the number of particles. We deal with correction terms due to finite number of particles effects for {rho}{sub MB}: for fermions, it seems that it exists only one behavior. We propose a semiclassical expression of {rho}{sub MB} for two types of particles with an angular momentum. It is decomposed into a smooth part coming from the saddle point method plus corrective terms due to the expansion of the number of partitions for two types of particles and an oscillating part coming from the fluctuations of the single-particle level density. Our model is validated by a numerical study. For the case of the atomic nucleus, the oscillating part of {rho}{sub MB} is controlled by a temperature factor which depends on the chaotic or integrable nature of the system and on the fluctuation of the ground state energy. This leads to consider in more detail this last quantity. For an isolated system, we give the general expression of the mean value for fixed potentials. We treat the self-bound system case through the example of the three dimensional harmonic oscillator (3DHO). Furthermore we study the oscillating part of {rho}{sub MB} for bosons in the low temperature regime for billiards and for isotropic 3DHO. We note the oscillations disappear leading to a power law correction. In the case of the isotropic 3DHO, these corrections have the same order of magnitude as the smooth part. In the same way, for the high temperature regime we show the oscillating part of {rho}{sub MB} is exponentially negligible compared to the smooth part. (author)
Pion propagator in relativistic quantum field theories of the nuclear many-body problem
International Nuclear Information System (INIS)
Matsui, T.; Serot, B.D.
1982-01-01
Pion interactions in the nuclear medium are studied using renormalizable relativistic quantum field theories. Previous studies using pseudoscalar πN coupling encountered difficulties due to the large strength of the πNN vertex. We therefore formulate renormalizable field theories with pseudovector πN coupling using techniques introduced by Weinberg and Schwinger. Calculations are performed for two specific models; the scalar-vector theory of Walecka, extended to include π and rho mesons in a non-chiral fashion, and the linear sigma-model with an additional neutral vector meson. Both models qualitatively reproduce low-energy πN phenomenology and lead to nuclear matter saturation in the relativistic Hartree formalism, which includes baryon vacuum fluctuations. The pions propagator is evaluated in the one-nucleon-loop approximation, which corresponds to a relativistic random-phase approximation built on the Hartree ground state. Virtual NN-bar loops are included, and suitable renormalization techniques are illustrated. The local-density approximation is used to compare the threshold pion self-energy to the s-wave pion-nucleus optical potential. In the non-chiral model, s-wave pion-nucleus scattering is too large in both pseudoscalar and pseudovector calculations, indicating that additional constraints must be imposed on the Lagrangian. In the chiral model, the threshold self-energy vanishes automatically in the pseudovector case, but does so for pseudoscalar coupling only if the baryon effective mass is chosen self-consistently Since extrapolation from free space to nuclear density can lead to large effects, pion propagation in the medium can determine which πN coupling is more suitable for the relativistic nuclear many-body problem. Conversely, pion interactions constrain the model Lagrangian and the nuclear matter equation of state. An approximately chiral model with pseudovector coupling is favored
DEFF Research Database (Denmark)
Houmark-Nielsen, Jakob; Nielsen, Torben Roland; Mørk, Jesper
2009-01-01
an important impact on the slow light properties. In the case of the Lambda and V schemes, the minimum required coupling power to achieve slow light is significantly reduced by many-body interactions. V type schemes are found to be generally preferable due to a favorable redistribution of carriers in energy......We investigate the impact of many-body interactions on group-velocity slowdown achieved via electromagnetically induced transparency in quantum dots using three different coupling-probe schemes (ladder, V, and Lambda, respectively). We find that for all schemes many-body interactions have...
International Nuclear Information System (INIS)
Moncrieff, D.; Wilson, S.
1992-06-01
The ab initio determination of the electronic structure of molecules is a many-fermion problem involving the approximate description of the motion of the electrons in the field of fixed nuclei. It is an area of research which demands considerable computational resources but having enormous potential in fields as diverse as interstellar chemistry and drug design, catalysis and solid state chemistry, molecular biology and environmental chemistry. Electronic structure calculations almost invariably divide into two main stages: the approximate solution of an independent electron model, in which each electron moves in the average field created by the other electrons in the system, and then, the more computationally demanding determination of a series of corrections to this model, the electron correlation effects. The many-body perturbation theory expansion affords a systematic description of correlation effects, which leads directly to algorithms which are suitable for concurrent computation. We term this concurrent computation Many-Body Perturbation Theory (ccMBPT). The use of a dynamic load balancing technique on the NEC SX-3/44 computer in electron correlation calculations is investigated for the calculation of the most demanding energy component in the most accurate of contemporary ab initio studies. An application to the ground state of the nitrogen molecule is described. We also briefly discuss the extent to which the calculation of the dominant corrections to such studies can be rendered computationally tractable by exploiting both the vector processing and parallel processor capabilities of the NEC SX-3/44 computer. (author)
International Nuclear Information System (INIS)
Kushnirenko, A.N.
1989-01-01
An attempt was made to substantiate statistical physics from the viewpoint of many-body quantum mechanics in the representation of occupation numbers. This approach enabled to develop the variation method for solution of stationary and nonstationary nonequilibrium problems
International Nuclear Information System (INIS)
Girardeau, M.D.; Oregon Univ., Eugene
1981-01-01
Many problems in several areas of physics and chemistry involve many-body systems of interacting composite particles, in regimes where their internal transitions and/or reactive collisions (breakup, recombination, rearrangement) are important. Standard many-body Green's function and quantum field theoretic techniques are not well adapted to such situations. I discuss generalized representations which allow application of standard techniques to more complicated systems of interacting composite particles and their constituents. (orig./HSI)
Relativistic Dirac-Fock and many-body perturbation calculations on He, He-like ions, Ne, and Ar
International Nuclear Information System (INIS)
Ishikawa, Y.
1990-01-01
Relativistic Dirac-Fock and diagrammatic many-body perturbation-theory calculations have been performed on He, several He-like ions, Ne, and Ar. The no-pair Dirac-Coulomb Hamiltonian is taken as the starting point. A solution of the Dirac-Fock equations is obtained by analytic expansion in basis sets of Gaussian-type functions. Many-body perturbation improvements of Coulomb correlation are done to third order
International Nuclear Information System (INIS)
Appel, H.
2007-05-01
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 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 propagation
Effect of imperfections on the hyperuniformity of many-body systems
Kim, Jaeuk; Torquato, Salvatore
2018-02-01
A hyperuniform many-body system is characterized by a structure factor S (k ) that vanishes in the small-wave-number limit or equivalently by a local number variance σN2(R ) associated with a spherical window of radius R that grows more slowly than Rd in the large-R limit. Thus, the hyperuniformity implies anomalous suppression of long-wavelength density fluctuations relative to those in typical disordered systems, i.e., σN2(R ) ˜Rd as R →∞ . Hyperuniform systems include perfect crystals, quasicrystals, and special disordered systems. Disordered hyperuniform systems are amorphous states of matter that lie between a liquid and crystal [S. Torquato et al., Phys. Rev. X 5, 021020 (2015), 10.1103/PhysRevX.5.021020], and have been the subject of many recent investigations due to their novel properties. In the same way that there is no perfect crystal in practice due to the inevitable presence of imperfections, such as vacancies and dislocations, there is no "perfect" hyperuniform system, whether it is ordered or not. Thus, it is practically and theoretically important to quantitatively understand the extent to which imperfections introduced in a perfectly hyperuniform system can degrade or destroy its hyperuniformity and corresponding physical properties. This paper begins such a program by deriving explicit formulas for S (k ) in the small-wave-number regime for three types of imperfections: (1) uncorrelated point defects, including vacancies and interstitials, (2) stochastic particle displacements, and (3) thermal excitations in the classical harmonic regime. We demonstrate that our results are in excellent agreement with numerical simulations. We find that "uncorrelated" vacancies or interstitials destroy hyperuniformity in proportion to the defect concentration p . We show that "uncorrelated" stochastic displacements in perfect lattices can never destroy the hyperuniformity but it can be degraded such that the perturbed lattices fall into class III
Many-body Anderson localization of strongly interacting bosons in random lattices
International Nuclear Information System (INIS)
Katzer, Roman
2015-05-01
In the present work, we investigate the problem of many-body localization of strongly interacting bosons in random lattices within the disordered Bose-Hubbard model. This involves treating both the local Mott-Hubbard physics as well as the non-local quantum interference processes, which give rise to the phenomenon of Anderson localization, within the same theory. In order to determine the interaction induced transition to the Mott insulator phase, it is necessary to treat the local particle interaction exactly. Therefore, here we use a mean-field approach that approximates only the kinetic term of the Hamiltonian. This way, the full problem of interacting bosons on a random lattice is reduced to a local problem of a single site coupled to a particle bath, which has to be solved self-consistently. In accordance to previous works, we find that a finite disorder width leads to a reduced size of the Mott insulating regions. The transition from the superfluid phase to the Bose glass phase is driven by the non-local effect of Anderson localization. In order to describe this transition, one needs to work within a theory that is non-local as well. Therefore, here we introduce a new approach to the problem. Based on the results for the local excitation spectrum obtained within the mean-field theory, we reduce the full, interacting model to an effective, non-interacting model by applying a truncation scheme to the Hilbert space. Evaluating the long-ranged current density within this approximation, we identify the transition from the Bose glass to the superfluid phase with the Anderson transition of the effective model. Resolving this transition using the self-consistent theory of localization, we obtain the full phase diagram of the disordered Bose-Hubbard model in the regime of strong interaction and larger disorder. In accordance to the theorem of inclusions, we find that the Mott insulator and the superfluid phase are always separated by the compressible, but insulating
Nuclear quantum many-body dynamics: from collective vibrations to heavy-ion collisions
International Nuclear Information System (INIS)
Simenel, Cedric
2012-01-01
This report gives a summary of my research on nuclear dynamics during the past ten years. The choice of this field has been motivated by the desire to understand the physics of complex systems obeying quantum mechanics. In particular, the interplay between collective motion and single-particle degrees of freedom is a source of complex and fascinating behaviours. For instance, giant resonances are characterised by a collective vibration of many nucleons, but their decay may occur by the emission of a single nucleon. Another example could be taken from the collision of nuclei where the transfer of few nucleons may have a strong impact on the formation of a compound system is non trivial. To describe these complex systems, one needs to solve the quantum many-body problem. The description of the dynamics of composite systems can be very challenging, especially when two such systems interact. An important goal of nuclear physics is to find a unified way to describe the dynamics of nuclear systems. Ultimately, the same theoretical model should be able to describe vibrations, rotations, fission, all the possible outcomes of heavy-ion collisions (elastic and inelastic scattering, particle transfer, fusion, and multifragmentation), and even the dynamics of neutron star crust. This desire for a global approach to nuclear dynamics has strongly influenced my research activities. In particular, all the numerical applications presented in this report have been obtained from few numerical codes solving equations derived from the same variational principle. Beside the quest for a unified model of nuclear dynamics, possible applications of heavy-ion collisions such as the formation of new nuclei is also a strong motivation for the experimental and theoretical studies of reaction mechanisms. This report is not a review article, but should be considered as a reading guide of the main papers my collaborators and myself have published. It also gives the opportunity to detail some
Zahedifar, Maedeh; Kratzer, Peter
2018-01-01
Various ab initio approaches to the band structure of A NiSn and A CoSb half-Heusler compounds (A = Ti, Zr, Hf) are compared and their consequences for the prediction of thermoelectric properties are explored. Density functional theory with the generalized-gradient approximation (GGA), as well as the hybrid density functional HSE06 and ab initio many-body perturbation theory in the form of the G W0 approach, are employed. The G W0 calculations confirm the trend of a smaller band gap (0.75 to 1.05 eV) in A NiSn compared to the A CoSb compounds (1.13 to 1.44 eV) already expected from the GGA calculations. While in A NiSn materials the G W0 band gap is 20% to 50% larger than in HSE06, the fundamental gap of A CoSb materials is smaller in G W0 compared to HSE06. This is because G W0 , similar to PBE, locates the valence band maximum at the L point of the Brillouin zone, whereas it is at the Γ point in the HSE06 calculations. The differences are attributed to the observation that the relative positions of the d levels of the transition metal atoms vary among the different methods. Using the calculated band structures and scattering rates taking into account the band effective masses at the extrema, the Seebeck coefficients, thermoelectric power factors, and figures of merit Z T are predicted for all six half-Heusler compounds. Comparable performance is predicted for the n -type A NiSn materials, whereas clear differences are found for the p -type A CoSb materials. Using the most reliable G W0 electronic structure, ZrCoSb is predicted to be the most efficient material with a power factor of up to 0.07 W/(K2 m) at a temperature of 600 K. We find strong variations among the different ab initio methods not only in the prediction of the maximum power factor and Z T value of a given material, but also in comparing different materials to each other, in particular in the p -type thermoelectric materials. Thus we conclude that the most elaborate, but also most costly G W0
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
Numerical methods for strongly correlated many-body systems with bosonic degrees of freedom
International Nuclear Information System (INIS)
Dorfner, Florian Guenter
2017-01-01
dimension also during time evolution. For the polaron problem on an infinite chain Krylov-space time evolution in a limited functional space has been shown to be very efficient. We adapt this algorithm to periodic boundary conditions and show that it is the most efficient method compared to standard Krylov space time evolution and the time-evolving block decimation method. We also study the properties of the local reduced density matrix as a function of model parameters and under non-equilibrium conditions in three different models: the Bose-Bose resonance model, the Holstein model and the Hubbard-Holstein model. It was shown for fermionic and spin models that the single-site von Neumann entropy is an indicator for phase transitions. In the Bose-Bose resonance model we find that both, the local von Neumann entropy and the eigenstates of the local reduced density matrix show features in the vicinity of a phase boundary. Also, we find that the eigenstates of the local reduced density matrix depend on time in quantum quench dynamics. Further, we study the relaxation dynamics of a single electron coupled to Holstein phonons in all parameter regimes. In the adiabatic case a net energy transfer from electron to phonons happens and we provide an analytic formula for the relaxation time in the weak-coupling adiabatic regime. Another main topic in this thesis is thermalization in closed quantum many-body systems. Our first example is the temporal decay of Neel order in the one-dimensional Fermi-Hubbard model. We find evidence that the relaxation dynamics of spin-related quantities are, in the long-time regime, controlled by spin excitations. Further, we study the thermalization of the double occupancy in the framework of the eigenstate thermalization hypothesis and find that it does not thermalize due to integrability of the model. As a second example, we consider many-body localization in a one-dimensional system of spinless fermions with attractive interactions. It is known for
Many-Body Quantum Theory in Condensed Matter Physics-An Introduction
International Nuclear Information System (INIS)
Logan, D E
2005-01-01
This is undoubtedly an ambitious book. It aims to provide a wide ranging, yet self-contained and pedagogical introduction to techniques of quantum many-body theory in condensed matter physics, without losing mathematical 'rigor' (which I hope means rigour), and with an eye on physical insight, motivation and application. The authors certainly bring plenty of experience to the task, the book having grown out of their graduate lectures at the Niels Bohr Institute in Copenhagen over a five year period, with the feedback and refinement this presumably brings. The book is also of course ambitious in another sense, for it competes in the tight market of general graduate/advanced undergraduate texts on many-particle physics. Prospective punters will thus want reasons to prefer it to, or at least give it space beside, well established texts in the field. Subject-wise, the book is a good mix of the ancient and modern, the standard and less so. Obligatory chapters deal with the formal cornerstones of many-body theory, from second quantization, time-dependence in quantum mechanics and linear response theory, to Green's function and Feynman diagrams. Traditional topics are well covered, including two chapters on the electron gas, chapters on phonons and electron-phonon coupling, and a concise account of superconductivity (confined, no doubt judiciously, to the conventional BCS case). Less mandatory, albeit conceptually vital, subjects are also aired. These include a chapter on Fermi liquid theory, from both semi-classical and microscopic perspectives, and a freestanding account of one-dimensional electron gases and Luttinger liquids which, given the enormity of the topic, is about as concise as it could be without sacrificing clarity. Quite naturally, the authors' own interests also influence the choice of material covered. A persistent theme, which brings a healthy topicality to the book, is the area of transport in mesoscopic systems or nanostructures. Two chapters, some
BOOK REVIEW: Many-Body Quantum Theory in Condensed Matter Physics—An Introduction
Logan, D. E.
2005-02-01
This is undoubtedly an ambitious book. It aims to provide a wide ranging, yet self-contained and pedagogical introduction to techniques of quantum many-body theory in condensed matter physics, without losing mathematical `rigor' (which I hope means rigour), and with an eye on physical insight, motivation and application. The authors certainly bring plenty of experience to the task, the book having grown out of their graduate lectures at the Niels Bohr Institute in Copenhagen over a five year period, with the feedback and refinement this presumably brings. The book is also of course ambitious in another sense, for it competes in the tight market of general graduate/advanced undergraduate texts on many-particle physics. Prospective punters will thus want reasons to prefer it to, or at least give it space beside, well established texts in the field. Subject-wise, the book is a good mix of the ancient and modern, the standard and less so. Obligatory chapters deal with the formal cornerstones of many-body theory, from second quantization, time-dependence in quantum mechanics and linear response theory, to Green's function and Feynman diagrams. Traditional topics are well covered, including two chapters on the electron gas, chapters on phonons and electron phonon coupling, and a concise account of superconductivity (confined, no doubt judiciously, to the conventional BCS case). Less mandatory, albeit conceptually vital, subjects are also aired. These include a chapter on Fermi liquid theory, from both semi-classical and microscopic perspectives, and a freestanding account of one-dimensional electron gases and Luttinger liquids which, given the enormity of the topic, is about as concise as it could be without sacrificing clarity. Quite naturally, the authors' own interests also influence the choice of material covered. A persistent theme, which brings a healthy topicality to the book, is the area of transport in mesoscopic systems or nanostructures. Two chapters, some
Numerical methods for strongly correlated many-body systems with bosonic degrees of freedom
Energy Technology Data Exchange (ETDEWEB)
Dorfner, Florian Guenter
2017-02-23
dimension also during time evolution. For the polaron problem on an infinite chain Krylov-space time evolution in a limited functional space has been shown to be very efficient. We adapt this algorithm to periodic boundary conditions and show that it is the most efficient method compared to standard Krylov space time evolution and the time-evolving block decimation method. We also study the properties of the local reduced density matrix as a function of model parameters and under non-equilibrium conditions in three different models: the Bose-Bose resonance model, the Holstein model and the Hubbard-Holstein model. It was shown for fermionic and spin models that the single-site von Neumann entropy is an indicator for phase transitions. In the Bose-Bose resonance model we find that both, the local von Neumann entropy and the eigenstates of the local reduced density matrix show features in the vicinity of a phase boundary. Also, we find that the eigenstates of the local reduced density matrix depend on time in quantum quench dynamics. Further, we study the relaxation dynamics of a single electron coupled to Holstein phonons in all parameter regimes. In the adiabatic case a net energy transfer from electron to phonons happens and we provide an analytic formula for the relaxation time in the weak-coupling adiabatic regime. Another main topic in this thesis is thermalization in closed quantum many-body systems. Our first example is the temporal decay of Neel order in the one-dimensional Fermi-Hubbard model. We find evidence that the relaxation dynamics of spin-related quantities are, in the long-time regime, controlled by spin excitations. Further, we study the thermalization of the double occupancy in the framework of the eigenstate thermalization hypothesis and find that it does not thermalize due to integrability of the model. As a second example, we consider many-body localization in a one-dimensional system of spinless fermions with attractive interactions. It is known for
Gauging Quantum States: From Global to Local Symmetries in Many-Body Systems
Directory of Open Access Journals (Sweden)
Jutho Haegeman
2015-02-01
Full Text Available We present an operational procedure to transform global symmetries into local symmetries at the level of individual quantum states, as opposed to typical gauging prescriptions for Hamiltonians or Lagrangians. We then construct a compatible gauging map for operators, which preserves locality and reproduces the minimal coupling scheme for simple operators. By combining this construction with the formalism of projected entangled-pair states (PEPS, we can show that an injective PEPS for the matter fields is gauged into a G-injective PEPS for the combined gauge-matter system, which potentially has topological order. We derive the corresponding parent Hamiltonian, which is a frustration-free gauge-theory Hamiltonian closely related to the Kogut-Susskind Hamiltonian at zero coupling constant. We can then introduce gauge dynamics at finite values of the coupling constant by applying a local filtering operation. This scheme results in a low-parameter family of gauge-invariant states of which we can accurately probe the phase diagram, as we illustrate by studying a Z_{2} gauge theory with Higgs matter.
Statistical analysis of complex systems with nonclassical invariant measures
Fratalocchi, Andrea
2011-01-01
I investigate the problem of finding a statistical description of a complex many-body system whose invariant measure cannot be constructed stemming from classical thermodynamics ensembles. By taking solitons as a reference system and by employing a
Assessing Many-Body Effects of Water Self-Ions. I: OH-(H2O) n Clusters.
Egan, Colin K; Paesani, Francesco
2018-04-10
The importance of many-body effects in the hydration of the hydroxide ion (OH - ) is investigated through a systematic analysis of the many-body expansion of the interaction energy carried out at the CCSD(T) level of theory, extrapolated to the complete basis set limit, for the low-lying isomers of OH - (H 2 O) n clusters, with n = 1-5. This is accomplished by partitioning individual fragments extracted from the whole clusters into "groups" that are classified by both the number of OH - and water molecules and the hydrogen bonding connectivity within each fragment. With the aid of the absolutely localized molecular orbital energy decomposition analysis (ALMO-EDA) method, this structure-based partitioning is found to largely correlate with the character of different many-body interactions, such as cooperative and anticooperative hydrogen bonding, within each fragment. This analysis emphasizes the importance of a many-body representation of inductive electrostatics and charge transfer in modeling OH - hydration. Furthermore, the rapid convergence of the many-body expansion of the interaction energy also suggests a rigorous path for the development of analytical potential energy functions capable of describing individual OH - -water many-body terms, with chemical accuracy. Finally, a comparison between the reference CCSD(T) many-body interaction terms with the corresponding values obtained with various exchange-correlation functionals demonstrates that range-separated, dispersion-corrected, hybrid functionals exhibit the highest accuracy, while GGA functionals, with or without dispersion corrections, are inadequate to describe OH - -water interactions.
Quantized Hall conductance as a topological invariant
International Nuclear Information System (INIS)
Niu, Q.; Thouless, Ds.J.; Wu, Y.S.
1984-10-01
Whenever the Fermi level lies in a gap (or mobility gap) the bulk Hall conductance can be expressed in a topologically invariant form showing the quantization explicitly. The new formulation generalizes the earlier result by TKNN to the situation where many body interaction and substrate disorder are also present. When applying to the fractional quantized Hall effect we draw the conclusion that there must be a symmetry breaking in the many body ground state. The possibility of writing the fractionally quantized Hall conductance as a topological invariant is also carefully discussed. 19 references
Radjavi, Heydar
2003-01-01
This broad survey spans a wealth of studies on invariant subspaces, focusing on operators on separable Hilbert space. Largely self-contained, it requires only a working knowledge of measure theory, complex analysis, and elementary functional analysis. Subjects include normal operators, analytic functions of operators, shift operators, examples of invariant subspace lattices, compact operators, and the existence of invariant and hyperinvariant subspaces. Additional chapters cover certain results on von Neumann algebras, transitive operator algebras, algebras associated with invariant subspaces,
Thermalization and out-of-equilibrium dynamics in open quantum many-body systems
Energy Technology Data Exchange (ETDEWEB)
Buchhold, Michael
2015-06-30
}-T{sub ∞}∝t{sup -η{sub D}} again witnesses the presence of these slow modes. As an immediate indication of thermalization, we determine the time evolution of the fermionic momentum distribution after a quench from non-interacting to interacting fermions. Finally, we consider a bosonic quantum fluid, which is driven away from equilibrium by permanent heating. The origin of the heating is atomic spontaneous emission of laser photons, which are used to create a coherent lattice potential in optical lattice experiments. This process preserves the system's U(1)-invariance, i.e. conserves the global particle number, and the corresponding long-wavelength description is a heated, interacting Luttinger Liquid, for which phonon modes are continuously populated with a momentum dependent rate ∂{sub t}n{sub q} ∝γ vertical stroke q vertical stroke. In the dynamics, we identify a quasi-thermal regime for large momenta, featuring an increasing time-dependent effective temperature. In this regime, due to fast phonon-phonon scattering, detailed balance has been achieved and is expressed by a time-local, increasing temperature. The thermal region emerges locally and spreads in space sub-ballistically according to x{sub t}∝t{sup 4/5}. For larger distances, the system is described by an non-equilibrium phonon distribution n{sub q}∝ vertical stroke q vertical stroke, which leads to a new, non-equilibrium behavior of large distance observables. This new, universal behavior is guaranteed by the U(1) invariant dynamics of the system and is insensitive to further subleading perturbations. The non-equilibrium long-distance behavior can be determined experimentally by measuring the static and dynamic structure factor, both of which clearly indicate the exponents for phonon decay, η=5/3 and for the spreading of thermalization η{sub T}=4/5.
Gog, Simon; Bader, Martin
2008-10-01
The problem of sorting signed permutations by reversals is a well-studied problem in computational biology. The first polynomial time algorithm was presented by Hannenhalli and Pevzner in 1995. The algorithm was improved several times, and nowadays the most efficient algorithm has a subquadratic running time. Simple permutations played an important role in the development of these algorithms. Although the latest result of Tannier et al. does not require simple permutations, the preliminary version of their algorithm as well as the first polynomial time algorithm of Hannenhalli and Pevzner use the structure of simple permutations. More precisely, the latter algorithms require a precomputation that transforms a permutation into an equivalent simple permutation. To the best of our knowledge, all published algorithms for this transformation have at least a quadratic running time. For further investigations on genome rearrangement problems, the existence of a fast algorithm for the transformation could be crucial. Another important task is the back transformation, i.e. if we have a sorting on the simple permutation, transform it into a sorting on the original permutation. Again, the naive approach results in an algorithm with quadratic running time. In this paper, we present a linear time algorithm for transforming a permutation into an equivalent simple permutation, and an O(n log n) algorithm for the back transformation of the sorting sequence.
International Nuclear Information System (INIS)
Van Leeuwen, Robert; Stefanucci, Gianluca
2013-01-01
We present a unified framework for equilibrium and nonequilibrium many-body perturbation theory. The most general nonequilibrium many-body theory valid for general initial states is based on a time-contour originally introduced by Konstantinov and Perel'. The various other well-known formalisms of Keldysh, Matsubara and the zero-temperature formalism are then derived as special cases that arise under different assumptions. We further present a single simple proof of Wick's theorem that is at the same time valid in all these flavors of many-body theory. It arises simply as a solution of the equations of the Martin-Schwinger hierarchy for the noninteracting many-particle Green's function with appropriate boundary conditions. We further discuss a generalized Wick theorem for general initial states on the Keldysh contour and derive how the formalisms based on the Keldysh and Konstantinov-Perel'-contours are related for the case of general initial states.
Permutation parity machines for neural synchronization
International Nuclear Information System (INIS)
Reyes, O M; Kopitzke, I; Zimmermann, K-H
2009-01-01
Synchronization of neural networks has been studied in recent years as an alternative to cryptographic applications such as the realization of symmetric key exchange protocols. This paper presents a first view of the so-called permutation parity machine, an artificial neural network proposed as a binary variant of the tree parity machine. The dynamics of the synchronization process by mutual learning between permutation parity machines is analytically studied and the results are compared with those of tree parity machines. It will turn out that for neural synchronization, permutation parity machines form a viable alternative to tree parity machines
Exact results for the many-body problem in one dimension with repulsive delta-function interaction
International Nuclear Information System (INIS)
Yang, C.N.
1983-01-01
The repulsive δ interaction problem in one dimension for N particles is reduced, through the use of Bethe's hypothesis, to an eigenvalue problem of matrices of the same sizes as the irreducible representations R of the permutation group S/sub N/. For some R's this eigenvalue problem itself is solved by a second use of Bethe's hypothesis, in a generalized form. In particular, the ground-state problem of spin-1/2 fermions is reduced to a generalized Fredholm equation
Self-consistent many-body perturbation theory in range-separated density-functional theory
DEFF Research Database (Denmark)
Fromager, Emmanuel; Jensen, Hans Jørgen Aagaard
2008-01-01
effects adequately which, on the other hand, can be described by many-body perturbation theory MBPT. It is therefore of interest to develop a hybrid model which combines the best of both the MBPT and DFT approaches. This can be achieved by splitting the two-electron interaction into long-range and short...
DEFF Research Database (Denmark)
Jin, Chengjun; Markussen, Troels; Thygesen, Kristian Sommer
2014-01-01
We investigate the electronic conductance and thermopower of a single-molecule junction consisting of bis-(4-aminophenyl) acetylene (B4APA) connected to gold electrodes. We use nonequilibrium Green's function methods in combination with density-functional theory (DFT) and the many-body GW...
Permutation parity machines for neural cryptography.
Reyes, Oscar Mauricio; Zimmermann, Karl-Heinz
2010-06-01
Recently, synchronization was proved for permutation parity machines, multilayer feed-forward neural networks proposed as a binary variant of the tree parity machines. This ability was already used in the case of tree parity machines to introduce a key-exchange protocol. In this paper, a protocol based on permutation parity machines is proposed and its performance against common attacks (simple, geometric, majority and genetic) is studied.
Permutation parity machines for neural cryptography
International Nuclear Information System (INIS)
Reyes, Oscar Mauricio; Zimmermann, Karl-Heinz
2010-01-01
Recently, synchronization was proved for permutation parity machines, multilayer feed-forward neural networks proposed as a binary variant of the tree parity machines. This ability was already used in the case of tree parity machines to introduce a key-exchange protocol. In this paper, a protocol based on permutation parity machines is proposed and its performance against common attacks (simple, geometric, majority and genetic) is studied.
EPC: A Provably Secure Permutation Based Compression Function
DEFF Research Database (Denmark)
Bagheri, Nasour; Gauravaram, Praveen; Naderi, Majid
2010-01-01
The security of permutation-based hash functions in the ideal permutation model has been studied when the input-length of compression function is larger than the input-length of the permutation function. In this paper, we consider permutation based compression functions that have input lengths sh...
Permutation on hybrid natural inflation
Carone, Christopher D.; Erlich, Joshua; Ramos, Raymundo; Sher, Marc
2014-09-01
We analyze a model of hybrid natural inflation based on the smallest non-Abelian discrete group S3. Leading invariant terms in the scalar potential have an accidental global symmetry that is spontaneously broken, providing a pseudo-Goldstone boson that is identified as the inflaton. The S3 symmetry restricts both the form of the inflaton potential and the couplings of the inflaton field to the waterfall fields responsible for the end of inflation. We identify viable points in the model parameter space. Although the power in tensor modes is small in most of the parameter space of the model, we identify parameter choices that yield potentially observable values of r without super-Planckian initial values of the inflaton field.
Rispoli, Matthew; Lukin, Alexander; Ma, Ruichao; Preiss, Philipp; Tai, M. Eric; Islam, Rajibul; Greiner, Markus
2015-05-01
Ultracold atoms in optical lattices provide a versatile tool box for observing the emergence of strongly correlated physics in quantum systems. Dynamic control of optical potentials on the single-site level allows us to prepare and probe many-body quantum states through local Hamiltonian engineering. We achieve these high precision levels of optical control through spatial light modulation with a DMD (digital micro-mirror device). This allows for both arbitrary beam shaping and aberration compensation in our imaging system to produce high fidelity optical potentials. We use these techniques to control state initialization, Hamiltonian dynamics, and measurement in experiments investigating low-dimensional many-body physics - from one-dimensional correlated quantum walks to characterizing entanglement.
Quantum gases. Observation of many-body dynamics in long-range tunneling after a quantum quench.
Meinert, Florian; Mark, Manfred J; Kirilov, Emil; Lauber, Katharina; Weinmann, Philipp; Gröbner, Michael; Daley, Andrew J; Nägerl, Hanns-Christoph
2014-06-13
Quantum tunneling is at the heart of many low-temperature phenomena. In strongly correlated lattice systems, tunneling is responsible for inducing effective interactions, and long-range tunneling substantially alters many-body properties in and out of equilibrium. We observe resonantly enhanced long-range quantum tunneling in one-dimensional Mott-insulating Hubbard chains that are suddenly quenched into a tilted configuration. Higher-order tunneling processes over up to five lattice sites are observed as resonances in the number of doubly occupied sites when the tilt per site is tuned to integer fractions of the Mott gap. This forms a basis for a controlled study of many-body dynamics driven by higher-order tunneling and demonstrates that when some degrees of freedom are frozen out, phenomena that are driven by small-amplitude tunneling terms can still be observed. Copyright © 2014, American Association for the Advancement of Science.
Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space
Directory of Open Access Journals (Sweden)
J. Schachenmayer
2015-02-01
Full Text Available Interacting spin systems are of fundamental relevance in different areas of physics, as well as in quantum information science and biology. These spin models represent the simplest, yet not fully understood, manifestation of quantum many-body systems. An important outstanding problem is the efficient numerical computation of dynamics in large spin systems. Here, we propose a new semiclassical method to study many-body spin dynamics in generic spin lattice models. The method is based on a discrete Monte Carlo sampling in phase space in the framework of the so-called truncated Wigner approximation. Comparisons with analytical and numerically exact calculations demonstrate the power of the technique. They show that it correctly reproduces the dynamics of one- and two-point correlations and spin squeezing at short times, thus capturing entanglement. Our results open the possibility to study the quantum dynamics accessible to recent experiments in regimes where other numerical methods are inapplicable.
Sous, John; Grant, Edward
2018-03-01
We argue that the quenched ultracold plasma presents an experimental platform for studying the quantum many-body physics of disordered systems in the long-time and finite energy-density limits. We consider an experiment that quenches a plasma of nitric oxide to an ultracold system of Rydberg molecules, ions, and electrons that exhibits a long-lived state of arrested relaxation. The qualitative features of this state fail to conform with classical models. Here, we develop a microscopic quantum description for the arrested phase based on an effective many-body spin Hamiltonian that includes both dipole-dipole and van der Waals interactions. This effective model appears to offer a way to envision the essential quantum disordered nonequilibrium physics of this system.
Agrawal, Piyush; Tkatchenko, Alexandre; Kronik, Leeor
2013-08-13
We propose a nonempirical, pair-wise or many-body dispersion-corrected, optimally tuned range-separated hybrid functional. This functional retains the advantages of the optimal-tuning approach in the prediction of the electronic structure. At the same time, it gains accuracy in the prediction of binding energies for dispersively bound systems, as demonstrated on the S22 and S66 benchmark sets of weakly bound dimers.
Mazzucchi, Gabriel; Kozlowski, Wojciech; Caballero-Benitez, Santiago F.; Elliott, Thomas J.; Mekhov, Igor B.
2016-02-01
Trapping ultracold atoms in optical lattices enabled numerous breakthroughs uniting several disciplines. Coupling these systems to quantized light leads to a plethora of new phenomena and has opened up a new field of study. Here we introduce an unusual additional source of competition in a many-body strongly correlated system: We prove that quantum backaction of global measurement is able to efficiently compete with intrinsic short-range dynamics of an atomic system. The competition becomes possible due to the ability to change the spatial profile of a global measurement at a microscopic scale comparable to the lattice period without the need of single site addressing. In coherence with a general physical concept, where new competitions typically lead to new phenomena, we demonstrate nontrivial dynamical effects such as large-scale multimode oscillations, long-range entanglement, and correlated tunneling, as well as selective suppression and enhancement of dynamical processes beyond the projective limit of the quantum Zeno effect. We demonstrate both the breakup and protection of strongly interacting fermion pairs by measurement. Such a quantum optical approach introduces into many-body physics novel processes, objects, and methods of quantum engineering, including the design of many-body entangled environments for open systems.
International Nuclear Information System (INIS)
Balatsky, A.V.; Scalapino, D.; Wilkins, J.; Pines, D.; Bedell, K.; Schrieffer, J.R.; Fisk, Z.
1998-01-01
This is the final report of a two-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The authors have obtained a description of symmetry of the order parameter and pairing state in high-Tc superconductors. They developed a theory of ferromagnetic instability of Fermi-liquid. They have conducted an experimental investigation of the intermetallic compounds and Zintl-type compound. They investigated the properties of Cu-0 ladders. They have developed the theory of liftshitz tails in superconductors. They have conducted a number of summer workshops
Permutation statistical methods an integrated approach
Berry, Kenneth J; Johnston, Janis E
2016-01-01
This research monograph provides a synthesis of a number of statistical tests and measures, which, at first consideration, appear disjoint and unrelated. Numerous comparisons of permutation and classical statistical methods are presented, and the two methods are compared via probability values and, where appropriate, measures of effect size. Permutation statistical methods, compared to classical statistical methods, do not rely on theoretical distributions, avoid the usual assumptions of normality and homogeneity of variance, and depend only on the data at hand. This text takes a unique approach to explaining statistics by integrating a large variety of statistical methods, and establishing the rigor of a topic that to many may seem to be a nascent field in statistics. This topic is new in that it took modern computing power to make permutation methods available to people working in the mainstream of research. This research monograph addresses a statistically-informed audience, and can also easily serve as a ...
International Nuclear Information System (INIS)
Mackrodt, C.; Reeh, H.
1997-01-01
General summational invariants, i.e., conservation laws acting additively on asymptotic particle states, are investigated within a classical framework for point particles with nontrivial scattering. copyright 1997 American Institute of Physics
Sorting signed permutations by short operations.
Galvão, Gustavo Rodrigues; Lee, Orlando; Dias, Zanoni
2015-01-01
During evolution, global mutations may alter the order and the orientation of the genes in a genome. Such mutations are referred to as rearrangement events, or simply operations. In unichromosomal genomes, the most common operations are reversals, which are responsible for reversing the order and orientation of a sequence of genes, and transpositions, which are responsible for switching the location of two contiguous portions of a genome. The problem of computing the minimum sequence of operations that transforms one genome into another - which is equivalent to the problem of sorting a permutation into the identity permutation - is a well-studied problem that finds application in comparative genomics. There are a number of works concerning this problem in the literature, but they generally do not take into account the length of the operations (i.e. the number of genes affected by the operations). Since it has been observed that short operations are prevalent in the evolution of some species, algorithms that efficiently solve this problem in the special case of short operations are of interest. In this paper, we investigate the problem of sorting a signed permutation by short operations. More precisely, we study four flavors of this problem: (i) the problem of sorting a signed permutation by reversals of length at most 2; (ii) the problem of sorting a signed permutation by reversals of length at most 3; (iii) the problem of sorting a signed permutation by reversals and transpositions of length at most 2; and (iv) the problem of sorting a signed permutation by reversals and transpositions of length at most 3. We present polynomial-time solutions for problems (i) and (iii), a 5-approximation for problem (ii), and a 3-approximation for problem (iv). Moreover, we show that the expected approximation ratio of the 5-approximation algorithm is not greater than 3 for random signed permutations with more than 12 elements. Finally, we present experimental results that show
Communication: Fitting potential energy surfaces with fundamental invariant neural network
Energy Technology Data Exchange (ETDEWEB)
Shao, Kejie; Chen, Jun; Zhao, Zhiqiang; Zhang, Dong H., E-mail: zhangdh@dicp.ac.cn [State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, People’s Republic of China and University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China. (China)
2016-08-21
A more flexible neural network (NN) method using the fundamental invariants (FIs) as the input vector is proposed in the construction of potential energy surfaces for molecular systems involving identical atoms. Mathematically, FIs finitely generate the permutation invariant polynomial (PIP) ring. In combination with NN, fundamental invariant neural network (FI-NN) can approximate any function to arbitrary accuracy. Because FI-NN minimizes the size of input permutation invariant polynomials, it can efficiently reduce the evaluation time of potential energy, in particular for polyatomic systems. In this work, we provide the FIs for all possible molecular systems up to five atoms. Potential energy surfaces for OH{sub 3} and CH{sub 4} were constructed with FI-NN, with the accuracy confirmed by full-dimensional quantum dynamic scattering and bound state calculations.
1-Colored Archetypal Permutations and Strings of Degree n
Directory of Open Access Journals (Sweden)
Gheorghe Eduard Tara
2012-10-01
Full Text Available New notions related to permutations are introduced here. We present the string of a 1-colored permutation as a closed planar curve, the fundamental 1-colored permutation as an equivalence class related to the equivalence in strings of the 1-colored permutations. We give formulas for the number of the 1-colored archetypal permutations of degree n. We establish an algorithm to identify the 1- colored archetypal permutations of degree n and we present the atlas of the 1-colored archetypal strings of degree n, n ≤ 7, based on this algorithm.
Ciofi degli Atti, Claudio; Morita, Hiko
2017-12-01
Background: The nuclear spectral function is a fundamental quantity that describes the mean-field and short-range correlation dynamics of nucleons embedded in the nuclear medium; its knowledge is a prerequisite for the interpretation of various electroweak scattering processes off nuclear targets aimed at providing fundamental information on strong and weak interactions. Whereas in the case of the three-nucleon and, partly, the four-nucleon systems, the spectral function can be calculated ab initio within a nonrelativistic many-body Schroedinger approach, in the case of complex nuclei only models of the correlated, high-momentum part of the spectral function are available so far. Purpose: The purpose of this paper is to present a new approach such that the spectral function for a specific nucleus can be obtained from a reliable many-body calculation based upon realistic nucleon-nucleon interactions, thus avoiding approximations leading to adjustable parameters. Methods: The expectation value of the nuclear many-body Hamiltonian, containing realistic nucleon-nucleon interaction of the Argonne family, is evaluated variationally by a normalization-conserving linked-cluster expansion and the resulting many-body correlated wave functions are used to calculate the one-nucleon and the two-nucleon momentum distributions; by analyzing the high-momentum behavior of the latter, the spectral function can be expressed in terms of a transparent convolution formula involving the relative and center-of-mass (c.m.) momentum distributions in specific regions of removal energy E and momentum k . Results: It is found that as a consequence of the factorization of the many-body wave functions at short internucleon separations, the high-momentum behavior of the two-nucleon momentum distributions in A =3 ,4 ,12 ,16 ,40 nuclei factorizes, at proper values of the relative and c.m. momenta, into the c.m. and relative momentum distributions, with the latter exhibiting a universal A
Time-dependent restricted-active-space self-consistent-field theory for bosonic many-body systems
International Nuclear Information System (INIS)
Lévêque, Camille; Madsen, Lars Bojer
2017-01-01
We develop an ab initio time-dependent wavefunction based theory for the description of a many-body system of cold interacting bosons. Like the multi-configurational time-dependent Hartree method for bosons (MCTDHB), the theory is based on a configurational interaction Ansatz for the many-body wavefunction with time-dependent self-consistent-field orbitals. The theory generalizes the MCTDHB method by incorporating restrictions on the active space of the orbital excitations. The restrictions are specified based on the physical situation at hand. The equations of motion of this time-dependent restricted-active-space self-consistent-field (TD-RASSCF) theory are derived. The similarity between the formal development of the theory for bosons and fermions is discussed. The restrictions on the active space allow the theory to be evaluated under conditions where other wavefunction based methods due to exponential scaling in the numerical effort cannot, and to clearly identify the excitations that are important for an accurate description, significantly beyond the mean-field approach. For ground state calculations we find it to be important to allow a few particles to have the freedom to move in many orbitals, an insight facilitated by the flexibility of the restricted-active-space Ansatz . Moreover, we find that a high accuracy can be obtained by including only even excitations in the many-body self-consistent-field wavefunction. Time-dependent simulations of harmonically trapped bosons subject to a quenching of their noncontact interaction, show failure of the mean-field Gross-Pitaevskii approach within a fraction of a harmonic oscillation period. The TD-RASSCF theory remains accurate at much reduced computational cost compared to the MCTDHB method. Exploring the effect of changes of the restricted-active-space allows us to identify that even self-consistent-field excitations are mainly responsible for the accuracy of the method. (paper)
Monthus, Cécile
2018-03-01
For the many-body-localized phase of random Majorana models, a general strong disorder real-space renormalization procedure known as RSRG-X (Pekker et al 2014 Phys. Rev. X 4 011052) is described to produce the whole set of excited states, via the iterative construction of the local integrals of motion (LIOMs). The RG rules are then explicitly derived for arbitrary quadratic Hamiltonians (free-fermions models) and for the Kitaev chain with local interactions involving even numbers of consecutive Majorana fermions. The emphasis is put on the advantages of the Majorana language over the usual quantum spin language to formulate unified RSRG-X rules.
Role of many-body effects in the coherent dynamics of excitons in low-temperature-grown GaAs
Energy Technology Data Exchange (ETDEWEB)
Webber, D.; Hacquebard, L.; Hall, K. C. [Department of Physics and Atmospheric Science, Dalhousie University, Halifax, Nova Scotia B3H 4R2 (Canada); Liu, X.; Dobrowolska, M.; Furdyna, J. K. [Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556 (United States)
2015-10-05
Femtosecond four-wave mixing experiments on low-temperature-grown (LT-) GaAs indicate a polarization-dependent nonlinear optical response at the exciton, which we attribute to Coulomb-mediated coupling between excitons and electron-hole pairs simultaneously excited by the broad-bandwidth laser pulses. Strong suppression of the exciton response through screening by carriers injected by a third pump pulse was observed, an effect that is transient due to rapid carrier trapping. Our findings highlight the need to account for the complex interplay of disorder and many-body effects in the design of ultrafast optoelectronic devices using this material.
Umari, P; Petrenko, O; Taioli, S; De Souza, M M
2012-05-14
Electronic band gaps for optically allowed transitions are calculated for a series of semiconducting single-walled zig-zag carbon nanotubes of increasing diameter within the many-body perturbation theory GW method. The dependence of the evaluated gaps with respect to tube diameters is then compared with those found from previous experimental data for optical gaps combined with theoretical estimations of exciton binding energies. We find that our GW gaps confirm the behavior inferred from experiment. The relationship between the electronic gap and the diameter extrapolated from the GW values is also in excellent agreement with a direct measurement recently performed through scanning tunneling spectroscopy.
Permutation Tests for Stochastic Ordering and ANOVA
Basso, Dario; Salmaso, Luigi; Solari, Aldo
2009-01-01
Permutation testing for multivariate stochastic ordering and ANOVA designs is a fundamental issue in many scientific fields such as medicine, biology, pharmaceutical studies, engineering, economics, psychology, and social sciences. This book presents advanced methods and related R codes to perform complex multivariate analyses
N ecklaces~ Periodic Points and Permutation Representations
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 11. Necklaces, Periodic Points and Permutation Representations - Fermat's Little Theorem. Somnath Basu Anindita Bose Sumit Kumar Sinha Pankaj Vishe. General Article Volume 6 Issue 11 November 2001 pp 18-26 ...
International Nuclear Information System (INIS)
Bereau, Tristan; Lilienfeld, O. Anatole von
2014-01-01
We estimate polarizabilities of atoms in molecules without electron density, using a Voronoi tesselation approach instead of conventional density partitioning schemes. The resulting atomic dispersion coefficients are calculated, as well as many-body dispersion effects on intermolecular potential energies. We also estimate contributions from multipole electrostatics and compare them to dispersion. We assess the performance of the resulting intermolecular interaction model from dispersion and electrostatics for more than 1300 neutral and charged, small organic molecular dimers. Applications to water clusters, the benzene crystal, the anti-cancer drug ellipticine—intercalated between two Watson-Crick DNA base pairs, as well as six macro-molecular host-guest complexes highlight the potential of this method and help to identify points of future improvement. The mean absolute error made by the combination of static electrostatics with many-body dispersion reduces at larger distances, while it plateaus for two-body dispersion, in conflict with the common assumption that the simple 1/R 6 correction will yield proper dissociative tails. Overall, the method achieves an accuracy well within conventional molecular force fields while exhibiting a simple parametrization protocol
Energy Technology Data Exchange (ETDEWEB)
Myo, Takayuki, E-mail: takayuki.myo@oit.ac.jp [General Education, Faculty of Engineering, Osaka Institute of Technology, Osaka 535-8585 (Japan); Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki 567-0047 (Japan); Toki, Hiroshi [Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki 567-0047 (Japan); Ikeda, Kiyomi [RIKEN Nishina Center, Wako, Saitama 351-0198 (Japan); Horiuchi, Hisashi [Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki 567-0047 (Japan); Suhara, Tadahiro [Matsue College of Technology, Matsue 690-8518 (Japan)
2017-06-10
We study the tensor-optimized antisymmetrized molecular dynamics (TOAMD) as a successive variational method in many-body systems with strong interaction for nuclei. In TOAMD, the correlation functions for the tensor force and the short-range repulsion and their multiples are operated to the AMD state as the variational wave function. The total wave function is expressed as the sum of all the components and the variational space can be increased successively with the multiple correlation functions to achieve convergence. All the necessary matrix elements of many-body operators, consisting of the multiple correlation functions and the Hamiltonian, are expressed analytically using the Gaussian integral formula. In this paper we show the results of TOAMD with up to the double products of the correlation functions for the s-shell nuclei, {sup 3}H and {sup 4}He, using the nucleon–nucleon interaction AV8′. It is found that the energies and Hamiltonian components of two nuclei converge rapidly with respect to the multiple of correlation functions. This result indicates the efficiency of TOAMD for the power series expansion in terms of the tensor and short-range correlation functions.
International Nuclear Information System (INIS)
Zhang Lu-Lu; Song Yu-Zhi; Gao Shou-Bao; Zhang Yuan; Meng Qing-Tian
2016-01-01
A globally accurate single-sheeted double many-body expansion potential energy surface is reported for the first excited state of HS 2 by fitting the accurate ab initio energies, which are calculated at the multireference configuration interaction level with the aug-cc-pV Q Z basis set. By using the double many-body expansion-scaled external correlation method, such calculated ab initio energies are then slightly corrected by scaling their dynamical correlation. A grid of 2767 ab initio energies is used in the least-square fitting procedure with the total root-mean square deviation being 1.406 kcal·mol −1 . The topographical features of the HS 2 (A 2 A′) global potential energy surface are examined in detail. The attributes of the stationary points are presented and compared with the corresponding ab initio results as well as experimental and other theoretical data, showing good agreement. The resulting potential energy surface of HS 2 (A 2 A′) can be used as a building block for constructing the global potential energy surfaces of larger S/H molecular systems and recommended for dynamic studies on the title molecular system. (paper)
Sandler, U.
2017-11-01
In this paper, we extend our generalized Lagrangian dynamics (i.e., S-Lagrangian dynamics, which can be applied equally to physical and non-physical systems as per Sandler (2014)) to many-body systems. Unlike common Lagrangian dynamics, this is not a trivial task. For many-body systems with S-dependent Lagrangians, the Lagrangian and the corresponding Hamiltonian or energy become vector functions, conjugated momenta become second-order tensors, and the system inevitably develops a hierarchical structure, even if all bodies initially have similar status and Lagrangians. As an application of our theory, we consider dominance and hierarchy formation, which is present in almost all communities of living species. As a biological basis for this application, we assume that the primary motivation of a groups activity is to attempt to cope with stress arising as pressure from the environment and from intrinsic unmet needs of individuals. It has been shown that the S-Lagrangian approach to a group's evolution naturally leads to formation of linear or despotic dominance hierarchies, depending on differences between individuals in coping with stress. That is, individuals that cope more readily with stress take leadership roles during the evolution. Experimental results in animal groups which support our assumption and findings are considered.
International Nuclear Information System (INIS)
Sanders, Lloyd P; Fogelmark, Karl; Ambjörnsson, Tobias; Lomholt, Michael A; Lizana, Ludvig; Metzler, Ralf
2014-01-01
Low-dimensional, many-body systems are often characterized by ultraslow dynamics. We study a labelled particle in a generic system of identical particles with hard-core interactions in a strongly disordered environment. The disorder is manifested through intermittent motion with scale-free sticking times at the single particle level. While for a non-interacting particle we find anomalous diffusion of the power-law form 〈x 2 (t)〉≃t α of the mean squared displacement with 0<α<1, we demonstrate here that the combination of the disordered environment with the many-body interactions leads to an ultraslow, logarithmic dynamics 〈x 2 (t)〉≃log 1/2 t with a universal 1/2 exponent. Even when a characteristic sticking time exists but the fluctuations of sticking times diverge we observe the mean squared displacement 〈x 2 (t)〉≃t γ with 0<γ<1/2, that is slower than the famed Harris law 〈x 2 (t)〉≃t 1/2 without disorder. We rationalize the results in terms of a subordination to a counting process, in which each transition is dominated by the forward waiting time of an ageing continuous time process. (paper)
Directory of Open Access Journals (Sweden)
Phillip Weinberg, Marin Bukov
2017-02-01
Full Text Available We present a new open-source Python package for exact diagonalization and quantum dynamics of spin(-photon chains, called QuSpin, supporting the use of various symmetries in 1-dimension and (imaginary time evolution for chains up to 32 sites in length. The package is well-suited to study, among others, quantum quenches at finite and infinite times, the Eigenstate Thermalisation hypothesis, many-body localisation and other dynamical phase transitions, periodically-driven (Floquet systems, adiabatic and counter-diabatic ramps, and spin-photon interactions. Moreover, QuSpin's user-friendly interface can easily be used in combination with other Python packages which makes it amenable to a high-level customisation. We explain how to use QuSpin using four detailed examples: (i Standard exact diagonalisation of XXZ chain (ii adiabatic ramping of parameters in the many-body localised XXZ model, (iii heating in the periodically-driven transverse-field Ising model in a parallel field, and (iv quantised light-atom interactions: recovering the periodically-driven atom in the semi-classical limit of a static Hamiltonian.
Klaiman, S.; Streltsov, A. I.; Alon, O. E.
2018-04-01
A solvable model of a generic trapped bosonic mixture, N 1 bosons of mass m 1 and N 2 bosons of mass m 2 trapped in an harmonic potential of frequency ω and interacting by harmonic inter-particle interactions of strengths λ 1, λ 2, and λ 12, is discussed. It has recently been shown for the ground state [J. Phys. A 50, 295002 (2017)] that in the infinite-particle limit, when the interaction parameters λ 1(N 1 ‑ 1), λ 2(N 2 ‑ 1), λ 12 N 1, λ 12 N 2 are held fixed, each of the species is 100% condensed and its density per particle as well as the total energy per particle are given by the solution of the coupled Gross-Pitaevskii equations of the mixture. In the present work we investigate properties of the trapped generic mixture at the infinite-particle limit, and find differences between the many-body and mean-field descriptions of the mixture, despite each species being 100%. We compute analytically and analyze, both for the mixture and for each species, the center-of-mass position and momentum variances, their uncertainty product, the angular-momentum variance, as well as the overlap of the exact and Gross-Pitaevskii wavefunctions of the mixture. The results obtained in this work can be considered as a step forward in characterizing how important are many-body effects in a fully condensed trapped bosonic mixture at the infinite-particle limit.
Energy Technology Data Exchange (ETDEWEB)
Bereau, Tristan, E-mail: bereau@mpip-mainz.mpg.de [Max-Planck-Institut für Polymerforschung, Ackermannweg 10, 55128 Mainz, Germany and Department of Chemistry, University of Basel, 4056 Basel (Switzerland); Lilienfeld, O. Anatole von [Department of Chemistry, Institute of Physical Chemistry, University of Basel, 4056 Basel, Switzerland and Argonne Leadership Computing Facility, Argonne National Laboratory, Argonne, Illinois 60439 (United States)
2014-07-21
We estimate polarizabilities of atoms in molecules without electron density, using a Voronoi tesselation approach instead of conventional density partitioning schemes. The resulting atomic dispersion coefficients are calculated, as well as many-body dispersion effects on intermolecular potential energies. We also estimate contributions from multipole electrostatics and compare them to dispersion. We assess the performance of the resulting intermolecular interaction model from dispersion and electrostatics for more than 1300 neutral and charged, small organic molecular dimers. Applications to water clusters, the benzene crystal, the anti-cancer drug ellipticine—intercalated between two Watson-Crick DNA base pairs, as well as six macro-molecular host-guest complexes highlight the potential of this method and help to identify points of future improvement. The mean absolute error made by the combination of static electrostatics with many-body dispersion reduces at larger distances, while it plateaus for two-body dispersion, in conflict with the common assumption that the simple 1/R{sup 6} correction will yield proper dissociative tails. Overall, the method achieves an accuracy well within conventional molecular force fields while exhibiting a simple parametrization protocol.
Defects and permutation branes in the Liouville field theory
DEFF Research Database (Denmark)
Sarkissian, Gor
2009-01-01
The defects and permutation branes for the Liouville field theory are considered. By exploiting cluster condition, equations satisfied by permutation branes and defects reflection amplitudes are obtained. It is shown that two types of solutions exist, discrete and continuous families.......The defects and permutation branes for the Liouville field theory are considered. By exploiting cluster condition, equations satisfied by permutation branes and defects reflection amplitudes are obtained. It is shown that two types of solutions exist, discrete and continuous families....
Complete permutation Gray code implemented by finite state machine
Directory of Open Access Journals (Sweden)
Li Peng
2014-09-01
Full Text Available An enumerating method of complete permutation array is proposed. The list of n! permutations based on Gray code defined over finite symbol set Z(n = {1, 2, …, n} is implemented by finite state machine, named as n-RPGCF. An RPGCF can be used to search permutation code and provide improved lower bounds on the maximum cardinality of a permutation code in some cases.
Moores, Brad A.; Sletten, Lucas R.; Viennot, Jeremie; Lehnert, K. W.
Man-made systems of interacting qubits are a promising and powerful way of exploring many-body spin physics beyond classical computation. Although transmon qubits are perhaps the most advanced quantum computing technology, building a system of such qubits designed to emulate a system of many interacting spins is hindered by the mismatch of scales between the transmons and the electromagnetic modes that couple them. We propose a strategy to overcome this mismatch by using surface acoustic waves, which couple to qubits piezoelectrically and have micron wavelengths at GHz frequencies. In this talk, we will present characterizations of transmon qubits fabricated on a piezoelectric material, and show that their coherence properties are sufficient to explore acoustically mediated qubit interactions.
Directory of Open Access Journals (Sweden)
Benjamin Siegert
2015-12-01
Full Text Available The interplay of exchange correlations and spin–orbit interaction (SOI on the many-body spectrum of a copper phtalocyanine (CuPc molecule and their signatures in transport are investigated. We first derive a minimal model Hamiltonian in a basis of frontier orbitals that is able to reproduce experimentally observed singlet–triplet splittings. In a second step SOI effects are included perturbatively. Major consequences of the SOI are the splitting of former degenerate levels and a magnetic anisotropy, which can be captured by an effective low-energy spin Hamiltonian. We show that scanning tunneling microscopy-based magnetoconductance measurements can yield clear signatures of both these SOI-induced effects.
Energy Technology Data Exchange (ETDEWEB)
Babichenko, V.S. [RRC Kurchatov Institute, Kurchatov Sq., 1, 123182 Moscow (Russian Federation); Polishchuk, I.Ya., E-mail: iyppolishchuk@gmail.com [RRC Kurchatov Institute, Kurchatov Sq., 1, 123182 Moscow (Russian Federation); Moscow Institute of Physics and Technology, 141700, 9, Institutskii per., Dolgoprudny, Moscow Region (Russian Federation)
2014-11-15
The many-body correlation effects in the spatially separated electron and hole layers in the coupled quantum wells are investigated. A special case of the many-component electron–hole system is considered. It is shown that if the hole mass is much greater than the electron mass, the negative correlation energy is mainly determined by the holes. The ground state of the system is found to be the 2D electron–hole liquid with the energy smaller than the exciton phase. It is shown that the system decays into the spatially separated neutral electron–hole drops if the initially created charge density in the layers is smaller than the certain critical value n{sub eq}.
Haber, Jonah; Refaely-Abramson, Sivan; da Jornada, Felipe H.; Louie, Steven G.; Neaton, Jeffrey B.
Multi-exciton generation processes, in which multiple charge carriers are generated from a single photon, are mechanisms of significant interest for achieving efficiencies beyond the Shockley-Queisser limit of conventional p-n junction solar cells. One well-studied multiexciton process is singlet fission, whereby a singlet decays into two spin-correlated triplet excitons. Here, we use a newly developed computational approach to calculate singlet-fission coupling terms and rates with an ab initio Green's function formalism based on many-body perturbation theory (MBPT) within the GW approximation and the Bethe-Salpeter equation approach. We compare results for crystalline pentacene and TIPS-pentacene and explore the effect of molecular packing on the singlet fission mechanism. This work is supported by the Department of Energy.
Quantum many-body effects in x-ray spectra efficiently computed using a basic graph algorithm
Liang, Yufeng; Prendergast, David
2018-05-01
The growing interest in using x-ray spectroscopy for refined materials characterization calls for an accurate electronic-structure theory to interpret the x-ray near-edge fine structure. In this work, we propose an efficient and unified framework to describe all the many-electron processes in a Fermi liquid after a sudden perturbation (such as a core hole). This problem has been visited by the Mahan-Noziéres-De Dominicis (MND) theory, but it is intractable to implement various Feynman diagrams within first-principles calculations. Here, we adopt a nondiagrammatic approach and treat all the many-electron processes in the MND theory on an equal footing. Starting from a recently introduced determinant formalism [Phys. Rev. Lett. 118, 096402 (2017), 10.1103/PhysRevLett.118.096402], we exploit the linear dependence of determinants describing different final states involved in the spectral calculations. An elementary graph algorithm, breadth-first search, can be used to quickly identify the important determinants for shaping the spectrum, which avoids the need to evaluate a great number of vanishingly small terms. This search algorithm is performed over the tree-structure of the many-body expansion, which mimics a path-finding process. We demonstrate that the determinantal approach is computationally inexpensive even for obtaining x-ray spectra of extended systems. Using Kohn-Sham orbitals from two self-consistent fields (ground and core-excited state) as input for constructing the determinants, the calculated x-ray spectra for a number of transition metal oxides are in good agreement with experiments. Many-electron aspects beyond the Bethe-Salpeter equation, as captured by this approach, are also discussed, such as shakeup excitations and many-body wave function overlap considered in Anderson's orthogonality catastrophe.
Universal many-body response of heavy impurities coupled to a Fermi sea: a review of recent progress
Schmidt, Richard; Knap, Michael; Ivanov, Dmitri A.; You, Jhih-Shih; Cetina, Marko; Demler, Eugene
2018-02-01
In this report we discuss the dynamical response of heavy quantum impurities immersed in a Fermi gas at zero and at finite temperature. Studying both the frequency and the time domain allows one to identify interaction regimes that are characterized by distinct many-body dynamics. From this theoretical study a picture emerges in which impurity dynamics is universal on essentially all time scales, and where the high-frequency few-body response is related to the long-time dynamics of the Anderson orthogonality catastrophe by Tan relations. Our theoretical description relies on different and complementary approaches: functional determinants give an exact numerical solution for time- and frequency-resolved responses, bosonization provides accurate analytical expressions at low temperatures, and the theory of Toeplitz determinants allows one to analytically predict response up to high temperatures. Using these approaches we predict the thermal decoherence rate of the fermionic system and prove that within the considered model the fastest rate of long-time decoherence is given by γ=π k_BT/4 . We show that Feshbach resonances in cold atomic systems give access to new interaction regimes where quantum effects can prevail even in the thermal regime of many-body dynamics. The key signature of this phenomenon is a crossover between different exponential decay rates of the real-time Ramsey signal. It is shown that the physics of the orthogonality catastrophe is experimentally observable up to temperatures T/T_F≲ 0.2 where it leaves its fingerprint in a power-law temperature dependence of thermal spectral weight and we review how this phenomenon is related to the physics of heavy ions in liquid {\\hspace{0pt}}3 He and the formation of Fermi polarons. The presented results are in excellent agreement with recent experiments on LiK mixtures, and we predict several new phenomena that can be tested using currently available experimental technology.
Permutation Entropy: New Ideas and Challenges
Directory of Open Access Journals (Sweden)
Karsten Keller
2017-03-01
Full Text Available Over recent years, some new variants of Permutation entropy have been introduced and applied to EEG analysis, including a conditional variant and variants using some additional metric information or being based on entropies that are different from the Shannon entropy. In some situations, it is not completely clear what kind of information the new measures and their algorithmic implementations provide. We discuss the new developments and illustrate them for EEG data.
International Nuclear Information System (INIS)
Noordhoek, Mark J.; Liang, Tao; Chiang, Tsu-Wu; Sinnott, Susan B.; Phillpot, Simon R.
2014-01-01
Highlights: • An interatomic potential for zirconium–zirconium oxide–zirconium hydride is presented. • Diffusion of oxygen and hydrogen into Zr (0 0 0 1). • Deposition of O 2 and H 2 O on low-index Zr surfaces. • Surface structure affects resulting corrosion behavior. - Abstract: A charge-optimized many-body (COMB) potential is proposed for the zirconium–zirconium oxide–zirconium hydride system. This potential is developed to describe the energetics of the interactions of oxygen and hydrogen with zirconium metal. We perform classical molecular dynamics simulations showing the initial corrosion behavior of three low-index zirconium surfaces via the deposition of O 2 and H 2 O molecules. The basal (0 0 0 1) surface shows greater resistance to oxygen diffusion than the prism (101 ¯ 0) and (112 ¯ 0) surfaces. We suggest ways in which the surface structure has a unique role in the experimentally observed enhanced corrosion of the prism surfaces
Baumeier, Björn; Andrienko, Denis; Rohlfing, Michael
2012-08-14
Excited states of donor-acceptor dimers are studied using many-body Green's functions theory within the GW approximation and the Bethe-Salpeter equation. For a series of prototypical small-molecule based pairs, this method predicts energies of local Frenkel and intermolecular charge-transfer excitations with the accuracy of tens of meV. Application to larger systems is possible and allowed us to analyze energy levels and binding energies of excitons in representative dimers of dicyanovinyl-substituted quarterthiophene and fullerene, a donor-acceptor pair used in state of the art organic solar cells. In these dimers, the transition from Frenkel to charge transfer excitons is endothermic and the binding energy of charge transfer excitons is still of the order of 1.5-2 eV. Hence, even such an accurate dimer-based description does not yield internal energetics favorable for the generation of free charges either by thermal energy or an external electric field. These results confirm that, for qualitative predictions of solar cell functionality, accounting for the explicit molecular environment is as important as the accurate knowledge of internal dimer energies.
Directory of Open Access Journals (Sweden)
C. Eichler
2015-12-01
Full Text Available Improving the understanding of strongly correlated quantum many-body systems such as gases of interacting atoms or electrons is one of the most important challenges in modern condensed matter physics, materials research, and chemistry. Enormous progress has been made in the past decades in developing both classical and quantum approaches to calculate, simulate, and experimentally probe the properties of such systems. In this work, we use a combination of classical and quantum methods to experimentally explore the properties of an interacting quantum gas by creating experimental realizations of continuous matrix product states—a class of states that has proven extremely powerful as a variational ansatz for numerical simulations. By systematically preparing and probing these states using a circuit quantum electrodynamics system, we experimentally determine a good approximation to the ground-state wave function of the Lieb-Liniger Hamiltonian, which describes an interacting Bose gas in one dimension. Since the simulated Hamiltonian is encoded in the measurement observable rather than the controlled quantum system, this approach has the potential to apply to a variety of models including those involving multicomponent interacting fields. Our findings also hint at the possibility of experimentally exploring general properties of matrix product states and entanglement theory. The scheme presented here is applicable to a broad range of systems exploiting strong and tunable light-matter interactions.
International Nuclear Information System (INIS)
Savukov, I. M.; Filin, D. V.
2014-01-01
Many applications are in need of accurate photoionization cross sections, especially in the case of complex atoms. Configuration-interaction relativistic-many-body-perturbation theory (CI-RMBPT) has been successful in predicting atomic energies, matrix elements between discrete states, and other properties, which is quite promising, but it has not been applied to photoionization problems owing to extra complications arising from continuum states. In this paper a method that will allow the conversion of discrete CI-(R)MPBT oscillator strengths (OS) to photoionization cross sections with minimal modifications of the codes is introduced and CI-RMBPT cross sections of Ne, Ar, Kr, and Xe are calculated. A consistent agreement with experiment is found. RMBPT corrections are particularly significant for Ar, Kr, and Xe and improve agreement with experimental results compared to the particle-hole CI method. As a result, the demonstrated conversion method can be applied to CI-RMBPT photoionization calculations for a large number of multivalence atoms and ions
International Nuclear Information System (INIS)
Säkkinen, Niko; Leeuwen, Robert van; Peng, Yang; Appel, Heiko
2015-01-01
We study ground-state properties of a two-site, two-electron Holstein model describing two molecules coupled indirectly via electron-phonon interaction by using both exact diagonalization and self-consistent diagrammatic many-body perturbation theory. The Hartree and self-consistent Born approximations used in the present work are studied at different levels of self-consistency. The governing equations are shown to exhibit multiple solutions when the electron-phonon interaction is sufficiently strong, whereas at smaller interactions, only a single solution is found. The additional solutions at larger electron-phonon couplings correspond to symmetry-broken states with inhomogeneous electron densities. A comparison to exact results indicates that this symmetry breaking is strongly correlated with the formation of a bipolaron state in which the two electrons prefer to reside on the same molecule. The results further show that the Hartree and partially self-consistent Born solutions obtained by enforcing symmetry do not compare well with exact energetics, while the fully self-consistent Born approximation improves the qualitative and quantitative agreement with exact results in the same symmetric case. This together with a presented natural occupation number analysis supports the conclusion that the fully self-consistent approximation describes partially the bipolaron crossover. These results contribute to better understanding how these approximations cope with the strong localizing effect of the electron-phonon interaction
A charge-optimized many-body potential for the U-UO2-O2 system
Li, Yangzhong; Liang, Tao; Sinnott, Susan B.; Phillpot, Simon R.
2013-12-01
Building on previous charge-optimized many-body (COMB) potentials for metallic α-U and gaseous O2, we have developed a new potential for UO2, which also allows the simulation of U-UO2-O2 systems. The UO2 lattice parameter, elastic constants and formation energies of stoichiometric and non-stoichiometric intrinsic defects are well reproduced. Moreover, this is the first rigid-ion potential that produces the correct deviation of the Cauchy relation, as well as the first classical interatomic potential that is able to determine the defect energies of non-stoichiometric intrinsic point defects in UO2 with an appropriate reference state. The oxygen molecule interstitial in the α-U structure is shown to decompose, with some U-O bonds approaching the natural bond length of perfect UO2. Finally, we demonstrate the capability of this COMB potential to simulate a complex system by performing a simulation of the α-U + O2 → UO2 phase transformation. We also identify a possible mechanism for uranium oxidation and the orientation of the resulting fluorite UO2 structure relative to the coordinate system of orthorhombic α-U.
International Nuclear Information System (INIS)
Tanaka, Toshiaki
2007-01-01
We propose an elegant formulation of parafermionic algebra and parasupersymmetry of arbitrary order in quantum many-body systems without recourse to any specific matrix representation of parafermionic operators and any kind of deformed algebra. Within our formulation, we show generically that every parasupersymmetric quantum system of order p consists of N-fold supersymmetric pairs with N≤p and thus has weak quasi-solvability and isospectral property. We also propose a new type of non-linear supersymmetries, called quasi-parasupersymmetry, which is less restrictive than parasupersymmetry and is different from N-fold supersymmetry even in one-body systems though the conserved charges are represented by higher-order linear differential operators. To illustrate how our formulation works, we construct second-order parafermionic algebra and three simple examples of parasupersymmetric quantum systems of order 2, one is essentially equivalent to the one-body Rubakov-Spiridonov type and the others are two-body systems in which two supersymmetries are folded. In particular, we show that the first model admits a generalized 2-fold superalgebra
Huang, Danhong; Iurov, Andrii; Gao, Fei; Gumbs, Godfrey; Cardimona, D. A.
2018-02-01
The effects of point defects on the loss of either energies of ballistic electron beams or incident photons are studied by using a many-body theory in a multi-quantum-well system. This theory includes the defect-induced vertex correction to a bare polarization function of electrons within the ladder approximation, and the intralayer and interlayer screening of defect-electron interactions is also taken into account in the random-phase approximation. The numerical results of defect effects on both energy-loss and optical-absorption spectra are presented and analyzed for various defect densities, numbers of quantum wells, and wave vectors. The diffusion-reaction equation is employed for calculating distributions of point defects in a layered structure. For completeness, the production rate for Frenkel-pair defects and their initial concentration are obtained based on atomic-level molecular-dynamics simulations. By combining the defect-effect, diffusion-reaction, and molecular-dynamics models with an available space-weather-forecast model, it will be possible in the future to enable specific designing for electronic and optoelectronic quantum devices that will be operated in space with radiation-hardening protection and, therefore, effectively extend the lifetime of these satellite onboard electronic and optoelectronic devices. Specifically, this theory can lead to a better characterization of quantum-well photodetectors not only for high quantum efficiency and low dark current density but also for radiation tolerance or mitigating the effects of the radiation.
Myo, Takayuki; Toki, Hiroshi; Ikeda, Kiyomi; Horiuchi, Hisashi; Suhara, Tadahiro
2017-07-01
We recently proposed a new variational theory of “tensor-optimized antisymmetrized molecular dynamics” (TOAMD), which treats the strong interaction explicitly for finite nuclei [T. Myo et al., Prog. Theor. Exp. Phys. 2015, 073D02 (2015)]. In TOAMD, the correlation functions for the tensor force and the short-range repulsion and their multiple products are successively operated to the AMD state. The correlated Hamiltonian is expanded into many-body operators by using the cluster expansion and all the resulting operators are taken into account in the calculation without any truncation. We show detailed results for TOAMD with the nucleon-nucleon interaction AV8‧ for s-shell nuclei. The binding energy and the Hamiltonian components are successively converged to exact values of the few-body calculations. We also apply TOAMD to the Malfliet-Tjon central potential having a strong short-range repulsion. TOAMD can treat the short-range correlation and provided accurate energies of s-shell nuclei, reproducing the results of few-body calculations. It turns out that the numerical accuracy of TOAMD with double products of the correlation functions is beyond the variational Monte Carlo method with Jastrow's product-type correlation functions.
Donner, Tobias
2015-03-01
A Bose-Einstein condensate whose motional degrees of freedom are coupled to a high-finesse optical cavity via a transverse pump beam constitutes a dissipative quantum many-body system with long range interactions. These interactions can induce a structural phase transition from a flat to a density-modulated state. The transverse pump field simultaneously represents a probe of the atomic density via cavity- enhanced Bragg scattering. By spectrally analyzing the light field leaking out of the cavity, we measure non-destructively the dynamic structure factor of the fluctuating atomic density while the system undergoes the phase transition. An observed asymmetry in the dynamic structure factor is attributed to the coupling to dissipative baths. Critical exponents for both sides of the phase transition can be extracted from the data. We further discuss our progress in adding strong short-range interactions to this system, in order to explore Bose-Hubbard physics with cavity-mediated long-range interactions and self-organization in lower dimensions.
Mortazavi, Majid; Brandenburg, Jan Gerit; Maurer, Reinhard J; Tkatchenko, Alexandre
2018-01-18
Accurate prediction of structure and stability of molecular crystals is crucial in materials science and requires reliable modeling of long-range dispersion interactions. Semiempirical electronic structure methods are computationally more efficient than their ab initio counterparts, allowing structure sampling with significant speedups. We combine the Tkatchenko-Scheffler van der Waals method (TS) and the many-body dispersion method (MBD) with third-order density functional tight-binding (DFTB3) via a charge population-based method. We find an overall good performance for the X23 benchmark database of molecular crystals, despite an underestimation of crystal volume that can be traced to the DFTB parametrization. We achieve accurate lattice energy predictions with DFT+MBD energetics on top of vdW-inclusive DFTB3 structures, resulting in a speedup of up to 3000 times compared with a full DFT treatment. This suggests that vdW-inclusive DFTB3 can serve as a viable structural prescreening tool in crystal structure prediction.
Directory of Open Access Journals (Sweden)
Marta Galanti
2016-08-01
Full Text Available Describing particle transport at the macroscopic or mesoscopic level in non-ideal environments poses fundamental theoretical challenges in domains ranging from inter and intra-cellular transport in biology to diffusion in porous media. Yet, often the nature of the constraints coming from many-body interactions or reflecting a complex and confining environment are better understood and modeled at the microscopic level.In this paper we review the subtle link between microscopic exclusion processes and the mean-field equations that ensue from them in the continuum limit. We show that in an inhomogeneous medium, i.e. when jumps are controlled by site-dependent hopping rates, one can obtain three different nonlinear advection-diffusion equations in the continuum limit, suitable for describing transport in the presence of quenched disorder and external fields, depending on the particular rule embodying site inequivalence at the microscopic level. In a situation that might be termed point-like scenario, when particles are treated as point-like objects, the effect of crowding as imposed at the microscopic level manifests in the mean-field equations only if some degree of inhomogeneity is enforced into the model. Conversely, when interacting agents are assigned a finite size, under the more realistic extended crowding framework, exclusion constraints persist in the unbiased macroscopic representation.
Lode, Axel U. J.; Diorico, Fritz S.; Wu, RuGway; Molignini, Paolo; Papariello, Luca; Lin, Rui; Lévêque, Camille; Exl, Lukas; Tsatsos, Marios C.; Chitra, R.; Mauser, Norbert J.
2018-05-01
We consider laser-pumped one-dimensional two-component bosons in a parabolic trap embedded in a high-finesse optical cavity. Above a threshold pump power, the photons that populate the cavity modify the effective atom trap and mediate a coupling between the two components of the Bose–Einstein condensate. We calculate the ground state of the laser-pumped system and find different stages of self-organization depending on the power of the laser. The modified potential and the laser-mediated coupling between the atomic components give rise to rich many-body physics: an increase of the pump power triggers a self-organization of the atoms while an even larger pump power causes correlations between the self-organized atoms—the BEC becomes fragmented and the reduced density matrix acquires multiple macroscopic eigenvalues. In this fragmented superradiant state, the atoms can no longer be described as two-level systems and the mapping of the system to the Dicke model breaks down.
Many-body effects in valleytronics: direct measurement of valley lifetimes in single-layer MoS2.
Mai, Cong; Barrette, Andrew; Yu, Yifei; Semenov, Yuriy G; Kim, Ki Wook; Cao, Linyou; Gundogdu, Kenan
2014-01-08
Single layer MoS2 is an ideal material for the emerging field of "valleytronics" in which charge carrier momentum can be finely controlled by optical excitation. This system is also known to exhibit strong many-body interactions as observed by tightly bound excitons and trions. Here we report direct measurements of valley relaxation dynamics in single layer MoS2, by using ultrafast transient absorption spectroscopy. Our results show that strong Coulomb interactions significantly impact valley population dynamics. Initial excitation by circularly polarized light creates electron-hole pairs within the K-valley. These excitons coherently couple to dark intervalley excitonic states, which facilitate fast electron valley depolarization. Hole valley relaxation is delayed up to about 10 ps due to nondegeneracy of the valence band spin states. Intervalley biexciton formation reveals the hole valley relaxation dynamics. We observe that biexcitons form with more than an order of magnitude larger binding energy compared to conventional semiconductors. These measurements provide significant insight into valley specific processes in 2D semiconductors. Hence they could be used to suggest routes to design semiconducting materials that enable control of valley polarization.
Liang, Yufeng; Vinson, John; Pemmaraju, Sri; Drisdell, Walter S; Shirley, Eric L; Prendergast, David
2017-03-03
Constrained-occupancy delta-self-consistent-field (ΔSCF) methods and many-body perturbation theories (MBPT) are two strategies for obtaining electronic excitations from first principles. Using the two distinct approaches, we study the O 1s core excitations that have become increasingly important for characterizing transition-metal oxides and understanding strong electronic correlation. The ΔSCF approach, in its current single-particle form, systematically underestimates the pre-edge intensity for chosen oxides, despite its success in weakly correlated systems. By contrast, the Bethe-Salpeter equation within MBPT predicts much better line shapes. This motivates one to reexamine the many-electron dynamics of x-ray excitations. We find that the single-particle ΔSCF approach can be rectified by explicitly calculating many-electron transition amplitudes, producing x-ray spectra in excellent agreement with experiments. This study paves the way to accurately predict x-ray near-edge spectral fingerprints for physics and materials science beyond the Bethe-Salpether equation.
International Nuclear Information System (INIS)
Niyaz, P.
1993-01-01
Quantum Monte Carlo techniques were used to study two quantum many-body systems, the one-dimensional extended boson-Hubbard Hamiltonian, a model of superfluid-insulator quantum phase transitions, and the two-dimensional Holstein Model, a model for electron-phonon interactions. For the extended boson-Hubbard model, the authors studied the ground state properties at commensurate filling (density = 1) and half-integer filling (density = 1/2). At commensurate filling, the system has two possible insulating phases for strong coupling. If the on-site repulsion dominates, the system freezes into an insulating phase where each site is singly occupied. If the intersite repulsion dominates, doubly occupied and empty sites alternate. At weak coupling, the system becomes a superfluid. The authors investigated the order of phase transitions between these different phases. At half-integer filling, the authors found one strong coupling insulating phase, where singly occupied and empty sites alternate, and a weak coupling superfluid phase. The authors also investigated the possibility of a supersolid phase and found no clear evidence of such a new phase. For the electron-phonon (Holstein) model, the authors focused on the finite temperature phase transition from a metallic state to an insulating charge density wave (CDW) state as the temperature is lowered. The authors present the first calculation of the spectral density from Monte Carlo data for this system. The authors also investigated the formation of a CDW state as a function of various parameters characterizing the electron-phonon interactions. Using these numerical results as benchmarks, the authors then investigated different levels of Migdal approximations. The authors found the solutions of a set of gapped Migdal-Eliashberg equations agreed qualitatively with the Monte Carlo results
International Nuclear Information System (INIS)
Griffin, J.J.; Lichtner, P.C.; Dworzecka, M.; Kan, K.K.
1979-01-01
The restrictions implied for the time dependent many-body reaction theory by the (TDHF) single determinantal assumption are explored by constructive analysis. A restructured TD-S-HF reaction theory is modelled, not after the initial-value form of the Schroedinger reaction theory, but after the (fully equivalent) S-matrix form, under the conditions that only self-consistent TDHF solutions occur in the theory, every wave function obeys the fundamental statistical interpretation of quantum mechanics, and the theory reduces to the exact Schroedinger theory for exact solutions which are single determinantal. All of these conditions can be accomodated provided that the theory is interpreted on a time-averaged basis, i.e., physical constants of the Schroedinger theory which are time-dependent in the TDHF theory, are interpreted in TD-S-HF in terms of their time averaged values. The resulting reaction theory, although formulated heuristically, prescribes a well defined and unambiguous calculational program which, although somewhat more demanding technically than the conventional initial-value TDHF method, is nevertheless more consonant with first principles, structurally and mechanistically. For its physical predictions do not depend upon the precise location of the distant measuring apparatus, and are in no way influenced by the spurious cross channel correlations which arise whenever the description of many reaction channels is imposed upon one single-determinantal solution. For nuclear structure physics, the TDHF-eigenfunctions provide the first plausible description of exact eigenstates in the time-dependent framework; moreover, they are unencumbered by any restriction to small amplitudes. 14 references
Magic informationally complete POVMs with permutations
Planat, Michel; Gedik, Zafer
2017-09-01
Eigenstates of permutation gates are either stabilizer states (for gates in the Pauli group) or magic states, thus allowing universal quantum computation (Planat, Rukhsan-Ul-Haq 2017 Adv. Math. Phys. 2017, 5287862 (doi:10.1155/2017/5287862)). We show in this paper that a subset of such magic states, when acting on the generalized Pauli group, define (asymmetric) informationally complete POVMs. Such informationally complete POVMs, investigated in dimensions 2-12, exhibit simple finite geometries in their projector products and, for dimensions 4 and 8 and 9, relate to two-qubit, three-qubit and two-qutrit contextuality.
Permutation 2-groups I: structure and splitness
Elgueta, Josep
2013-01-01
By a 2-group we mean a groupoid equipped with a weakened group structure. It is called split when it is equivalent to the semidirect product of a discrete 2-group and a one-object 2-group. By a permutation 2-group we mean the 2-group $\\mathbb{S}ym(\\mathcal{G})$ of self-equivalences of a groupoid $\\mathcal{G}$ and natural isomorphisms between them, with the product given by composition of self-equivalences. These generalize the symmetric groups $\\mathsf{S}_n$, $n\\geq 1$, obtained when $\\mathca...
Permutation Entropy for Random Binary Sequences
Directory of Open Access Journals (Sweden)
Lingfeng Liu
2015-12-01
Full Text Available In this paper, we generalize the permutation entropy (PE measure to binary sequences, which is based on Shannon’s entropy, and theoretically analyze this measure for random binary sequences. We deduce the theoretical value of PE for random binary sequences, which can be used to measure the randomness of binary sequences. We also reveal the relationship between this PE measure with other randomness measures, such as Shannon’s entropy and Lempel–Ziv complexity. The results show that PE is consistent with these two measures. Furthermore, we use PE as one of the randomness measures to evaluate the randomness of chaotic binary sequences.
Young module multiplicities and classifying the indecomposable Young permutation modules
Gill, Christopher C.
2012-01-01
We study the multiplicities of Young modules as direct summands of permutation modules on cosets of Young subgroups. Such multiplicities have become known as the p-Kostka numbers. We classify the indecomposable Young permutation modules, and, applying the Brauer construction for p-permutation modules, we give some new reductions for p-Kostka numbers. In particular we prove that p-Kostka numbers are preserved under multiplying partitions by p, and strengthen a known reduction given by Henke, c...
A transposase strategy for creating libraries of circularly permuted proteins.
Mehta, Manan M; Liu, Shirley; Silberg, Jonathan J
2012-05-01
A simple approach for creating libraries of circularly permuted proteins is described that is called PERMutation Using Transposase Engineering (PERMUTE). In PERMUTE, the transposase MuA is used to randomly insert a minitransposon that can function as a protein expression vector into a plasmid that contains the open reading frame (ORF) being permuted. A library of vectors that express different permuted variants of the ORF-encoded protein is created by: (i) using bacteria to select for target vectors that acquire an integrated minitransposon; (ii) excising the ensemble of ORFs that contain an integrated minitransposon from the selected vectors; and (iii) circularizing the ensemble of ORFs containing integrated minitransposons using intramolecular ligation. Construction of a Thermotoga neapolitana adenylate kinase (AK) library using PERMUTE revealed that this approach produces vectors that express circularly permuted proteins with distinct sequence diversity from existing methods. In addition, selection of this library for variants that complement the growth of Escherichia coli with a temperature-sensitive AK identified functional proteins with novel architectures, suggesting that PERMUTE will be useful for the directed evolution of proteins with new functions.
International Nuclear Information System (INIS)
Goepfert, A.
1994-01-01
This thesis develops a new model, and related numerical methods, to describe classical time-dependent many-body systems interacting through central forces, spin-orbit forces and spin-spin forces. The model is based on two-particle interactions. The two-body forces consist of attractive and repulsive parts. In this model the investigated multi-particle systems are self-bound. Also the total potential of the whole ensemble is derived from the two-particle potential and is not imposed 'from outside'. Each particle has the three degrees of freedom of its centre-of-mass motion and the spin degree of freedom. The model allows for the particles to be either charged or uncharged. Furthermore, each particle has an angular momentum, an intrinsic spin, and a magnetic dipole moment. Through the electromagnetic forces between these charges and moments there arise dynamical couplings between them. The internal interactions between the charges and moments are well described by electromagnetic coupling mechanisms. In fact, compared to conventional classical molecular dynamics calculations in van der Waals clusters, which have no spin degrees of freedom, or for Heisenberg spin Systems, which have no orbital degrees of freedom, the model presented here contains both types of degrees of freedom with a highly non-trivial coupling. The model allows to study the fundamental effects resulting from the dynamical coupling of the spin and the orbital-motion sub-systems. In particular, the dynamics of the particle mass points show a behaviour basically different from the one of particles in a potential with only central forces. Furthermore, a special type of quenching procedure was invented, which tends to drive the multi-particle Systems into states with highly periodic, non-ergodic behaviour. Application of the model to cluster simulations has provided evidence that the model can also be used to investigate items like solid-to-liquid phase transitions (melting), isomerism and specific heat
Energy Technology Data Exchange (ETDEWEB)
Kong, Bo, E-mail: kong79@yeah.net, E-mail: yachao.zhang@pku.edu.cn [School of Physics and Electronic Sciences, Guizhou Education University, Guiyang 550018 (China); Guizhou Provincial Key Laboratory of Computational Nano-Material Science, Guizhou Education University, Guiyang 550018 (China); Zhang, Yachao, E-mail: kong79@yeah.net, E-mail: yachao.zhang@pku.edu.cn [Guizhou Provincial Key Laboratory of Computational Nano-Material Science, Guizhou Education University, Guiyang 550018 (China)
2016-07-07
The electronic structures of the cubic GdH{sub 3} are extensively investigated using the ab initio many-body GW calculations treating the Gd 4f electrons either in the core (4f-core) or in the valence states (4f-val). Different degrees of quasiparticle (QP) self-consistent calculations with the different starting points are used to correct the failures of the GGA/GGA + U/HSE03 calculations. In the 4f-core case, GGA + G{sub 0}W{sub 0} calculations give a fundamental band gap of 1.72 eV, while GGA+ GW{sub 0} or GGA + GW calculations present a larger band gap. In the 4f-val case, the nonlocal exchange-correlation (xc) functional HSE03 can account much better for the strong localization of the 4f states than the semilocal or Hubbard U corrected xc functional in the Kohn–Sham equation. We show that the fundamental gap of the antiferromagnetic (AFM) or ferromagnetic (FM) GdH{sub 3} can be opened up by solving the QP equation with improved starting point of eigenvalues and wave functions given by HSE03. The HSE03 + G{sub 0}W{sub 0} calculations present a fundamental band gap of 2.73 eV in the AFM configuration, and the results of the corresponding GW{sub 0} and GW calculations are 2.89 and 3.03 eV, respectively. In general, for the cubic structure, the fundamental gap from G{sub 0}W{sub 0} calculations in the 4f-core case is the closest to the real result. By G{sub 0}W{sub 0} calculations in the 4f-core case, we find that H or Gd defects can strongly affect the band structure, especially the H defects. We explain the mechanism in terms of the possible electron correlation on the hydrogen site. Under compression, the insulator-to-metal transition in the cubic GdH{sub 3} occurs around 40 GPa, which might be a satisfied prediction.
Energy Technology Data Exchange (ETDEWEB)
Canetta, G.; Maino, G.; Magnani, M.; Visparelli, D. [ENEA, Centro Ricerche Ezio Clementel, Bologna (Italy). Dipt. Innovazione
1999-07-01
The interacting boson model (IBM) is a realistic model of nuclear structure, since it allows to cut off in a suitable way the complete space of the shell model states. In such a way, it offers a great simplicity of the numerical computation of the eigenvalue problem for a many-body non-relativistic quantum system, like a nucleus. In particular, the analytical solutions obtained in the case of dynamical symmetries correspond, in the classical limit, to completely integrable systems showing a regular dynamic behaviour. In this report, a detailed analysis is performed of the IBM version 2 (IBM-2), which explicitly introduces the isospin degree of freedom. The different forms of the IBM-2 Hamiltonian usually considered in the literature, are discussed, and the explicit relations existing between them are deduced. Moreover, the semiclassical limit of the most general IBM-2 Hamiltonian is studied in the details. Finally, the expectation of chaotic dynamic behaviour near to regular dynamics, in the IBM, and, in particular, the fact that the latter ones persist more than expected a priori, is shown. Maybe, this behaviour is to adduce to the existence of partial dynamic symmetries. [Italian] Il modello a bosoni interagenti (IBM) rappresenta un modello realistico della struttura nucleare, premettendo di troncare opportunamente lo spazio completo degli stati di modello a shell, e percio' offre una notevole semplicita' computazionale nella risoluzione numerica del problema degli autovalori per un sistema quantico non relativistico a molti corpi, quale e' un nucleo. In particolare, le soluzioni analitiche ottenute nel caso di simmetrie dinamiche corrispondono, nel limite classico, a sistemi completamente integrabili che mostrano un comportamento dinamico regolare. In questo rapporto viene condotta un'analisi dettagliata del modello IBM nella versione (IBM-2), il quale introduce esplicitamente il grado di liberta' di isospin. In particolare, sono
SCOPES: steganography with compression using permutation search
Boorboor, Sahar; Zolfaghari, Behrouz; Mozafari, Saadat Pour
2011-10-01
LSB (Least Significant Bit) is a widely used method for image steganography, which hides the secret message as a bit stream in LSBs of pixel bytes in the cover image. This paper proposes a variant of LSB named SCOPES that encodes and compresses the secret message while being hidden through storing addresses instead of message bytes. Reducing the length of the stored message improves the storage capacity and makes the stego image visually less suspicious to the third party. The main idea behind the SCOPES approach is dividing the message into 3-character segments, seeking each segment in the cover image and storing the address of the position containing the segment instead of the segment itself. In this approach, every permutation of the 3 bytes (if found) can be stored along with some extra bits indicating the permutation. In some rare cases the segment may not be found in the image and this can cause the message to be expanded by some overhead bits2 instead of being compressed. But experimental results show that SCOPES performs overlay better than traditional LSB even in the worst cases.
Ordered groups and infinite permutation groups
1996-01-01
The subjects of ordered groups and of infinite permutation groups have long en joyed a symbiotic relationship. Although the two subjects come from very different sources, they have in certain ways come together, and each has derived considerable benefit from the other. My own personal contact with this interaction began in 1961. I had done Ph. D. work on sequence convergence in totally ordered groups under the direction of Paul Conrad. In the process, I had encountered "pseudo-convergent" sequences in an ordered group G, which are like Cauchy sequences, except that the differences be tween terms of large index approach not 0 but a convex subgroup G of G. If G is normal, then such sequences are conveniently described as Cauchy sequences in the quotient ordered group GIG. If G is not normal, of course GIG has no group structure, though it is still a totally ordered set. The best that can be said is that the elements of G permute GIG in an order-preserving fashion. In independent investigations around that t...
Jaschke, Daniel; Wall, Michael L.; Carr, Lincoln D.
2018-04-01
Numerical simulations are a powerful tool to study quantum systems beyond exactly solvable systems lacking an analytic expression. For one-dimensional entangled quantum systems, tensor network methods, amongst them Matrix Product States (MPSs), have attracted interest from different fields of quantum physics ranging from solid state systems to quantum simulators and quantum computing. Our open source MPS code provides the community with a toolset to analyze the statics and dynamics of one-dimensional quantum systems. Here, we present our open source library, Open Source Matrix Product States (OSMPS), of MPS methods implemented in Python and Fortran2003. The library includes tools for ground state calculation and excited states via the variational ansatz. We also support ground states for infinite systems with translational invariance. Dynamics are simulated with different algorithms, including three algorithms with support for long-range interactions. Convenient features include built-in support for fermionic systems and number conservation with rotational U(1) and discrete Z2 symmetries for finite systems, as well as data parallelism with MPI. We explain the principles and techniques used in this library along with examples of how to efficiently use the general interfaces to analyze the Ising and Bose-Hubbard models. This description includes the preparation of simulations as well as dispatching and post-processing of them.
The magic of universal quantum computing with permutations
Planat, Michel; Rukhsan-Ul-Haq
2017-01-01
The role of permutation gates for universal quantum computing is investigated. The \\lq magic' of computation is clarified in the permutation gates, their eigenstates, the Wootters discrete Wigner function and state-dependent contextuality (following many contributions on this subject). A first classification of main types of resulting magic states in low dimensions $d \\le 9$ is performed.
Some topics on permutable subgroups in infinite groups
Ialenti, Roberto
2017-01-01
The aim of this thesis is to study permutability in different aspects of the theory of infinite groups. In particular, it will be studied the structure of groups in which all the members of a relevant system of subgroups satisfy a suitable generalized condition of permutability.
A permutations representation that knows what " Eulerian" means
Directory of Open Access Journals (Sweden)
Roberto Mantaci
2001-12-01
Full Text Available Eulerian numbers (and ``Alternate Eulerian numbers'' are often interpreted as distributions of statistics defined over the Symmetric group. The main purpose of this paper is to define a way to represent permutations that provides some other combinatorial interpretations of these numbers. This representation uses a one-to-one correspondence between permutations and the so-called subexceedant functions.
A Fast Algorithm for Generating Permutation Distribution of Ranks in ...
African Journals Online (AJOL)
... function of the distribution of the ranks. This further gives insight into the permutation distribution of a rank statistics. The algorithm is implemented with the aid of the computer algebra system Mathematica. Key words: Combinatorics, generating function, permutation distribution, rank statistics, partitions, computer algebra.
The Magic of Universal Quantum Computing with Permutations
Directory of Open Access Journals (Sweden)
Michel Planat
2017-01-01
Full Text Available The role of permutation gates for universal quantum computing is investigated. The “magic” of computation is clarified in the permutation gates, their eigenstates, the Wootters discrete Wigner function, and state-dependent contextuality (following many contributions on this subject. A first classification of a few types of resulting magic states in low dimensions d≤9 is performed.
Permutation entropy with vector embedding delays
Little, Douglas J.; Kane, Deb M.
2017-12-01
Permutation entropy (PE) is a statistic used widely for the detection of structure within a time series. Embedding delay times at which the PE is reduced are characteristic timescales for which such structure exists. Here, a generalized scheme is investigated where embedding delays are represented by vectors rather than scalars, permitting PE to be calculated over a (D -1 ) -dimensional space, where D is the embedding dimension. This scheme is applied to numerically generated noise, sine wave and logistic map series, and experimental data sets taken from a vertical-cavity surface emitting laser exhibiting temporally localized pulse structures within the round-trip time of the laser cavity. Results are visualized as PE maps as a function of embedding delay, with low PE values indicating combinations of embedding delays where correlation structure is present. It is demonstrated that vector embedding delays enable identification of structure that is ambiguous or masked, when the embedding delay is constrained to scalar form.
Permutation importance: a corrected feature importance measure.
Altmann, André; Toloşi, Laura; Sander, Oliver; Lengauer, Thomas
2010-05-15
In life sciences, interpretability of machine learning models is as important as their prediction accuracy. Linear models are probably the most frequently used methods for assessing feature relevance, despite their relative inflexibility. However, in the past years effective estimators of feature relevance have been derived for highly complex or non-parametric models such as support vector machines and RandomForest (RF) models. Recently, it has been observed that RF models are biased in such a way that categorical variables with a large number of categories are preferred. In this work, we introduce a heuristic for normalizing feature importance measures that can correct the feature importance bias. The method is based on repeated permutations of the outcome vector for estimating the distribution of measured importance for each variable in a non-informative setting. The P-value of the observed importance provides a corrected measure of feature importance. We apply our method to simulated data and demonstrate that (i) non-informative predictors do not receive significant P-values, (ii) informative variables can successfully be recovered among non-informative variables and (iii) P-values computed with permutation importance (PIMP) are very helpful for deciding the significance of variables, and therefore improve model interpretability. Furthermore, PIMP was used to correct RF-based importance measures for two real-world case studies. We propose an improved RF model that uses the significant variables with respect to the PIMP measure and show that its prediction accuracy is superior to that of other existing models. R code for the method presented in this article is available at http://www.mpi-inf.mpg.de/ approximately altmann/download/PIMP.R CONTACT: altmann@mpi-inf.mpg.de, laura.tolosi@mpi-inf.mpg.de Supplementary data are available at Bioinformatics online.
An Affine Invariant Bivariate Version of the Sign Test.
1987-06-01
words: affine invariance, bivariate quantile, bivariate symmetry, model,. generalized median, influence function , permutation test, normal efficiency...calculate a bivariate version of the influence function , and the resulting form is bounded, as is the case for the univartate sign test, and shows the...terms of a blvariate analogue of IHmpel’s (1974) influence function . The latter, though usually defined as a von-Mises derivative of certain
Fröhlich, Jürg; Knowles, Antti; Schlein, Benjamin; Sohinger, Vedran
2017-12-01
We prove that Gibbs measures of nonlinear Schrödinger equations arise as high-temperature limits of thermal states in many-body quantum mechanics. Our results hold for defocusing interactions in dimensions {d =1,2,3}. The many-body quantum thermal states that we consider are the grand canonical ensemble for d = 1 and an appropriate modification of the grand canonical ensemble for {d =2,3}. In dimensions d = 2, 3, the Gibbs measures are supported on singular distributions, and a renormalization of the chemical potential is necessary. On the many-body quantum side, the need for renormalization is manifested by a rapid growth of the number of particles. We relate the original many-body quantum problem to a renormalized version obtained by solving a counterterm problem. Our proof is based on ideas from field theory, using a perturbative expansion in the interaction, organized by using a diagrammatic representation, and on Borel resummation of the resulting series.
DEFF Research Database (Denmark)
Martinez, Jose Ignacio; García Lastra, Juan Maria; Lopez, M. J.
2010-01-01
The optical spectra of sandwich clusters formed by transition metal atoms (titanium, vanadium, and chromium) intercalated between parallel benzene molecules have been studied by time-dependent density functional theory (TDDFT) and many-body perturbation theory. Sandwiches with different number...
Koop, E. J.; Lerescu, A. I.; Liu, J.; van Wees, B. J.; Reuter, D.; Wieck, A. D.; van der Wal, C. H.
The conductance of a quantum point contact (QPC) shows several features that result from many-body electron interactions. The spin degeneracy in zero magnetic field appears to be spontaneously lifted due to the so-called 0.7 anomaly. Further, the g-factor for electrons in the QPC is enhanced, and a
Ziaei, Vafa; Bredow, Thomas
2017-03-17
The reliable calculation of the excited states of charge-transfer (CT) compounds poses a major challenge to the ab initio community because the frequently employed method, time-dependent density functional theory (TD-DFT), massively relies on the underlying density functional, resulting in heavily Hartree-Fock (HF) exchange-dependent excited-state energies. By applying the highly sophisticated many-body perturbation approach, we address the encountered unreliabilities and inconsistencies of not optimally tuned (standard) TD-DFT regarding photo-excited CT phenomena, and present results concerning accurate vertical transition energies and the correct energetic ordering of the CT and the first visible singlet state of a recently synthesized thermodynamically stable large hybrid perylene bisimide-macrocycle complex. This is a large-scale application of the quantum many-body perturbation approach to a chemically relevant CT system, demonstrating the system-size independence of the quality of the many-body-based excitation energies. Furthermore, an optimal tuning of the ωB97X hybrid functional can well reproduce the many-body results, making TD-DFT a suitable choice but at the expense of introducing a range-separation parameter, which needs to be optimally tuned. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Multiscale permutation entropy analysis of electrocardiogram
Liu, Tiebing; Yao, Wenpo; Wu, Min; Shi, Zhaorong; Wang, Jun; Ning, Xinbao
2017-04-01
To make a comprehensive nonlinear analysis to ECG, multiscale permutation entropy (MPE) was applied to ECG characteristics extraction to make a comprehensive nonlinear analysis of ECG. Three kinds of ECG from PhysioNet database, congestive heart failure (CHF) patients, healthy young and elderly subjects, are applied in this paper. We set embedding dimension to 4 and adjust scale factor from 2 to 100 with a step size of 2, and compare MPE with multiscale entropy (MSE). As increase of scale factor, MPE complexity of the three ECG signals are showing first-decrease and last-increase trends. When scale factor is between 10 and 32, complexities of the three ECG had biggest difference, entropy of the elderly is 0.146 less than the CHF patients and 0.025 larger than the healthy young in average, in line with normal physiological characteristics. Test results showed that MPE can effectively apply in ECG nonlinear analysis, and can effectively distinguish different ECG signals.
Permutation based decision making under fuzzy environment using Tabu search
Directory of Open Access Journals (Sweden)
Mahdi Bashiri
2012-04-01
Full Text Available One of the techniques, which are used for Multiple Criteria Decision Making (MCDM is the permutation. In the classical form of permutation, it is assumed that weights and decision matrix components are crisp. However, when group decision making is under consideration and decision makers could not agree on a crisp value for weights and decision matrix components, fuzzy numbers should be used. In this article, the fuzzy permutation technique for MCDM problems has been explained. The main deficiency of permutation is its big computational time, so a Tabu Search (TS based algorithm has been proposed to reduce the computational time. A numerical example has illustrated the proposed approach clearly. Then, some benchmark instances extracted from literature are solved by proposed TS. The analyses of the results show the proper performance of the proposed method.
Permutation groups and transformation semigroups : results and problems
Araujo, Joao; Cameron, Peter Jephson
2015-01-01
J.M. Howie, the influential St Andrews semigroupist, claimed that we value an area of pure mathematics to the extent that (a) it gives rise to arguments that are deep and elegant, and (b) it has interesting interconnections with other parts of pure mathematics. This paper surveys some recent results on the transformation semigroup generated by a permutation group $G$ and a single non-permutation $a$. Our particular concern is the influence that properties of $G$ (related to homogeneity, trans...
Energy Technology Data Exchange (ETDEWEB)
Kolb, Brian [Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131 (United States); Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); Zhao, Bin; Guo, Hua, E-mail: hguo@unm.edu [Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131 (United States); Li, Jun [School of Chemistry and Chemical Engineering, Chongqing University, Chongqing 401331 (China); Jiang, Bin [Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China)
2016-06-14
The applicability and accuracy of the Behler-Parrinello atomistic neural network method for fitting reactive potential energy surfaces is critically examined in three systems, H + H{sub 2} → H{sub 2} + H, H + H{sub 2}O → H{sub 2} + OH, and H + CH{sub 4} → H{sub 2} + CH{sub 3}. A pragmatic Monte Carlo method is proposed to make efficient choice of the atom-centered mapping functions. The accuracy of the potential energy surfaces is not only tested by fitting errors but also validated by direct comparison in dynamically important regions and by quantum scattering calculations. Our results suggest this method is both accurate and efficient in representing multidimensional potential energy surfaces even when dissociation continua are involved.
International Nuclear Information System (INIS)
Kolb, Brian; Zhao, Bin; Guo, Hua; Li, Jun; Jiang, Bin
2016-01-01
The applicability and accuracy of the Behler-Parrinello atomistic neural network method for fitting reactive potential energy surfaces is critically examined in three systems, H + H 2 → H 2 + H, H + H 2 O → H 2 + OH, and H + CH 4 → H 2 + CH 3 . A pragmatic Monte Carlo method is proposed to make efficient choice of the atom-centered mapping functions. The accuracy of the potential energy surfaces is not only tested by fitting errors but also validated by direct comparison in dynamically important regions and by quantum scattering calculations. Our results suggest this method is both accurate and efficient in representing multidimensional potential energy surfaces even when dissociation continua are involved.
Molecular symmetry: Why permutation-inversion (PI) groups don't render the point groups obsolete
Groner, Peter
2018-01-01
The analysis of spectra of molecules with internal large-amplitude motions (LAMs) requires molecular symmetry (MS) groups that are larger than and significantly different from the more familiar point groups. MS groups are described often by the permutation-inversion (PI) group method. It is shown that point groups still can and should play a significant role together with the PI groups for a class of molecules with internal rotors. In molecules of this class, several simple internal rotors are attached to a rigid molecular frame. The PI groups for this class are semidirect products like H ^ F, where the invariant subgroup H is a direct product of cyclic groups and F is a point group. This result is used to derive meaningful labels for MS groups, and to derive correlation tables between MS groups and point groups. MS groups of this class have many parallels to space groups of crystalline solids.
Energy Technology Data Exchange (ETDEWEB)
Issaoui, Noureddine, E-mail: issaoui-noureddine@yahoo.fr; Abdessalem, Kawther; Ghalla, Houcine [Faculty of Sciences, Quantum Physics Laboratory, University of Monastir, Monastir 5079 (Tunisia); Yaghmour, Saud Jamil [Faculty of Science, King Abdul-Aziz University, Jeddah (Saudi Arabia); Calvo, Florent [University of Grenoble Alpes, LIPHY, F-38000 Grenoble, France and CNRS, LIPHY, F-38000 Grenoble (France); Oujia, Brahim [Faculty of Sciences, Quantum Physics Laboratory, University of Monastir, Monastir 5079 (Tunisia); Faculty of Science, King Abdul-Aziz University, Jeddah (Saudi Arabia)
2014-11-07
The solvation of the Na{sup +} ion in helium clusters has been studied theoretically using optimization methods. A many-body empirical potential was developed to account for Na{sup +}–He and polarization interactions, and the most stable structures of Na{sup +}He{sub n} clusters were determined using the basin-hopping method. Vibrational delocalization was accounted for using zero-point energy corrections at the harmonic or anharmonic levels, the latter being evaluated from quantum Monte Carlo simulations for spinless particles. From the static perspective, many-body effects are found to play a minor role, and the structures obtained reflect homogeneous covering up to n = 10, followed by polyicosahedral packing above this size, the cluster obtained at n = 12 appearing particularly stable. The cationic impurity binds the closest helium atoms sufficiently to negate vibrational delocalization at small sizes. However, this snowball effect is obliterated earlier than shell completion, the nuclear wavefunctions of {sup 4}He{sub n}Na{sup +} with n = 5–7, and n > 10 already exhibiting multiple inherent structures. The decrease in the snowball size due to many-body effects is consistent with recent mass spectrometry measurements.
Slow dynamics in translation-invariant quantum lattice models
Michailidis, Alexios A.; Žnidarič, Marko; Medvedyeva, Mariya; Abanin, Dmitry A.; Prosen, Tomaž; Papić, Z.
2018-03-01
Many-body quantum systems typically display fast dynamics and ballistic spreading of information. Here we address the open problem of how slow the dynamics can be after a generic breaking of integrability by local interactions. We develop a method based on degenerate perturbation theory that reveals slow dynamical regimes and delocalization processes in general translation invariant models, along with accurate estimates of their delocalization time scales. Our results shed light on the fundamental questions of the robustness of quantum integrable systems and the possibility of many-body localization without disorder. As an example, we construct a large class of one-dimensional lattice models where, despite the absence of asymptotic localization, the transient dynamics is exceptionally slow, i.e., the dynamics is indistinguishable from that of many-body localized systems for the system sizes and time scales accessible in experiments and numerical simulations.
International Nuclear Information System (INIS)
Oshima, Hiraku; Kinoshita, Masahiro
2015-01-01
In earlier works, we showed that the entropic effect originating from the translational displacement of water molecules plays the pivotal role in protein folding and denaturation. The two different solvent models, hard-sphere solvent and model water, were employed in theoretical methods wherein the entropic effect was treated as an essential factor. However, there were similarities and differences in the results obtained from the two solvent models. In the present work, to unveil the physical origins of the similarities and differences, we simultaneously consider structural transition, cold denaturation, and pressure denaturation for the same protein by employing the two solvent models and considering three different thermodynamic states for each solvent model. The solvent-entropy change upon protein folding/unfolding is decomposed into the protein-solvent pair (PA) and many-body (MB) correlation components using the integral equation theories. Each component is further decomposed into the excluded-volume (EV) and solvent-accessible surface (SAS) terms by applying the morphometric approach. The four physically insightful constituents, (PA, EV), (PA, SAS), (MB, EV), and (MB, SAS), are thus obtained. Moreover, (MB, SAS) is discussed by dividing it into two factors. This all-inclusive investigation leads to the following results: (1) the protein-water many-body correlation always plays critical roles in a variety of folding/unfolding processes; (2) the hard-sphere solvent model fails when it does not correctly reproduce the protein-water many-body correlation; (3) the hard-sphere solvent model becomes problematic when the dependence of the many-body correlation on the solvent number density and temperature is essential: it is not quite suited to studies on cold and pressure denaturating of a protein; (4) when the temperature and solvent number density are limited to the ambient values, the hard-sphere solvent model is usually successful; and (5) even at the ambient
Paesani, Francesco
2016-09-20
The central role played by water in fundamental processes relevant to different disciplines, including chemistry, physics, biology, materials science, geology, and climate research, cannot be overemphasized. It is thus not surprising that, since the pioneering work by Stillinger and Rahman, many theoretical and computational studies have attempted to develop a microscopic description of the unique properties of water under different thermodynamic conditions. Consequently, numerous molecular models based on either molecular mechanics or ab initio approaches have been proposed over the years. However, despite continued progress, the correct prediction of the properties of water from small gas-phase clusters to the liquid phase and ice through a single molecular model remains challenging. To large extent, this is due to the difficulties encountered in the accurate modeling of the underlying hydrogen-bond network in which both number and strength of the hydrogen bonds vary continuously as a result of a subtle interplay between energetic, entropic, and nuclear quantum effects. In the past decade, the development of efficient algorithms for correlated electronic structure calculations of small molecular complexes, accompanied by tremendous progress in the analytical representation of multidimensional potential energy surfaces, opened the doors to the design of highly accurate potential energy functions built upon rigorous representations of the many-body expansion (MBE) of the interaction energies. This Account provides a critical overview of the performance of the MB-pol many-body potential energy function through a systematic analysis of energetic, structural, thermodynamic, and dynamical properties as well as of vibrational spectra of water from the gas to the condensed phase. It is shown that MB-pol achieves unprecedented accuracy across all phases of water through a quantitative description of each individual term of the MBE, with a physically correct representation
Energy Technology Data Exchange (ETDEWEB)
Olver, Peter J [School of Mathematics, University of Minnesota, Minneapolis, MN 55455 (United States)], E-mail: olver@math.umn.edu
2008-08-29
Given a Lie group acting on a manifold, our aim is to analyze the evolution of differential invariants under invariant submanifold flows. The constructions are based on the equivariant method of moving frames and the induced invariant variational bicomplex. Applications to integrable soliton dynamics, and to the evolution of differential invariant signatures, used in equivalence problems and object recognition and symmetry detection in images, are discussed.
Rotationally invariant correlation filtering
International Nuclear Information System (INIS)
Schils, G.F.; Sweeney, D.W.
1985-01-01
A method is presented for analyzing and designing optical correlation filters that have tailored rotational invariance properties. The concept of a correlation of an image with a rotation of itself is introduced. A unified theory of rotation-invariant filtering is then formulated. The unified approach describes matched filters (with no rotation invariance) and circular-harmonic filters (with full rotation invariance) as special cases. The continuum of intermediate cases is described in terms of a cyclic convolution operation over angle. The angular filtering approach allows an exact choice for the continuous trade-off between loss of the correlation energy (or specificity regarding the image) and the amount of rotational invariance desired
International Nuclear Information System (INIS)
Levin, F.S.; Krueger, H.
1977-01-01
We propose in this article that the non-Hermitian equations typical of some many-body scattering theories be used to help solve many-body bound-state problems. The basic idea is to exploit the channel nature of many-body bound states that must exist because bound states are obvious negative-energy extensions of scattering states. Since atomic, molecular, and nuclear systems all display multichannel effects for E > 0, at least through Pauli-principle effects if not through mass-transfer reactions, this use of positive-energy methods for solving bound-state problems could have wide applicability. The development used here is based on the channel-component-state method of the channel-coupling-array theory, recently described in detail for the E > 0 case, and various aspects of the formalism are discussed. Detailed calculations using simple approximations are discussed for H 2 + , one of the simplest systems displaying channel structure. Comparison with the exact, Born-Oppenheimer results of Wind show that the non-Hermitian-equation, channel-component values of the equilibrium separation and total binding energy are accurate to within 2%, while the dissociation energy is accurate to 10%. The resulting wave function is identical to that arising from the simplest MO calculation, for which these numbers are less accurate than the preceding by at least a factor of 3. We also show that identical particle symmetry for the H 2 + case reduces the pair of coupled (two-channel) equations to a single equation with an exchange term. Similar reductions will occur for larger numbers of identical particles, thus suggesting application of the formalism to atomic structure problems. A detailed analysis of the present numerical results, their general implications, and possible applications is also given
Wzgarda-Raj, Kinga; Rybarczyk-Pirek, Agnieszka J; Wojtulewski, Sławomir; Palusiak, Marcin
2018-02-01
Pentachloropyridine N-oxide, C 5 Cl 5 NO, crystallizes in the monoclinic space group P2 1 /c. In the crystal structure, molecules are linked by C-Cl...Cl halogen bonds into infinite ribbons extending along the crystallographic [100] direction. These molecular aggregates are further stabilized by very short intermolecular N-oxide-N-oxide interactions into herringbone motifs. Computations based on quantum chemistry methods allowed for a more detailed description of the N-oxide-N-oxide interactions and Cl...Cl halogen bonds. For this purpose, Hirshfeld surface analysis and the many-body approach to interaction energy were applied.
International Nuclear Information System (INIS)
Vilkas, Marius J; Ishikawa, Yasuyuki; Traebert, Elmar
2006-01-01
Many-body perturbation theory (MBPT) has been employed to calculate with high wavelength accuracy the extreme ultraviolet (EUV) spectra of F-like to P-like Xe ions. We discuss the reliability of the new calculations using the example of EUV beam-foil spectra of Xe, in which n = 3, Δn = 0 transitions of Na-, Mg-, Al- and Si-like ions have been found to dominate. A further comparison is made with spectra from an electron beam ion trap, that is, from a device with a very different (low density) excitation balance
International Nuclear Information System (INIS)
Crabtree, G.W.; Johanson, W.R.; Campbell, S.A.; Dye, D.H.; Karim, D.P.; Ketterson, J.B.
1980-01-01
Examples are given which demonstrate the power and versatility of the dHvA effect in studying electronic behavior in metals. In transition metals the parametrization schemes give a very complete and consistent picture of the k-dependent and surface averaged electronic properties. Because the one-electron behavior is fairly well known, the many body contribution to the Fermi velocity can be isolated and its detailed anisotropy can be displayed. This kind of information is directly relevant to the calculation of electron-phonon interaction effects and cannot be derived by any other means
Computational invariant theory
Derksen, Harm
2015-01-01
This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Gröbner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be ...
Determination of Pavement Rehabilitation Activities through a Permutation Algorithm
Directory of Open Access Journals (Sweden)
Sangyum Lee
2013-01-01
Full Text Available This paper presents a mathematical programming model for optimal pavement rehabilitation planning. The model maximized the rehabilitation area through a newly developed permutation algorithm, based on the procedures outlined in the harmony search (HS algorithm. Additionally, the proposed algorithm was based on an optimal solution method for the problem of multilocation rehabilitation activities on pavement structure, using empirical deterioration and rehabilitation effectiveness models, according to a limited maintenance budget. Thus, nonlinear pavement performance and rehabilitation activity decision models were used to maximize the objective functions of the rehabilitation area within a limited budget, through the permutation algorithm. Our results showed that the heuristic permutation algorithm provided a good optimum in terms of maximizing the rehabilitation area, compared with a method of the worst-first maintenance currently used in Seoul.
Permutational symmetries for coincidence rates in multimode multiphotonic interferometry
Khalid, Abdullah; Spivak, Dylan; Sanders, Barry C.; de Guise, Hubert
2018-06-01
We obtain coincidence rates for passive optical interferometry by exploiting the permutational symmetries of partially distinguishable input photons, and our approach elucidates qualitative features of multiphoton coincidence landscapes. We treat the interferometer input as a product state of any number of photons in each input mode with photons distinguished by their arrival time. Detectors at the output of the interferometer count photons from each output mode over a long integration time. We generalize and prove the claim of Tillmann et al. [Phys. Rev. X 5, 041015 (2015), 10.1103/PhysRevX.5.041015] that coincidence rates can be elegantly expressed in terms of immanants. Immanants are functions of matrices that exhibit permutational symmetries and the immanants appearing in our coincidence-rate expressions share permutational symmetries with the input state. Our results are obtained by employing representation theory of the symmetric group to analyze systems of an arbitrary number of photons in arbitrarily sized interferometers.
Secure physical layer using dynamic permutations in cognitive OFDMA systems
DEFF Research Database (Denmark)
Meucci, F.; Wardana, Satya Ardhy; Prasad, Neeli R.
2009-01-01
This paper proposes a novel lightweight mechanism for a secure Physical (PHY) layer in Cognitive Radio Network (CRN) using Orthogonal Frequency Division Multiplexing (OFDM). User's data symbols are mapped over the physical subcarriers with a permutation formula. The PHY layer is secured...... with a random and dynamic subcarrier permutation which is based on a single pre-shared information and depends on Dynamic Spectrum Access (DSA). The dynamic subcarrier permutation is varying over time, geographical location and environment status, resulting in a very robust protection that ensures...... confidentiality. The method is shown to be effective also for existing non-cognitive systems. The proposed mechanism is effective against eavesdropping even if the eavesdropper adopts a long-time patterns analysis, thus protecting cryptography techniques of higher layers. The correlation properties...
Permutation entropy of fractional Brownian motion and fractional Gaussian noise
International Nuclear Information System (INIS)
Zunino, L.; Perez, D.G.; Martin, M.T.; Garavaglia, M.; Plastino, A.; Rosso, O.A.
2008-01-01
We have worked out theoretical curves for the permutation entropy of the fractional Brownian motion and fractional Gaussian noise by using the Bandt and Shiha [C. Bandt, F. Shiha, J. Time Ser. Anal. 28 (2007) 646] theoretical predictions for their corresponding relative frequencies. Comparisons with numerical simulations show an excellent agreement. Furthermore, the entropy-gap in the transition between these processes, observed previously via numerical results, has been here theoretically validated. Also, we have analyzed the behaviour of the permutation entropy of the fractional Gaussian noise for different time delays
International Nuclear Information System (INIS)
Masiello, David J.; Reinhardt, William P.
2007-01-01
A time-dependent multiconfigurational self-consistent field theory is presented to describe the many-body dynamics of a gas of identical bosonic atoms confined to an external trapping potential at zero temperature from first principles. A set of generalized evolution equations are developed, through the time-dependent variational principle, which account for the complete and self-consistent coupling between the expansion coefficients of each configuration and the underlying one-body wave functions within a restricted two state Fock space basis that includes the full effects of the condensate's mean field as well as atomic correlation. The resulting dynamical equations are a classical Hamiltonian system and, by construction, form a well-defined initial value problem. They are implemented in an efficient numerical algorithm. An example is presented, highlighting the generality of the theory, in which the ballistic expansion of a fragmented condensate ground state is compared to that of a macroscopic quantum superposition state, taken here to be a highly entangled number state, upon releasing the external trapping potential. Strikingly different many-body matter-wave dynamics emerge in each case, accentuating the role of both atomic correlation and mean-field effects in the two condensate states
Many-body effects on the structures and stability of Ba{sup 2+}Xe{sub n} (n = 1–39, 54) clusters
Energy Technology Data Exchange (ETDEWEB)
Abdessalem, Kawther, E-mail: kawtherabdessalem@yahoo.fr; Habli, Héla; Ghalla, Houcine [Laboratoire de Physique Quantique, Faculté des Sciences de Monastir, Université de Monastir, Avenue de l’Environnement, 5019 Monastir (Tunisia); Yaghmour, Saud Jamil [Physics Department, Faculty of Science, King Abdulaziz University, Jeddah (Saudi Arabia); Calvo, Florent [University of Grenoble Alpes, LIPHY, F-38000 Grenoble, France and CNRS, LIPHY, F-38000 Grenoble (France); Oujia, Brahim [Laboratoire de Physique Quantique, Faculté des Sciences de Monastir, Université de Monastir, Avenue de l’Environnement, 5019 Monastir (Tunisia); Physics Department, Faculty of Science, King Abdulaziz University, Jeddah (Saudi Arabia)
2014-10-21
The structures and relative stabilities of mixed Ba{sup 2+}Xe{sub n} (n = 1–39, 54) clusters have been theoretically studied using basin-hopping global optimization. Analytical potential energy surfaces were constructed from ab initio or experimental data, assuming either purely additive interactions or including many-body polarization effects and the mutual contribution of self-consistent induced dipoles. For both models the stable structures are characterized by the barium cation being coated by a shell of xenon atoms, as expected from simple energetic arguments. Icosahedral packing is dominantly found, the exceptional stability of the icosahedral motif at n = 12 being further manifested at the size n = 32 where the basic icosahedron is surrounded by a dodecahedral cage, and at n = 54 where the transition to multilayer Mackay icosahedra has occurred. Interactions between induced dipoles generally tend to decrease the Xe-Xe binding, leading to different solvation patterns at small sizes but also favoring polyicosahedral growth. Besides attenuating relative energetic stability, many-body effects affect the structures by expanding the clusters by a few percents and allowing them to deform more.
Energy Technology Data Exchange (ETDEWEB)
Sakmann, Kaspar
2010-07-21
In this thesis, the physics of trapped, interacting Bose-Einstein condensates is analyzed by solving the many-body Schroedinger equation. Particular emphasis is put on coherence, fragmentation and reduced density matrices. First, the ground state of a trapped Bose-Einstein condensate and its correlation functions are obtained. Then the dynamics of a bosonic Josephson junction is investigated by solving the time-dependent many-body Schroedinger equation numerically exactly. These are the first exact results in literature in this context. It is shown that the standard approximations of the field, Gross-Pitaevskii theory and the Bose-Hubbard model fail at weak interaction strength and within their range of expected validity. For stronger interactions the dynamics becomes strongly correlated and a new equilibration phenomenon is discovered. By comparison with exact results it is shown that a symmetry of the Bose- Hubbard model between attractive and repulsive interactions must be considered an artefact of the model. A conceptual innovation of this thesis are time-dependent Wannier functions. Equations of motion for time-dependent Wannier functions are derived from the variational principle. By comparison with exact results it is shown that lattice models can be greatly improved at little computational cost by letting the Wannier functions of a lattice model become time-dependent. (orig.)
Rotation Invariance Neural Network
Li, Shiyuan
2017-01-01
Rotation invariance and translation invariance have great values in image recognition tasks. In this paper, we bring a new architecture in convolutional neural network (CNN) named cyclic convolutional layer to achieve rotation invariance in 2-D symbol recognition. We can also get the position and orientation of the 2-D symbol by the network to achieve detection purpose for multiple non-overlap target. Last but not least, this architecture can achieve one-shot learning in some cases using thos...
Infinity-Norm Permutation Covering Codes from Cyclic Groups
Karni, Ronen; Schwartz, Moshe
2017-01-01
We study covering codes of permutations with the $\\ell_\\infty$-metric. We provide a general code construction, which uses smaller building-block codes. We study cyclic transitive groups as building blocks, determining their exact covering radius, and showing linear-time algorithms for finding a covering codeword. We also bound the covering radius of relabeled cyclic transitive groups under conjugation.
A discriminative syntactic model for source permutation via tree transduction
Khalilov, M.; Sima'an, K.; Wu, D.
2010-01-01
A major challenge in statistical machine translation is mitigating the word order differences between source and target strings. While reordering and lexical translation choices are often conducted in tandem, source string permutation prior to translation is attractive for studying reordering using
A permutation test for the race model inequality
DEFF Research Database (Denmark)
Gondan, Matthias
2010-01-01
signals. Several statistical procedures have been used for testing the race model inequality. However, the commonly employed procedure does not control the Type I error. In this article a permutation test is described that keeps the Type I error at the desired level. Simulations show that the power...
Testing for changes using permutations of U-statistics
Czech Academy of Sciences Publication Activity Database
Horvath, L.; Hušková, Marie
2005-01-01
Roč. 2005, č. 128 (2005), s. 351-371 ISSN 0378-3758 R&D Projects: GA ČR GA201/00/0769 Institutional research plan: CEZ:AV0Z10750506 Keywords : U-statistics * permutations * change-point * weighted approximation * Brownian bridge Subject RIV: BD - Theory of Information Impact factor: 0.481, year: 2005
Calogero, Francesco
2001-01-01
This book focuses on exactly treatable classical (i.e. non-quantal non-relativistic) many-body problems, as described by Newton's equation of motion for mutually interacting point particles. Most of the material is based on the author's research and is published here for the first time in book form. One of the main novelties is the treatment of problems in two- and three-dimensional space. Many related techniques are presented, e.g. the theory of generalized Lagrangian-type interpolation in higher-dimensional spaces. This book is written for students as well as for researchers; it works out detailed examples before going on to treat more general cases. Many results are presented via exercises, with clear hints pointing to their solutions.
Caruso, Fabio; Rohr, Daniel R; Hellgren, Maria; Ren, Xinguo; Rinke, Patrick; Rubio, Angel; Scheffler, Matthias
2013-04-05
For the paradigmatic case of H(2) dissociation, we compare state-of-the-art many-body perturbation theory in the GW approximation and density-functional theory in the exact-exchange plus random-phase approximation (RPA) for the correlation energy. For an unbiased comparison and to prevent spurious starting point effects, both approaches are iterated to full self-consistency (i.e., sc-RPA and sc-GW). The exchange-correlation diagrams in both approaches are topologically identical, but in sc-RPA they are evaluated with noninteracting and in sc-GW with interacting Green functions. This has a profound consequence for the dissociation region, where sc-RPA is superior to sc-GW. We argue that for a given diagrammatic expansion, sc-RPA outperforms sc-GW when it comes to bond breaking. We attribute this to the difference in the correlation energy rather than the treatment of the kinetic energy.
Energy Technology Data Exchange (ETDEWEB)
Yourshaw, Ivan [Univ. of California, Berkeley, CA (United States)
1998-07-09
The diatomic halogen atom-rare gas diatomic complexes KrBr^{-}, XeBr^{-}, and KrCl^{-} are studied in this work by zero electron kinetic energy (ZEKE) spectroscopy in order to characterize the weak intermolecular diatomic potentials of these species. Also, the ZEKE and threshold photodetachment spectra of the polyatomic clusters Ar_{n}Br^{-} (n = 2-9) and Ar_{n}I^{-} (n = 2-19) are studied to obtain information about the non-additive effects on the interactions among the atoms. This work is part of an ongoing effort to characterize the pair and many-body potentials of the complete series of rare gas halide clusters. In these studies we obtain information about both the anionic and neutral clusters.
International Nuclear Information System (INIS)
Brand, J.; Cederbaum, L.S.
1996-01-01
An extension of the fermionic particle-particle propagator is presented that possesses similar algebraic properties to the single-particle Green close-quote s function. In particular, this extended two-particle Green close-quote s function satisfies Dyson close-quote s equation and its self energy has the same analytic structure as the self energy of the single-particle Green close-quote s function. For the case of a system interacting with one-particle potentials only, the two-particle self energy takes on a particularly simple form, just like the common self energy does. The new two-particle self energy also serves as a well behaved optical potential for the elastic scattering of a two-particle projectile by a many-body target. Due to its analytic structure, the two-particle self energy avoids divergences that appear with effective potentials derived by other means. Copyright copyright 1996 Academic Press, Inc
Lorentz invariance with an invariant energy scale.
Magueijo, João; Smolin, Lee
2002-05-13
We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory at low energies. This is accomplished by a nonlinear modification of the action of the Lorentz group on momentum space, generated by adding a dilatation to each boost in such a way that the Planck energy remains invariant. The associated algebra has unmodified structure constants. We also discuss the resulting modifications of field theory and suggest a modification of the equivalence principle which determines how the new theory is embedded in general relativity.
Liu, Kuan-Yu; Herbert, John M
2017-10-28
Papers I and II in this series [R. M. Richard et al., J. Chem. Phys. 141, 014108 (2014); K. U. Lao et al., ibid. 144, 164105 (2016)] have attempted to shed light on precision and accuracy issues affecting the many-body expansion (MBE), which only manifest in larger systems and thus have received scant attention in the literature. Many-body counterpoise (CP) corrections are shown to accelerate convergence of the MBE, which otherwise suffers from a mismatch between how basis-set superposition error affects subsystem versus supersystem calculations. In water clusters ranging in size up to (H 2 O) 37 , four-body terms prove necessary to achieve accurate results for both total interaction energies and relative isomer energies, but the sheer number of tetramers makes the use of cutoff schemes essential. To predict relative energies of (H 2 O) 20 isomers, two approximations based on a lower level of theory are introduced and an ONIOM-type procedure is found to be very well converged with respect to the appropriate MBE benchmark, namely, a CP-corrected supersystem calculation at the same level of theory. Results using an energy-based cutoff scheme suggest that if reasonable approximations to the subsystem energies are available (based on classical multipoles, say), then the number of requisite subsystem calculations can be reduced even more dramatically than when distance-based thresholds are employed. The end result is several accurate four-body methods that do not require charge embedding, and which are stable in large basis sets such as aug-cc-pVTZ that have sometimes proven problematic for fragment-based quantum chemistry methods. Even with aggressive thresholding, however, the four-body approach at the self-consistent field level still requires roughly ten times more processors to outmatch the performance of the corresponding supersystem calculation, in test cases involving 1500-1800 basis functions.
Liu, Kuan-Yu; Herbert, John M.
2017-10-01
Papers I and II in this series [R. M. Richard et al., J. Chem. Phys. 141, 014108 (2014); K. U. Lao et al., ibid. 144, 164105 (2016)] have attempted to shed light on precision and accuracy issues affecting the many-body expansion (MBE), which only manifest in larger systems and thus have received scant attention in the literature. Many-body counterpoise (CP) corrections are shown to accelerate convergence of the MBE, which otherwise suffers from a mismatch between how basis-set superposition error affects subsystem versus supersystem calculations. In water clusters ranging in size up to (H2O)37, four-body terms prove necessary to achieve accurate results for both total interaction energies and relative isomer energies, but the sheer number of tetramers makes the use of cutoff schemes essential. To predict relative energies of (H2O)20 isomers, two approximations based on a lower level of theory are introduced and an ONIOM-type procedure is found to be very well converged with respect to the appropriate MBE benchmark, namely, a CP-corrected supersystem calculation at the same level of theory. Results using an energy-based cutoff scheme suggest that if reasonable approximations to the subsystem energies are available (based on classical multipoles, say), then the number of requisite subsystem calculations can be reduced even more dramatically than when distance-based thresholds are employed. The end result is several accurate four-body methods that do not require charge embedding, and which are stable in large basis sets such as aug-cc-pVTZ that have sometimes proven problematic for fragment-based quantum chemistry methods. Even with aggressive thresholding, however, the four-body approach at the self-consistent field level still requires roughly ten times more processors to outmatch the performance of the corresponding supersystem calculation, in test cases involving 1500-1800 basis functions.
Réal, Florent; Vallet, Valérie; Flament, Jean-Pierre; Masella, Michel
2013-09-21
We present a revised version of the water many-body model TCPE [M. Masella and J.-P. Flament, J. Chem. Phys. 107, 9105 (1997)], which is based on a static three charge sites and a single polarizable site to model the molecular electrostatic properties of water, and on an anisotropic short range many-body energy term specially designed to accurately model hydrogen bonding in water. The parameters of the revised model, denoted TCPE/2013, are here developed to reproduce the ab initio energetic and geometrical properties of small water clusters (up to hexamers) and the repulsive water interactions occurring in cation first hydration shells. The model parameters have also been refined to reproduce two liquid water properties at ambient conditions, the density and the vaporization enthalpy. Thanks to its computational efficiency, the new model range of applicability was validated by performing simulations of liquid water over a wide range of temperatures and pressures, as well as by investigating water liquid/vapor interfaces over a large range of temperatures. It is shown to reproduce several important water properties at an accurate enough level of precision, such as the existence liquid water density maxima up to a pressure of 1000 atm, the water boiling temperature, the properties of the water critical point (temperature, pressure, and density), and the existence of a "singularity" temperature at about 225 K in the supercooled regime. This model appears thus to be particularly well-suited for characterizing ion hydration properties under different temperature and pressure conditions, as well as in different phases and interfaces.
International Nuclear Information System (INIS)
Moriyasu, K.
1978-01-01
A pedagogical approach to gauge invariance is presented which is based on the analogy between gauge transformations and relativity. By using the concept of an internal space, purely geometrical arguments are used to teach the physical ideas behind gauge invariance. Many of the results are applicable to general gauge theories
Measurement invariance versus selection invariance: Is fair selection possible?
Borsboom, D.; Romeijn, J.W.; Wicherts, J.M.
2008-01-01
This article shows that measurement invariance (defined in terms of an invariant measurement model in different groups) is generally inconsistent with selection invariance (defined in terms of equal sensitivity and specificity across groups). In particular, when a unidimensional measurement
Measurement invariance versus selection invariance : Is fair selection possible?
Borsboom, Denny; Romeijn, Jan-Willem; Wicherts, Jelte M.
This article shows that measurement invariance (defined in terms of an invariant measurement model in different groups) is generally inconsistent with selection invariance (defined in terms of equal sensitivity and specificity across groups). In particular, when a unidimensional measurement
Invariance Signatures: Characterizing contours by their departures from invariance
Squire, David; Caelli, Terry M.
1997-01-01
In this paper, a new invariant feature of two-dimensional contours is reported: the Invariance Signature. The Invariance Signature is a measure of the degree to which a contour is invariant under a variety of transformations, derived from the theory of Lie transformation groups. It is shown that the Invariance Signature is itself invariant under shift, rotation and scaling of the contour. Since it is derived from local properties of the contour, it is well-suited to a neural network implement...
A Weak Quantum Blind Signature with Entanglement Permutation
Lou, Xiaoping; Chen, Zhigang; Guo, Ying
2015-09-01
Motivated by the permutation encryption algorithm, a weak quantum blind signature (QBS) scheme is proposed. It involves three participants, including the sender Alice, the signatory Bob and the trusted entity Charlie, in four phases, i.e., initializing phase, blinding phase, signing phase and verifying phase. In a small-scale quantum computation network, Alice blinds the message based on a quantum entanglement permutation encryption algorithm that embraces the chaotic position string. Bob signs the blinded message with private parameters shared beforehand while Charlie verifies the signature's validity and recovers the original message. Analysis shows that the proposed scheme achieves the secure blindness for the signer and traceability for the message owner with the aid of the authentic arbitrator who plays a crucial role when a dispute arises. In addition, the signature can neither be forged nor disavowed by the malicious attackers. It has a wide application to E-voting and E-payment system, etc.
Optimization and experimental realization of the quantum permutation algorithm
Yalçınkaya, I.; Gedik, Z.
2017-12-01
The quantum permutation algorithm provides computational speed-up over classical algorithms for determining the parity of a given cyclic permutation. For its n -qubit implementations, the number of required quantum gates scales quadratically with n due to the quantum Fourier transforms included. We show here for the n -qubit case that the algorithm can be simplified so that it requires only O (n ) quantum gates, which theoretically reduces the complexity of the implementation. To test our results experimentally, we utilize IBM's 5-qubit quantum processor to realize the algorithm by using the original and simplified recipes for the 2-qubit case. It turns out that the latter results in a significantly higher success probability which allows us to verify the algorithm more precisely than the previous experimental realizations. We also verify the algorithm for the first time for the 3-qubit case with a considerable success probability by taking the advantage of our simplified scheme.
Information sets as permutation cycles for quadratic residue codes
Directory of Open Access Journals (Sweden)
Richard A. Jenson
1982-01-01
Full Text Available The two cases p=7 and p=23 are the only known cases where the automorphism group of the [p+1, (p+1/2] extended binary quadratic residue code, O(p, properly contains PSL(2,p. These codes have some of their information sets represented as permutation cycles from Aut(Q(p. Analysis proves that all information sets of Q(7 are so represented but those of Q(23 are not.
Successful attack on permutation-parity-machine-based neural cryptography.
Seoane, Luís F; Ruttor, Andreas
2012-02-01
An algorithm is presented which implements a probabilistic attack on the key-exchange protocol based on permutation parity machines. Instead of imitating the synchronization of the communicating partners, the strategy consists of a Monte Carlo method to sample the space of possible weights during inner rounds and an analytic approach to convey the extracted information from one outer round to the next one. The results show that the protocol under attack fails to synchronize faster than an eavesdropper using this algorithm.
Gerosa, M.; E Bottani, C.; Di Valentin, C.; Onida, G.; Pacchioni, G.
2018-01-01
Understanding the electronic structure of metal oxide semiconductors is crucial to their numerous technological applications, such as photoelectrochemical water splitting and solar cells. The needed experimental and theoretical knowledge goes beyond that of pristine bulk crystals, and must include the effects of surfaces and interfaces, as well as those due to the presence of intrinsic defects (e.g. oxygen vacancies), or dopants for band engineering. In this review, we present an account of the recent efforts in predicting and understanding the optoelectronic properties of oxides using ab initio theoretical methods. In particular, we discuss the performance of recently developed dielectric-dependent hybrid functionals, providing a comparison against the results of many-body GW calculations, including G 0 W 0 as well as more refined approaches, such as quasiparticle self-consistent GW. We summarize results in the recent literature for the band gap, the band level alignment at surfaces, and optical transition energies in defective oxides, including wide gap oxide semiconductors and transition metal oxides. Correlated transition metal oxides are also discussed. For each method, we describe successes and drawbacks, emphasizing the challenges faced by the development of improved theoretical approaches. The theoretical section is preceded by a critical overview of the main experimental techniques needed to characterize the optoelectronic properties of semiconductors, including absorption and reflection spectroscopy, photoemission, and scanning tunneling spectroscopy (STS).
Energy Technology Data Exchange (ETDEWEB)
Babamoradi, Mohsen, E-mail: babamoradi@iust.ac.ir [Department of Physics, Iran University of Science and Technology, Narmak,16846-13114 Tehran (Iran, Islamic Republic of); Asgari, Sussan [Department of Physics, Iran University of Science and Technology, Narmak,16846-13114 Tehran (Iran, Islamic Republic of); Ranjbar, Ahmad [Computational Materials Science Research Team, RIKEN Advanced Institute for Computational Science, Kobe, Hyogo 650-0047 (Japan); Belosludov, Rodion V. [Institute for Materials Research, Tohoku University, Sendai 980-8577 (Japan); Yunoki, Seiji [Computational Materials Science Research Team, RIKEN Advanced Institute for Computational Science, Kobe, Hyogo 650-0047 (Japan); Computational Condensed Matter Physics Laboratory, RIKEN, Wako, Saitama 351-0198 (Japan); Computational Quantum Matter Research Team, RIKEN Center for Emergent Matter Science, Wako, Saitama 351-0198 (Japan)
2017-01-15
A new model is applied to calculate the many-body properties of the neutral N3 color center in diamond. This model is based on the first-principles density functional theory (DFT) and cluster method, which is combined with the generalized Hubbard model. In contrast to the previous models for N3 centers, our model does not require the configuration interaction (CI) and molecular orbital (MO) techniques. The N3 defect in diamond is simulated with an empty site next to three substitutional nitrogen atoms in the center of a hydrogen-terminated diamond cluster. The method is shown to be highly accurate for describing the symmetries and spin properties of the ground state and the first dipole-allowed excited state for the N3 center. We obtain the transition energy as 412 nm for the first dipole-allowed transition, which is in good agreement with the corresponding experimental value as 415 nm. We assigned the dipole-allowed transition between the first and second excited states as the N2 optical peak, and evaluated the N2 optical peak to be 463 nm, which is close to the experimental value as 478 nm.
International Nuclear Information System (INIS)
Rao, B.K.; Das, T.P.
1982-01-01
Using linked cluster many-body perturbation theory, the frequency-dependent dipole polarizabilities a(ω) has been calculated for the lithium atom. The value of a(ω) at the static limit (169.04 a 0 3 ) matches well with other available theoretical values and experimental results. These values have been used to calculate the van der Waals constants for interactions of lithium, helium and neon atoms. The values of the van der Waals constants for dipole-dipole interaction in atomic units are -22.9, -44.8, -1465.8, 184950.0, 2011.8, 3896.5, 30.3, 59.0 and 115.1 for Li-He, Li-Ne, Li-Li, Li-Li-Li, Li-Li-He, Li-Li-Ne, Li-He-He, Li-He-Ne and Li-Ne-Ne interactions respectively. Obtaining the suitable response functions for lithium and helium atoms, the long range contribution to Δa(r)/a 0 in the study of fractional frequency shift in hyperfine pressure and temperature shift measurements is obtained as -541 atomic units. (author)
Energy Technology Data Exchange (ETDEWEB)
Millis, Andrew [Columbia Univ., New York, NY (United States). Dept. of Physics
2016-11-17
Understanding the behavior of interacting electrons in molecules and solids so that one can predict new superconductors, catalysts, light harvesters, energy and battery materials and optimize existing ones is the ``quantum many-body problem’’. This is one of the scientific grand challenges of the 21^{st} century. A complete solution to the problem has been proven to be exponentially hard, meaning that straightforward numerical approaches fail. New insights and new methods are needed to provide accurate yet feasible approximate solutions. This CMSCN project brought together chemists and physicists to combine insights from the two disciplines to develop innovative new approaches. Outcomes included the Density Matrix Embedding method, a new, computationally inexpensive and extremely accurate approach that may enable first principles treatment of superconducting and magnetic properties of strongly correlated materials, new techniques for existing methods including an Adaptively Truncated Hilbert Space approach that will vastly expand the capabilities of the dynamical mean field method, a self-energy embedding theory and a new memory-function based approach to the calculations of the behavior of driven systems. The methods developed under this project are now being applied to improve our understanding of superconductivity, to calculate novel topological properties of materials and to characterize and improve the properties of nanoscale devices.
Morozov, Albert D; Dragunov, Timothy N; Malysheva, Olga V
1999-01-01
This book deals with the visualization and exploration of invariant sets (fractals, strange attractors, resonance structures, patterns etc.) for various kinds of nonlinear dynamical systems. The authors have created a special Windows 95 application called WInSet, which allows one to visualize the invariant sets. A WInSet installation disk is enclosed with the book.The book consists of two parts. Part I contains a description of WInSet and a list of the built-in invariant sets which can be plotted using the program. This part is intended for a wide audience with interests ranging from dynamical
A chronicle of permutation statistical methods 1920–2000, and beyond
Berry, Kenneth J; Mielke Jr , Paul W
2014-01-01
The focus of this book is on the birth and historical development of permutation statistical methods from the early 1920s to the near present. Beginning with the seminal contributions of R.A. Fisher, E.J.G. Pitman, and others in the 1920s and 1930s, permutation statistical methods were initially introduced to validate the assumptions of classical statistical methods. Permutation methods have advantages over classical methods in that they are optimal for small data sets and non-random samples, are data-dependent, and are free of distributional assumptions. Permutation probability values may be exact, or estimated via moment- or resampling-approximation procedures. Because permutation methods are inherently computationally-intensive, the evolution of computers and computing technology that made modern permutation methods possible accompanies the historical narrative. Permutation analogs of many well-known statistical tests are presented in a historical context, including multiple correlation and regression, ana...
Directory of Open Access Journals (Sweden)
Gabriel Recchia
2015-01-01
Full Text Available Circular convolution and random permutation have each been proposed as neurally plausible binding operators capable of encoding sequential information in semantic memory. We perform several controlled comparisons of circular convolution and random permutation as means of encoding paired associates as well as encoding sequential information. Random permutations outperformed convolution with respect to the number of paired associates that can be reliably stored in a single memory trace. Performance was equal on semantic tasks when using a small corpus, but random permutations were ultimately capable of achieving superior performance due to their higher scalability to large corpora. Finally, “noisy” permutations in which units are mapped to other units arbitrarily (no one-to-one mapping perform nearly as well as true permutations. These findings increase the neurological plausibility of random permutations and highlight their utility in vector space models of semantics.
Sorting signed permutations by inversions in O(nlogn) time.
Swenson, Krister M; Rajan, Vaibhav; Lin, Yu; Moret, Bernard M E
2010-03-01
The study of genomic inversions (or reversals) has been a mainstay of computational genomics for nearly 20 years. After the initial breakthrough of Hannenhalli and Pevzner, who gave the first polynomial-time algorithm for sorting signed permutations by inversions, improved algorithms have been designed, culminating with an optimal linear-time algorithm for computing the inversion distance and a subquadratic algorithm for providing a shortest sequence of inversions--also known as sorting by inversions. Remaining open was the question of whether sorting by inversions could be done in O(nlogn) time. In this article, we present a qualified answer to this question, by providing two new sorting algorithms, a simple and fast randomized algorithm and a deterministic refinement. The deterministic algorithm runs in time O(nlogn + kn), where k is a data-dependent parameter. We provide the results of extensive experiments showing that both the average and the standard deviation for k are small constants, independent of the size of the permutation. We conclude (but do not prove) that almost all signed permutations can be sorted by inversions in O(nlogn) time.
Optimal control of hybrid qubits: Implementing the quantum permutation algorithm
Rivera-Ruiz, C. M.; de Lima, E. F.; Fanchini, F. F.; Lopez-Richard, V.; Castelano, L. K.
2018-03-01
The optimal quantum control theory is employed to determine electric pulses capable of producing quantum gates with a fidelity higher than 0.9997, when noise is not taken into account. Particularly, these quantum gates were chosen to perform the permutation algorithm in hybrid qubits in double quantum dots (DQDs). The permutation algorithm is an oracle based quantum algorithm that solves the problem of the permutation parity faster than a classical algorithm without the necessity of entanglement between particles. The only requirement for achieving the speedup is the use of a one-particle quantum system with at least three levels. The high fidelity found in our results is closely related to the quantum speed limit, which is a measure of how fast a quantum state can be manipulated. Furthermore, we model charge noise by considering an average over the optimal field centered at different values of the reference detuning, which follows a Gaussian distribution. When the Gaussian spread is of the order of 5 μ eV (10% of the correct value), the fidelity is still higher than 0.95. Our scheme also can be used for the practical realization of different quantum algorithms in DQDs.
Cosmological disformal invariance
Energy Technology Data Exchange (ETDEWEB)
Domènech, Guillem; Sasaki, Misao [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan); Naruko, Atsushi, E-mail: guillem.domenech@yukawa.kyoto-u.ac.jp, E-mail: naruko@th.phys.titech.ac.jp, E-mail: misao@yukawa.kyoto-u.ac.jp [Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551 (Japan)
2015-10-01
The invariance of physical observables under disformal transformations is considered. It is known that conformal transformations leave physical observables invariant. However, whether it is true for disformal transformations is still an open question. In this paper, it is shown that a pure disformal transformation without any conformal factor is equivalent to rescaling the time coordinate. Since this rescaling applies equally to all the physical quantities, physics must be invariant under a disformal transformation, that is, neither causal structure, propagation speed nor any other property of the fields are affected by a disformal transformation itself. This fact is presented at the action level for gravitational and matter fields and it is illustrated with some examples of observable quantities. We also find the physical invariance for cosmological perturbations at linear and high orders in perturbation, extending previous studies. Finally, a comparison with Horndeski and beyond Horndeski theories under a disformal transformation is made.
Algorithms in invariant theory
Sturmfels, Bernd
2008-01-01
J. Kung and G.-C. Rota, in their 1984 paper, write: "Like the Arabian phoenix rising out of its ashes, the theory of invariants, pronounced dead at the turn of the century, is once again at the forefront of mathematics". The book of Sturmfels is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory. The Groebner bases method is the main tool by which the central problems in invariant theory become amenable to algorithmic solutions. Students will find the book an easy introduction to this "classical and new" area of mathematics. Researchers in mathematics, symbolic computation, and computer science will get access to a wealth of research ideas, hints for applications, outlines and details of algorithms, worked out examples, and research problems.
Coordinate-invariant regularization
International Nuclear Information System (INIS)
Halpern, M.B.
1987-01-01
A general phase-space framework for coordinate-invariant regularization is given. The development is geometric, with all regularization contained in regularized DeWitt Superstructures on field deformations. Parallel development of invariant coordinate-space regularization is obtained by regularized functional integration of the momenta. As representative examples of the general formulation, the regularized general non-linear sigma model and regularized quantum gravity are discussed. copyright 1987 Academic Press, Inc
International Nuclear Information System (INIS)
Ohno, Masahide
2007-01-01
Recently Danger et al. [J. Danger, H. Magnan, D. Chandesris, P. Le Fevre, S. Bourgeois, J. Jupille, A. Verdini, R. Gotter, A. Morgante, Phys. Rev. B 64 (2001) 045110] and Le Fevre et al. [P. Le Fevre, J. Danger, H. Magnan, D. Chandesris, J. Jupille, S. Bourgeois, M.-A. Arrio, R. Gotter, A. Verdini, A. Morgante, Phys. Rev. B 69 (2004) 155421] showed the absence of resonant Raman scattering feature in the Ti L 23 -M 23 V resonant Auger-electron spectroscopy (RAES) spectra of Ti oxides measured across the Ti 2p edges. They attributed the absence to the covalent character of the Ti-O bond which allows an effective delocalization of 3d electrons. It is shown by a many-body theory that when the time scale of relaxation of the resonantly excited core-hole state to the fully relaxed core-hole state is much shorter than that of core-hole decay, any sizeable Raman scattering is absent in the RAES spectra measured across the Ti 2p edges. The relaxation width depends on the hybridization strength and the charge transfer (CT) energy between the two states. The L 2 -L 3 V Coster-Kronig (CK) decay widths of TiO 2 and TiO 2-x are determined from the L 23 -M 23 V Auger-photoelectron coincidence spectroscopy (APECS) spectra reported in the aforementioned papers. They are about 0.18 and 0.35 eV, respectively. The CK-decay width in the reduced Ti oxide increases compared to that of TiO 2 in rutile because of filling of the 3d states just below the Fermi level in the former
Hirata, So; Doran, Alexander E; Knowles, Peter J; Ortiz, J V
2017-07-28
A thorough analytical and numerical characterization of the whole perturbation series of one-particle many-body Green's function (MBGF) theory is presented in a pedagogical manner. Three distinct but equivalent algebraic (first-quantized) recursive definitions of the perturbation series of the Green's function are derived, which can be combined with the well-known recursion for the self-energy. Six general-order algorithms of MBGF are developed, each implementing one of the three recursions, the ΔMPn method (where n is the perturbation order) [S. Hirata et al., J. Chem. Theory Comput. 11, 1595 (2015)], the automatic generation and interpretation of diagrams, or the numerical differentiation of the exact Green's function with a perturbation-scaled Hamiltonian. They all display the identical, nondivergent perturbation series except ΔMPn, which agrees with MBGF in the diagonal and frequency-independent approximations at 1≤n≤3 but converges at the full-configuration-interaction (FCI) limit at n=∞ (unless it diverges). Numerical data of the perturbation series are presented for Koopmans and non-Koopmans states to quantify the rate of convergence towards the FCI limit and the impact of the diagonal, frequency-independent, or ΔMPn approximation. The diagrammatic linkedness and thus size-consistency of the one-particle Green's function and self-energy are demonstrated at any perturbation order on the basis of the algebraic recursions in an entirely time-independent (frequency-domain) framework. The trimming of external lines in a one-particle Green's function to expose a self-energy diagram and the removal of reducible diagrams are also justified mathematically using the factorization theorem of Frantz and Mills. Equivalence of ΔMPn and MBGF in the diagonal and frequency-independent approximations at 1≤n≤3 is algebraically proven, also ascribing the differences at n = 4 to the so-called semi-reducible and linked-disconnected diagrams.