Fock expansion of multimode pure Gaussian states
Energy Technology Data Exchange (ETDEWEB)
Cariolaro, Gianfranco; Pierobon, Gianfranco, E-mail: gianfranco.pierobon@unipd.it [Università di Padova, Padova (Italy)
2015-12-15
The Fock expansion of multimode pure Gaussian states is derived starting from their representation as displaced and squeezed multimode vacuum states. The approach is new and appears to be simpler and more general than previous ones starting from the phase-space representation given by the characteristic or Wigner function. Fock expansion is performed in terms of easily evaluable two-variable Hermite–Kampé de Fériet polynomials. A relatively simple and compact expression for the joint statistical distribution of the photon numbers in the different modes is obtained. In particular, this result enables one to give a simple characterization of separable and entangled states, as shown for two-mode and three-mode Gaussian states.
The light-cone Fock state expansion and hadron physics phenomenology
Energy Technology Data Exchange (ETDEWEB)
Brodsky, S.J.
1997-06-01
The light-cone Fock expansion is defined in the following way: one first constructs the light-cone time evolution operator and the invariant mass operator in light-cone gauge from the QCD Lagrangian. The total longitudinal momentum and transverse momenta are conserved, i.e. are independent of the interactions. The matrix elements of the invariant mass operator on the complete orthonormal basis of the free theory can then be constructed. The matrix elements connect Fock states differing by 0, 1, or 2 quark or gluon quanta, and they include the instantaneous quark and gluon contributions imposed by eliminating dependent degrees of freedom in light-cone gauge. Applications of light-cone methods to QCD phenomenology are briefly described.
Coherent states in the fermionic Fock space
Oeckl, Robert
2015-01-01
We construct the coherent states in the sense of Gilmore and Perelomov for the fermionic Fock space. Our treatment is from the outset adapted to the infinite-dimensional case. The fermionic Fock space becomes in this way a reproducing kernel Hilbert space of continuous holomorphic functions.
Atomic Fock State Preparation Using Rydberg Blockade
Ebert, Matthew; Gibbons, Michael; Zhang, Xianli; Saffman, Mark; Walker, Thad G
2013-01-01
We use coherent excitation of 3-16 atom ensembles to demonstrate collective Rabi flopping mediated by Rydberg blockade. Using calibrated atom number measurements, we quantitatively confirm the expected $\\sqrt{N}$ Rabi frequency enhancement to within 4%. The resulting atom number distributions are consistent with essentially perfect blockade. We then use collective Rabi $\\pi$ pulses to produce ${\\cal N}=1,2$ atom number Fock states with fidelities of 62% and 48% respectively. The ${\\cal N}=2$ Fock state shows the collective Rabi frequency enhancement without corruption from atom number fluctuations.
Poisson process Fock space representation, chaos expansion and covariance inequalities
Last, Guenter
2009-01-01
We consider a Poisson process $\\eta$ on an arbitrary measurable space with an arbitrary sigma-finite intensity measure. We establish an explicit Fock space representation of square integrable functions of $\\eta$. As a consequence we identify explicitly, in terms of iterated difference operators, the integrands in the Wiener-Ito chaos expansion. We apply these results to extend well-known variance inequalities for homogeneous Poisson processes on the line to the general Poisson case. The Poincare inequality is a special case. Further applications are covariance identities for Poisson processes on (strictly) ordered spaces and Harris-FKG-inequalities for monotone functions of $\\eta$.
Nonlinear Interferometry via Fock State Projection
Khoury, G; Eisenberg, H S; Fonseca, E J S
2006-01-01
We use a photon-number resolving detector to monitor the photon number distribution of the output of an interferometer, as a function of phase delay. As inputs we use coherent states with mean photon number up to seven. The postselection of a specific Fock (photon-number) state effectively induces high-order optical non-linearities. Following a scheme by Bentley and Boyd [S.J. Bentley and R.W. Boyd, Optics Express 12, 5735 (2004)] we explore this effect to demonstrate interference patterns a factor of five smaller than the Rayleigh limit.
Nonlinear Interferometry via Fock-State Projection
Khoury, G.; Eisenberg, H. S.; Fonseca, E. J. S.; Bouwmeester, D.
2006-05-01
We use a photon-number-resolving detector to monitor the photon-number distribution of the output of an interferometer, as a function of phase delay. As inputs we use coherent states with mean photon number up to seven. The postselection of a specific Fock (photon-number) state effectively induces high-order optical nonlinearities. Following a scheme by Bentley and Boyd [Opt. Express 12, 5735 (2004).OPEXFF1094-408710.1364/OPEX.12.005735], we explore this effect to demonstrate interference patterns a factor of 5 smaller than the Rayleigh limit.
Many-body expansion of the Fock matrix in the fragment molecular orbital method
Fedorov, Dmitri G.; Kitaura, Kazuo
2017-09-01
A many-body expansion of the Fock matrix in the fragment molecular orbital method is derived up to three-body terms for restricted Hartree-Fock and density functional theory in the atomic orbital basis and compared to the expansion in the basis of fragment molecular orbitals (MOs). The physical nature of many-body corrections is revealed in terms of charge transfer terms. An improvement of the fragment MO expansion is proposed by adding exchange to the embedding. The accuracy of all developed methods is demonstrated in comparison to unfragmented results for polyalanines, a water cluster, Trp-cage (PDB: 1L2Y) and crambin (PDB: 1CRN) proteins, a zeolite cluster, a Si nano-wire, and a boron nitride ribbon. The physical nature of metallicity is discussed, and it is shown what kinds of metallic systems can be treated by fragment-based methods. The density of states is calculated for a fully closed and a partially open nano-ring of boron nitride with a diameter of 105 nm.
The Light-Cone Fock Expansion in Quantum Chromodynamics
Brodsky, S J
2000-01-01
A fundamental question in QCD is the non-perturbative structure of hadrons at the amplitude level--not just the single-particle flavor, momentum, and helicity distributions of the quark constituents, but also the multi-quark, gluonic, and hidden-color correlations intrinsic to hadronic and nuclear wavefunctions. The light-cone Fock-state representation of QCD encodes the properties of a hadrons in terms of frame-independent wavefunctions. A number of applications are discussed, including semileptonic B decays, deeply virtual Compton scattering, and dynamical higher twist effects in inclusive reactions. A new type of jet production reaction, "self-resolving diffractive interactions" can provide direct information on the light-cone wavefunctions of hadrons in terms of their quark and gluon degrees of freedom as well as the composition of nuclei in terms of their nucleon and mesonic degrees of freedom. The relation of the intrinsic sea to the light-cone wavefunctions is discussed. The physics of light-cone wavef...
Quantum Harmonic Oscillator State Control in a Squeezed Fock Basis
Kienzler, D.; Lo, H.-Y.; Negnevitsky, V.; Flühmann, C.; Marinelli, M.; Home, J. P.
2017-07-01
We demonstrate control of a trapped-ion quantum harmonic oscillator in a squeezed Fock state basis, using engineered Hamiltonians analogous to the Jaynes-Cummings and anti-Jaynes-Cummings forms. We demonstrate that for squeezed Fock states with low n the engineered Hamiltonians reproduce the √{n } scaling of the matrix elements which is typical of Jaynes-Cummings physics, and also examine deviations due to the finite wavelength of our control fields. Starting from a squeezed vacuum state, we apply sequences of alternating transfer pulses which allow us to climb the squeezed Fock state ladder, creating states up to excitations of n =6 with up to 8.7 dB of squeezing, as well as demonstrating superpositions of these states. These techniques offer access to new sets of states of the harmonic oscillator which may be applicable for precision metrology or quantum information science.
Quantum homodyne tomography of a two-photon Fock state
Ourjoumtsev, A; Grangier, P; Ourjoumtsev, Alexei; Tualle-Brouri, Rosa; Grangier, Philippe
2006-01-01
We present a continuous-variable experimental analysis of a two-photon Fock state of free-propagating light. This state is obtained from a pulsed non-degenerate parametric amplifier, which produces two intensity-correlated twin beams. Counting two photons in one beam projects the other beam in the desired two-photon Fock state, which is analyzed by using a pulsed homodyne detection. The Wigner function of the measured state is clearly negative. We developed a detailed analytic model which allows a fast and efficient analysis of the experimental results.
Quantum homodyne tomography of a two-photon Fock state.
Ourjoumtsev, Alexei; Tualle-Brouri, Rosa; Grangier, Philippe
2006-06-02
We present a continuous-variable experimental analysis of a two-photon Fock state of free-propagating light. This state is obtained from a pulsed nondegenerate parametric amplifier, which produces two intensity-correlated twin beams. Counting two photons in one beam projects the other beam in the desired two-photon Fock state, which is analyzed by using a pulsed homodyne detection. The Wigner function of the measured state is clearly negative. We developed a detailed analytic model which allows a fast and efficient analysis of the experimental results.
Generation of Fock states in a superconducting quantum circuit.
Hofheinz, Max; Weig, E M; Ansmann, M; Bialczak, Radoslaw C; Lucero, Erik; Neeley, M; O'Connell, A D; Wang, H; Martinis, John M; Cleland, A N
2008-07-17
Spin systems and harmonic oscillators comprise two archetypes in quantum mechanics. The spin-1/2 system, with two quantum energy levels, is essentially the most nonlinear system found in nature, whereas the harmonic oscillator represents the most linear, with an infinite number of evenly spaced quantum levels. A significant difference between these systems is that a two-level spin can be prepared in an arbitrary quantum state using classical excitations, whereas classical excitations applied to an oscillator generate a coherent state, nearly indistinguishable from a classical state. Quantum behaviour in an oscillator is most obvious in Fock states, which are states with specific numbers of energy quanta, but such states are hard to create. Here we demonstrate the controlled generation of multi-photon Fock states in a solid-state system. We use a superconducting phase qubit, which is a close approximation to a two-level spin system, coupled to a microwave resonator, which acts as a harmonic oscillator, to prepare and analyse pure Fock states with up to six photons. We contrast the Fock states with coherent states generated using classical pulses applied directly to the resonator.
Baryons as Fock states of 3,5,... Quarks
Energy Technology Data Exchange (ETDEWEB)
Dmitri Diakonov; Victor Petrov
2004-09-01
We present a generating functional producing quark wave functions of all Fock states in the octet, decuplet and antidecuplet baryons in the mean field approximation, both in the rest and infinite momentum frames. In particular, for the usual octet and decuplet baryons we get the SU(6)-symmetric wave functions for their 3-quark component but with specific corrections from relativism and from additional quark-antiquark pairs. For the exotic antidecuplet baryons we obtain the 5-quark wave function.
Proposal for generating Fock states in traveling wave fields
Energy Technology Data Exchange (ETDEWEB)
Benmoussa, Adil [Department of Physics and Astronomy, Lehman College, The City University of New York, Bronx, NY 10468-1589 (United States)]. E-mail: adil.benmoussa@lehman.cuny.edu; Gerry, Christopher C. [Department of Physics and Astronomy, Lehman College, The City University of New York, Bronx, NY 10468-1589 (United States)
2007-05-28
We describe a proposal for the generation of a single-mode photonic number state, |N>, in a traveling wave optical field. The state is obtained by state reduction from an input coherent state using Kerr media. Our method is based on a previous scheme used for hole burning in the Fock space by minimizing the Mandel Q parameter. The same method was used by Maia et al., but ours is different, it requires only one single photon injected in the entire setup and one photon detection at the end.
Ground state properties of graphene in Hartree-Fock theory
Hainzl, Christian; Sparber, Christof
2012-01-01
We study the Hartree-Fock approximation of graphene in infinite volume, with instantaneous Coulomb interactions. First we construct its translation-invariant ground state and we recover the well-known fact that, due to the exchange term, the effective Fermi velocity is logarithmically divergent at zero momentum. In a second step we prove the existence of a ground state in the presence of local defects and we discuss some properties of the linear response to an external electric field. All our results are non perturbative.
A Phenomenological Analysis of Higher Fock State Contributions to the XcJ Decays
Institute of Scientific and Technical Information of China (English)
HUANG Tao; WU Hui-Fang
2001-01-01
We present a phenomenological analysis of higher Fock state contributions to the XcJ decays by using the recent BES experimental data.It is found that the higher Fock state (cc)8g) makes an important contribution to the inclusive and exclusive processes with respect to that from the valence Fock state cc) of the XcJ and some constraints of these contributions are obtained for the Xco and Xc2 states in order to fit the experimental data.``
Quantum Interference between a Single-Photon Fock State and a Coherent State
Windhager, Armin; Pacher, Christoph; Peev, Momtchil; Poppe, Andreas
2010-01-01
We derive analytical expressions for the single mode quantum field state at the individual output ports of a beam splitter when a single-photon Fock state and a coherent state are incident on the input ports. The output states turn out to be a statistical mixture between a displaced Fock state and a coherent state. Consequently we are able to find an analytical expression for the corresponding Wigner function. Because of the generality of our calculations the obtained results are valid for all passive and lossless optical four port devices. We show further how the results can be adapted to the case of the Mach-Zehnder interferometer. In addition we consider the case for which the single-photon Fock state is replaced with a general input state: a coherent input state displaces each general quantum state at the output port of a beam splitter with the displacement parameter being the amplitude of the coherent state.
Quantum interference between a single-photon Fock state and a coherent state
Windhager, A.; Suda, M.; Pacher, C.; Peev, M.; Poppe, A.
2011-04-01
We derive analytical expressions for the single mode quantum field state at the individual output ports of a beam splitter when a single-photon Fock state and a coherent state are incident on the input ports. The output states turn out to be a statistical mixture between a displaced Fock state and a coherent state. Consequently we are able to find an analytical expression for the corresponding Wigner function. Because of the generality of our calculations the obtained results are valid for all passive and lossless optical four port devices. We show further how the results can be adapted to the case of the Mach-Zehnder interferometer. In addition we consider the case for which the single-photon Fock state is replaced with a general input state: a coherent input state displaces each general quantum state at the output port of a beam splitter with the displacement parameter being the amplitude of the coherent state.
Quantum Interference between a Single-Photon Fock State and a Coherent State
Windhager, Armin; Suda, Martin; Pacher, Christoph; Peev, Momtchil; Poppe, Andreas
2010-01-01
We derive analytical expressions for the single mode quantum field state at the individual output ports of a beam splitter when a single-photon Fock state and a coherent state are incident on the input ports. The output states turn out to be a statistical mixture between a displaced Fock state and a coherent state. Consequently we are able to find an analytical expression for the corresponding Wigner function. Because of the generality of our calculations the obtained results are valid for al...
Quantum scattering theory of a single-photon Fock state in three-dimensional spaces.
Liu, Jingfeng; Zhou, Ming; Yu, Zongfu
2016-09-15
A quantum scattering theory is developed for Fock states scattered by two-level systems in three-dimensional free space. It is built upon the one-dimensional scattering theory developed in waveguide quantum electrodynamics. The theory fully quantizes the incident light as Fock states and uses a non-perturbative method to calculate the scattering matrix.
Heisenberg-limited quantum sensing and metrology with superpositions of twin-Fock states
Gerry, Christopher C.; Mimih, Jihane
2011-03-01
We discuss the prospects of performing Heisenberg-limited quantum sensing and metrology using a Mach-Zehnder interferometer with input states that are superpositions of twin-Fock states and where photon number parity measurements are made on one of the output beams of the interferometer. This study is motivated by the experimental challenge of producing twin-Fock states on opposite sides of a beam splitter. We focus on the use of the so-called pair coherent states for this purpose and discuss a possible mechanism for generating them. We also discuss the prospect of using other superstitions of twin-Fock states, for the purpose of interferometry.
Statistical signatures of states orthogonal to the Fock-state ladder of composite bosons
Bouvrie, P. Alexander; Tichy, Malte C.; Mølmer, Klaus
2016-11-01
The theory of composite bosons (cobosons) made of two fermions [C. K. Law, Phys. Rev. A 71, 034306 (2005), 10.1103/PhysRevA.71.034306; M. C. Tichy et al., Phys. Rev. Lett. 109, 260403 (2012), 10.1103/PhysRevLett.109.260403] converges to ordinary structureless bosons in the limit of infinitely strong entanglement between the fermionic constituents. For finite entanglement, the annihilation operator c ̂ of a composite boson couples the N -coboson Fock state not only to the (N -1 ) -coboson state—as for ordinary bosons—but also to a component which is orthogonal to the Fock-state ladder of cobosons. Coupling with states orthogonal to the Fock ladder arises also in dynamical processes of cobosons. Here, with a Gedanken experiment involving both mode splitting and collective Hong-Ou-Mandel-like interference, we derive the characteristic physical signature of the states orthogonal to the Fock ladder generated in the splitting process. This allows us to extract the microscopic properties of many-fermion wave functions from the collective coboson behavior. We show that consecutive beam-splitter dynamics increases the deviation from the ideal bosonic behavior pattern, which opens up a rigorous approach to the falsification of coboson theory.
Lin, G W; Huang, T; Lin, X M; Wang, Z Y; Gong, S Q
2012-01-01
We propose a technique for quantum nondemolition (QND) measurement and preparation of fock states by dynamics of electromagnetically induced transparency (EIT). An atomic medium trapped in an optical cavity is driven by two continuous-wave classical fields under steady-state EIT. The weak coherent fields are sequently injected into the cavity. During the process of photons passing through the cavity, a measurement on the changes of absorption loss of the probe field will be used for QND measurement of the small photon number, and thus create photon fock states, in particular single-photon states, in a heralded way.
Conditional large Fock state preparation and field state reconstruction in cavity QED.
Santos, M F; Solano, E; de Matos Filho, R L
2001-08-27
We propose a scheme for producing large Fock states in cavity QED via the implementation of a highly selective atom-field interaction. It is based on Raman excitation of a three-level atom by a classical field and a quantized field mode. Selectivity appears when one tunes to resonance a specific transition inside a chosen atom-field subspace, while other transitions remain dispersive, as a consequence of the field dependent electronic energy shifts. We show that this scheme can be also employed for reconstructing, in a new and efficient way, the Wigner function of the cavity field state.
Wigner spectrum and coherent feedback control of continuous-mode single-photon Fock states
Dong, Zhiyuan; Cui, Lei; Zhang, Guofeng; Fu, Hongchen
2016-10-01
Single photons are very useful resources in quantum information science. In real applications it is often required that the photons have a well-defined spectral (or equivalently temporal) modal structure. For example, a rising exponential pulse is able to fully excite a two-level atom while a Gaussian pulse cannot. This motivates the study of continuous-mode single-photon Fock states. Such states are characterized by a spectral (or temporal) pulse shape. In this paper we investigate the statistical property of continuous-mode single-photon Fock states. Instead of the commonly used normal ordering (Wick order), the tool we proposed is the Wigner spectrum. The Wigner spectrum has two advantages: (1) it allows to study continuous-mode single-photon Fock states in the time domain and frequency domain simultaneously; (2) because it can deal with the Dirac delta function directly, it has the potential to provide more information than the normal ordering where the Dirac delta function is always discarded. We also show how various control methods in particular coherent feedback control can be used to manipulate the pulse shapes of continuous-mode single-photon Fock states.
Controlling single-photon Fock-state propagation through opaque scattering media
Huisman, T.J.; Huisman, S.R.; Mosk, A.P.; Pinkse, P.W.H.
2014-01-01
The control of light scattering is essential in many quantum optical experiments. Wavefront shaping is a technique used for ultimate control over wave propagation through multiple-scattering media by adaptive manipulation of incident waves. We control the propagation of single-photon Fock states thr
Generation of motional Fock states of a trappedion in the mediate-excitation regime
Institute of Scientific and Technical Information of China (English)
Zheng Shi-Biao
2004-01-01
We propose a scheme to prepare Fock states for the vibrational motion of a trapped ion. Unlike previous schemes,the present scheme works in the mediate-excitation regime, in which the corresponding Rabi frequency is equal to the trap frequency. Thus, the required time is greatly shortened, which is important in view of decoherence.
Heavy Quarks Production in Hadronic Processes: Qualitative Study of Higher-Order Fock States
Institute of Scientific and Technical Information of China (English)
N. Mebarki; K. Benhizia; Z. Belghobsi; D. Bouaziz
2009-01-01
The contribution of the two particles Fock states for the production of a heavy quark in proton-pion and photon-pion collisions is studied. It is shown that the effect depends strongly on the produced heavy quark mass, and the choice of the factorization scale.
Fock space expansion of {sigma} meson in leading-N{sub c}
Energy Technology Data Exchange (ETDEWEB)
Llanes-Estrada, Felipe J.; Pelaez, Jose Ramon; Ruiz de Elvira, Jacobo [Departamentos de Fisica Teorica I y II, Universidad Complutense de Madrid, 28040 Madrid (Spain)
2010-10-15
We examine the leading-N{sub c} behavior of the masses and transition matrix elements of some low-lying, few-particle configurations in QCD. A truncation of the Fock space produces an effective, symmetric Hamiltonian that we diagonalize. The lowest eigenvalue is identified as the {sigma} meson if the Hamiltonian is chosen to represent the scalar sector. As an application, the coefficients of the N{sub c} powers are then fit to two-loop Unitarized SU(2) Chiral Perturbation Theory results for the {sigma} mass and width as a function of the number of colors, and we show that those results can be accommodated using the QCD N{sub c} dependence previously derived for matrix elements, without the need for unnatural parameters or fine tunings. Finally, we show a very preliminary good quality fit, estimating the proportion of tetraquark/molecule-like (dominant), qq-bar -like (subdominant) and exotic-like (marginal) configurations in the {sigma}.
Manipulating Fock states of a harmonic oscillator while preserving its linearity
Juliusson, K.; Bernon, S.; Zhou, X.; Schmitt, V.; le Sueur, H.; Bertet, P.; Vion, D.; Mirrahimi, M.; Rouchon, P.; Esteve, D.
2016-12-01
We present a scheme for controlling the quantum state of a harmonic oscillator by coupling it to an anharmonic multilevel system (MLS) with first- to second-excited-state transition on resonance with the oscillator. In this scheme, which we call ef-resonant, the spurious oscillator Kerr nonlinearity inherited from the MLS is very small, while its Fock states can still be selectively addressed via an MLS transition at a frequency that depends on the number of photons. We implement this concept in a circuit-QED setup with a microwave three-dimensional cavity (the oscillator, with frequency 6.4 GHz and quality factor QO=2 ×106 ) embedding a frequency tunable transmon qubit (the MLS). We characterize the system spectroscopically and demonstrate selective addressing of Fock states and a Kerr nonlinearity below 350 Hz. At times much longer than the transmon coherence times, a nonlinear cavity response with driving power is also observed and explained.
Entanglement of remote transmon qubits by concurrent measurement using Fock states
Narla, A.; Hatridge, M.; Shankar, S.; Leghtas, Z.; Sliwa, K. M.; Vlastakis, B.; Zalys-Geller, E.; Mirrahimi, M.; Devoret, M. H.
2015-03-01
A requirement of any modular quantum computer is the ability to maintain individual qubits in isolated environments while also being able to entangle arbitrary distant qubits on demand. For superconducting qubits, such a protocol can be realized by first entangling the qubits with flying microwave coherent states which are then concurrently detected by a parametric amplifier. This protocol has a 50% success probability but is vulnerable to losses between the qubits and the amplifier which reduce the entanglement fidelity. An alternative is to use itinerant Fock states, since losses now tend to reduce the success probability of creating an entangled state but not its fidelity. Such single-photon protocols have been implemented in trapped-ion and NV-center experiments. We present such a protocol tailored for entangling two transmon qubits in the circuit QED architecture. Each qubit is entangled with a Fock state of its cavity using sideband pulses. The Fock states leak out of the cavity, interfere on a beam-splitter which erases their which-path information, and are subsequently detected using a novel photo-detector realized by another qubit-cavity system. Simulations suggest that we can realize a high-fidelity entangled state with a success probability as large as 1%.
Representations of coherent and squeezed states in an extended two-parameter Fock space
Institute of Scientific and Technical Information of China (English)
M. K. Tavassoly; M. H. Lake
2012-01-01
Recently an f-deformed Fock space which is spanned by ｜n〉λ was introduced.These bases are the eigenstates of a deformed non-Hermitian Hamiltonian.In this contribution,we will use rather new nonorthogonal basis vectors for the construction of coherent and squeezed states,which in special case lead to the earlier known states.For this purpose,we first generalize the previously introduced Fock space spanned by ｜n〉λ bases,to a new one,spanned by extended two-parameters bases ｜n〉λ1,λ2.These bases are now the eigenstates of a non-Hermitian Hamiltonian Hλ1,λ2 =a(+)1,λ2a +1/2,where a(+)λ1,λ2 =a(+) + λ1a + λ2 and a are,respectively,the deformed creation and ordinary bosonic annihilation operators.The bases ｜n〉λ1,λ2 are nonorthogonal (squeezed states),but normalizable.Then,we deduce the new representations of coherent and squeezed states in our two-parameter Fock space.Finally,we discuss the quantum statistical properties,as well as the non-classical properties of the obtained states numerically.
Complete equation of state for neutron stars using the relativistic Hartree-Fock approximation
Energy Technology Data Exchange (ETDEWEB)
Miyatsu, Tsuyoshi; Cheoun, Myung-Ki [Department of Physics, Soongsil University, Seoul 156-743 (Korea, Republic of); Yamamuro, Sachiko; Nakazato, Ken' ichiro [Department of Physics, Faculty of Science and Technology, Tokyo University of Science (TUS), Noda 278-8510 (Japan)
2014-05-02
We construct the equation of state in a wide-density range for neutron stars within relativistic Hartree-Fock approximation. The properties of uniform and nonuniform nuclear matter are studied consistently. The tensor couplings of vector mesons to baryons due to exchange contributions (Fock terms) are included, and the change of baryon internal structure in matter is also taken into account using the quark-meson coupling model. The Thomas-Fermi calculation is adopted to describe nonuniform matter, where the lattice of nuclei and the neutron drip out of nuclei are considered. Even if hyperons exist in the core of a neutron star, we obtain the maximum neutron-star mass of 1.95M{sub ⊙}, which is consistent with the recently observed massive pulsar, PSR J1614-2230. In addition, the strange vector (φ) meson also plays a important role in supporting a massive neutron star.
Multipartite State Representations in Multi-mode Fock Space and Their Squeezing Transformations
Institute of Scientific and Technical Information of China (English)
YUAN Hong-Chun; LI Heng-Mei; QI Kai-Guo
2007-01-01
We present the continuous state vector of the total coordinate of multi-particle and the state vector of their total momentum, respectively, which possess completeness relation in multi-mode Fock space by virtue of the integration within an order product (IWOP) technique. We also calculate the transition from classical transformation of variables in the states to quantum unitary operator, deduce a new multi-mode squeezing operator, and discuss its squeezing effect. In progress, it indicates that the IWOP technique provides a convenient way to construct new representation in quantum mechanics.
Representations of Coherent and Squeezed States in an Extended Two-parameters Fock Space
Tavassoly, M K
2012-01-01
Recently a $f$-deformed Fock space which is spanned by $|n>_{\\lambda}$ has been introduced. These bases are indeed the eigen-states of a deformed non-Hermitian Hamiltonian. In this contribution, we will use a rather new non-orthogonal basis vectors for the construction of coherent and squeezed states, which in special case lead to the earlier known states. For this purpose, we first generalize the previously introduced Fock space spanned by $|n>_{\\lambda}$ bases, to a new one, spanned by an extended two-parameters bases $|n>_{\\lambda_{1},\\lambda_{2}}$. These bases are now the eigen-states of a non-Hermitian Hamiltonian $H_{\\lambda_{1},\\lambda_{2}}=a^{\\dagger}_{\\lambda_{1},\\lambda_{2}}a+1/2$, where $a^{\\dagger}_{\\lambda_{1},\\lambda_{2}}=a^{\\dagger}+\\lambda_{1}a + \\lambda_{2}$ and $a$ are respectively, the deformed creation and ordinary bosonic annihilation operators. The bases $|n>_{\\lambda_{1},\\lambda_{2}}$ are non-orthogonal (squeezed states), but normalizable. Then, we deduce the new representations of cohe...
Fock-Darwin-like quantum dot states formed by charged Mn interstitial ions.
Makarovsky, O; Thomas, O; Balanov, A G; Eaves, L; Patanè, A; Campion, R P; Foxon, C T; Vdovin, E E; Maude, D K; Kiesslich, G; Airey, R J
2008-11-28
We report a method of creating electrostatically induced quantum dots by thermal diffusion of interstitial Mn ions out of a p-type (GaMn)As layer into the vicinity of a GaAs quantum well. This approach creates deep, approximately circular, and strongly confined dotlike potential minima in a large (200 microm) mesa diode structure without need for advanced lithography or electrostatic gating. Magnetotunneling spectroscopy of an individual dot reveals the symmetry of its electronic eigenfunctions and a rich energy level spectrum of Fock-Darwin-like states with an orbital angular momentum component |lz| from 0 to 11.
QUANTUM FLUCTUATIONS IN A MESOSCOPIC DAMPED LC PARALLEL CIRCUIT IN DISPLACED SQUEEZED FOCK STATE
Institute of Scientific and Technical Information of China (English)
GU YONG-JIAN
2001-01-01
We study the quantum effects of a damped LC parallel circuit considering its different performance from an RLC series circuit in classical physics. The damped LC parallel circuit with a source is quantized and the quantum fluctuations of magnetic flux and electric charge in the circuit in displaced squeezed Fock state are investigated. It is shown that, as in the RLC series circuit, the fluctuations only depend on the squeezing parameter and the parameters of the circuit components in the damped LC parallel circuit, but the effects of the circuit components on the fluctuations are different in the two circuits.
Jiménez-Hoyos, Carlos A; Scuseria, Gustavo E
2013-01-01
Recent work from our research group has demonstrated that symmetry-projected Hartree--Fock (HF) methods provide a compact representation of molecular ground state wavefunctions based on a superposition of non-orthogonal Slater determinants. The symmetry-projected ansatz can account for static correlations in a computationally efficient way. Here we present a variational extension of this methodology applicable to excited states of the same symmetry as the ground state. Benchmark calculations on the C$_2$ dimer with a modest basis set, which allows comparison with full configuration interaction results, indicate that this extension provides a high quality description of the low-lying spectrum for the entire dissociation profile. We apply the same methodology to obtain the full low-lying vertical excitation spectrum of formaldehyde, in good agreement with available theoretical and experimental data, as well as to a challenging model $C_{2v}$ insertion pathway for BeH$_2$. The variational excited state methodolo...
Energy Technology Data Exchange (ETDEWEB)
Ebran, J-P [CEA/DAM/DIF, F-91297 Arpajon (France); Khan, E; Arteaga, D Pena [Institut de Physique Nucleaire, University Paris-Sud, IN2P3-CNRS, F-91406 Orsay Cedex (France); Vretenar, D, E-mail: jean-paul.ebran@cea.fr [Physics Department, Faculty of Science, University of Zagreb, 10000 Zagreb (Croatia)
2011-09-16
The Relativistic Hartree-Fock-Bogoliubov model for axially deformed nuclei (RHFBz) is presented. The model involves a phenomenological Lagrangian with density-dependent meson-nucleon couplings in the particle-hole channel and the central part of the Gogny force in the particle-particle channel. The RHFBz equations are solved by expansion in the basis of a deformed harmonic oscillator. Illustrative RHFBz calculations are performed for Neon isotopes.
Institute of Scientific and Technical Information of China (English)
GUO Lu; ZHAO En-Guang; SAKATA Fumihiko
2003-01-01
Ground-state.properties of C, O, and Ne isotopes are described in the framework of Hartree-FockBogoliubov theory with density-dependent finite-range Gogny interaction D1S. We include all the contributions to the Hartree-Fock and pairing field arising from Gogny and Coulomb interaction as well as the center of mass correction in the numerical calculations. These ground-state properties of C, O, and Ne isotopes are compared with available experimental results, Hartree-Fock plus BCS, shell model and relativistic Hartree-Bogoliubov calculations. The agreement between experiments and our theoretical results is pretty well. The predicted drip-line is dependent strongly on the model and effective interaction due to their sensitivity to various theoretical details. The calculations predict no evidence for halo structure predicted for C, O, and Ne isotopes in a previous RHB study.
Institute of Scientific and Technical Information of China (English)
GUOLu; ZHAOEn-Guang; SAKATAFumihiko
2003-01-01
Ground-state properties of C, O, and Ne isotopes are described in the framework of Hartree-Fock-Bogoliubov theory with density-dependent finite-range Gogny interaction D1S. We include all the contributions to the Hartree-Fock and pairing feld arising from Gogny and Coulomb interaction as well as the center of mass correction in the numerical calcu/ations. These ground-state properties of C, O, and Ne isotopes are compared with available experimental results, Hartree-Fock plus BCS, shell model and relativistic Hartree--Bogoliubov calculations. The agreement between experiments and our theoretical results is pretty well. The predicted drip-line is dependent strongly on the model and effective interaction due to their sensitivity to various theoretical details. The calculations predict no evidence for halo structure predicted for C,O, and Ne isotopes in a previous RHB study.
Hartree-Fock Many-Body Perturbation Theory for Nuclear Ground-States
Tichai, Alexander; Binder, Sven; Roth, Robert
2016-01-01
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 to construct the unperturbed basis leads to a convergent MBPT series for soft interactions, in contrast to, e.g., a harmonic oscillator basis. For larger model spaces and heavier nuclei, where a direct high-order MBPT calculation in not feasible, we perform third-order calculation and compare to advanced ab initio coupled-cluster calculations for the same interactions and model spaces. We demonstrate that third-order MBPT provides ground-state energies for nuclei up into tin isotopic chain that are in excellent agreement with the best available coupled-cluster results at a fraction of the computational cost.
Bassem, Y El
2016-01-01
In a previous work [Int. J. Mod. Phys. E 24, 1550073 (2015)], hereafter referred as paper I, we have investigated the ground-state properties of Nd, Ce and Sm isotopes within Hartree-Fock-Bogoliubov method with SLy5 skyrme force in which the pairing strength has been generalized with a new proposed formula. However, that formula is more appropriate for the region of Nd. In this work, we have studied the ground-state properties of both even-even and odd Mo and Ru isotopes. For this, we have used Hartree- Fock-Bogoliubov method with SLy4 skyrme force, and a new formula of the pairing strength which is more accurate for this region of nuclei. The results have been compared with available experimental data, the results of Hartree-Fock-Bogoliubov calculations based on the D1S Gogny effective nucleon-nucleon interaction and predictions of some nuclear models such as Finite Range Droplet Model (FRDM) and Relativistic Mean Field (RMF) theory.
Guerra, E S
2004-01-01
In this article we discuss the realization of atomic GHZ states involving three-level atoms in a cascade and in a lambda configuration and we show explicitly how to use this state to perform the GHZ test in which it is possible to decide between local realism theories and quantum mechanics. The experimental realizations proposed makes use the interaction of Rydberg atoms with a cavity prepared in a state which is a superposition of zero and one Fock states.
Evolution of Arbitrary States under Fock-Darwin Hamiltonian and a Time-Dependent Electric Field
Institute of Scientific and Technical Information of China (English)
徐晓飞; 杨涛; 翟智远; 潘孝胤
2012-01-01
The method of path integral is employed to calculate the time evolution of the eigenstates of a charged particle under the Fock-Darwin （FD） Hamiltonian subjected to a time-dependent electric field in the plane of the system. An exact analytical expression is established for the evolution of the eigenstates. This result then provides a general solution to the time-dependent Schrodinger equation.
Staker, Joshua T
2013-01-01
We make numerical comparison of spectra from angular-momentum projection on Hartree-Fock states with spectra from configuration-interaction nuclear shell-model calculations, all carried out in the same model spaces (in this case the sd, lower pf, and p-sd_5/2 shells) and using the same input Hamiltonians. We find, unsurprisingly, that the low-lying excitation spectra for rotational nuclides are well reproduced, but the spectra for vibrational nuclides, and more generally the complex specta for odd-A and odd-odd nuclides are less well reproduced in detail.
Dyall, Kenneth G.
1992-01-01
The effect of omission of two-electron integrals involving basis functions for the small component of the wavefunction on the eigenvalue spectrum in the Dirac-Hartree-Fock problem is studied. From an analysis of the Fock matrix it is shown that omission of these integrals moves the negative-energy states down, not up. Their complete omission does not give rise to intruder states. The appearance of intruder states occurs when only some of the core integrals are omitted, due to the nature of particular contraction schemes used for the core basis functions. Use of radially localized functions rather than atomic functions alleviates the intruder state problem.
Kambe, Takahide; Saito, Koichi
2016-01-01
As the interior density of a neutron star can become very high, it has been expected and discussed that quark matter may exist inside it. To describe the transition from hadron to quark phases (and vice versa), there are mainly two methods; one is the first-order phase transition, and the other is the crossover phenomenon. In the present study, using the flavor-SU (3) NJL model with the vector coupling interaction, we have calculated the equation of state for the quark phase at high density. Furthermore, for the hadron phase at low density, we have used two kinds of the equations of state; one is a relatively soft one by the QHD model, and the other is a stiff one calculated with relativistic Brueckner-Hartree-Fock approximation. Using those equations of state for the two phases, we have investigated the influence of various choices of parameters concerning the crossover region on the mass and radius of a neutron star.
Selective truncations of an optical state using projection synthesis
Miranowicz, A; Bajer, J; Koashi, M; Imoto, N; Miranowicz, Adam; Ozdemir, Sahin Kaya; Bajer, Jiri; Koashi, Masato; Imoto, Nobuyuki
2006-01-01
Selective truncation of Fock-state expansion of an optical field can be achieved using projection synthesis. The process removes predetermined Fock states from the input field by conditional measurement and teleportation. We present a scheme based on multiport interferometry to perform projection synthesis. This scheme can be used both as a generalized quantum scissors device, which filters out Fock states with photon numbers higher than a predetermined value, and also as a quantum punching device, which selectively removes specific Fock states making holes in the Fock-state expansion of the input field.
Directory of Open Access Journals (Sweden)
Y. Sajeev
2015-08-01
Full Text Available The equation-of-motion coupled cluster (EOMCC method based on the excited state Hartree-Fock (ESHF solutions is shown to be appropriate for computing the entire ground state potential energy curves of strongly correlated higher-order bonds. The new approach is best illustrated for the homolytic dissociation of higher-order bonds in molecules. The required multireference character of the true ground state wavefunction is introduced through the linear excitation operator of the EOMCC method. Even at the singles and doubles level of cluster excitation truncation, the nonparallelity error of the ground state potential energy curve from the ESHF based EOMCC method is small.
Resonant-state expansion Born Approximation
Doost, M B
2015-01-01
The Born Approximation is a fundamental formula in Physics, it allows the calculation of weak scattering via the Fourier transform of the scattering potential. I extend the Born Approximation by including in the formula the Fourier transform of a truncated basis of the infinite number of appropriately normalised resonant states. This extension of the Born Approximation is named the Resonant-State Expansion Born Approximation or RSE Born Approximation. The resonant-states of the system can be calculated using the recently discovered RSE perturbation theory for electrodynamics and normalised correctly to appear in spectral Green's functions via the flux volume normalisation.
Dubey, Archana; Badu, S. R.; Scheicher, R. H.; Sahoo, N.; Pink, R. H.; Schulte, A.; Saha, H. P.; Chow, Lee; Nagamine, K.; Das, T. P.
2008-03-01
The observation of paramagnetic susceptibility [1] in Oxy-Hb from measurements over a broad temperature range has stimulated interest in the occurrence of a low-lying excited triplet state close to the ground singlet state of Oxy-Hb. An earlier theoretical investigation [2] has shown the existence of such a triplet state providing support to the interpretation of the susceptibility data [1]. Support for the low-lying excited triplet state has been augmented recently [3] from microscopic relaxation rate measurements for muon attached to the heme group of Oxy-Hb. We are studying by first principles Hartree-Fock procedure the energies and the electronic wave functions of the ground and triplet states and the quantitative theoretical prediction of muon magnetic hyperfine interaction in room temperature μSR measurements on Oxy-Hb. Results will be presented for hyperfine interactions of muon and other nuclei in Oxy-Hb [1] M.Cerdonio etal. Proc. Nat. Acad. Sci USA 75, 4916(1978). [2] Zalek S. Herman and Gilda H Loew JACS 102, 1815(1980).[ 3] K. Nagamine etal Proc. Jpn. Acad.Ser.B 83,120(2007).
Quiney, HM; Glushkov, VN; Wilson, S
2002-01-01
Using basis sets of distributed s-type Gaussian functions with positions and exponents optimized so as to support Hartree-Fock total energies with an accuracy approaching the sub-muHartree level, Dirac-Hartree-Fock-Coulomb calculations are reported for the ground states of the H-2, LiH, and BH molec
Entanglement in fermionic Fock space
Sárosi, Gábor
2013-01-01
We propose a generalization of the usual SLOCC and LU classification of entangled pure state fermionic systems based on the Spin group. Our generalization uses the fact that there is a representation of this group acting on the fermionic Fock space which when restricted to fixed particle number subspaces recovers naturally the usual SLOCC transformations. The new ingredient is the occurrence of Bogoliubov transformations of the whole Fock space changing the particle number. The classification scheme built on the Spin group prohibits naturally entanglement between states containing even and odd number of fermions. In our scheme the problem of classification of entanglement types boils down to the classification of spinors where totally separable states are represented by so called pure spinors. We construct the basic invariants of the Spin group and show how some of the known SLOCC invariants are just their special cases. As an example we present the classification of fermionic systems with a Fock space based ...
Ground state properties of even-even and odd Nd,Ce and Sm isotopes in Hartree-Fock-Bogoliubov method
Bassem, Younes El
2015-01-01
In this work, we have studied ground-state properties of both even-even and odd Nd isotopes within Hartree-Fock-Bogoliubov method with SLy5 Skyrme force in which the pairing strength has been generalized with a new proposed formula. We calculated bind- ing energies, two-neutron separation energies, quadrupole deformation, charge, neutron and proton radii. Similar calculations have been carried out for Ce and Sm in order to verify the validity of our pairing strength formula. The results have been compared with available experimental data, the results of Hartree-Fock-Bogoliubov calculations based on the D1S Gogny effective nucleon-nucleon interaction and predictions of some nuclear models such as Finite Range Droplet Model (FRDM) and Relativistic Mean Field (RMF) theory.
How to construct a consistent and physically relevant the Fock space of neutrino flavor states?
Directory of Open Access Journals (Sweden)
Lobanov A. E.
2016-01-01
Full Text Available We propose a modification of the electroweak theory, where the fermions with the same electroweak quantum numbers are combined in multiplets and are treated as different quantum states of a single particle. Thereby, in describing the electroweak interactions it is possible to use four fundamental fermions only. In this model, the mixing and oscillations of the particles arise as a direct consequence of the general principles of quantum field theory. The developed approach enables one to calculate the probabilities of the processes taking place in the detector at long distances from the particle source. Calculations of higher-order processes including the computation of the contributions due to radiative corrections can be performed in the framework of perturbation theory using the regular diagram technique.
New optical field operator expansion in number state representation
Institute of Scientific and Technical Information of China (English)
Yang Yang; Fan Hong-Yi
2013-01-01
By virtue of the Weyl ordering method,we find a new formalism of optical field operator expansion in number state representation.Miscellaneous optical fields' (coherent state,squeezed field,Wigner operator,etc.) new expansions are therefore exhibited.Some new generating functions of special polynomials are derived herewith.
Guerra, E S
2004-01-01
In this article we discuss two schemes of teleportation of atomic states. In the first scheme we consider atoms in a three-level cascade configuration and in the second scheme we consider atoms in a three-level lambda configuration. The experimental realization proposed makes use of cavity Quatum Electrodynamics involving the interaction of Rydberg atoms with a micromaser cavity prepared in a state $|\\psi >_{C}=(|0> +|1>)/\\sqrt{2}$
Adequacy of the virial equation of state and cluster expansion
Ushcats, M. V.
2013-04-01
The limits for the accuracy of the virial expansion and the problem of its divergence have been investigated using the exact cluster expansion of the configuration integral. In the subcritical temperature regimes the virial equation of state is applicable up to the singularity point of the isothermal compressibility, i.e., to the possible beginning of the condensation process. At supercritical temperatures this equation should be applicable within the region where the cluster expansion is adequate. The problem of the virial series divergence has been found to be irrelevant to the actual behavior of the cluster expansion. Considering the Lennard-Jones fluid as well as the system of hard spheres, the inadequate behavior of the cluster expansion has been discovered in the high density regime. The major reason for this inadequacy should be the basic simplification of the cluster expansion: the integration of irreducible diagrams over the infinite limits.
Angular Fock coefficients. Fixing the errors, and further development
Liverts, Evgeny Z
2015-01-01
The angular coefficients $\\psi_{k,p}(\\alpha,\\theta)$ of the Fock expansion characterizing the S-state wave function of the two-electron atomic system, are calculated in hyperspherical angular coordinates $\\alpha$ and $\\theta$. To solve the problem the Fock recurrence relations separated into the independent individual equations associated with definite power $j$ of the nucleus charge $Z$, are applied. The "pure" $j$-components of the angular Fock coefficients, orthogonal to of the hyperspherical harmonics $Y_{kl}$, are found for even values of $k$. To this end, the specific coupling equation is proposed and applied. Effective techniques for solving the individual equations with simplest nonseparable and separable right-hand sides are proposed. Some mistakes/misprints made earlier in representations of $\\psi_{2,0}$, were noted and corrected. All $j$-components of $\\psi_{4,1}$ and the majority of components and subcomponents of $\\psi_{3,0}$ are calculated and presented for the first time. All calculations were ...
Akamatsu, Hirofumi; Kumagai, Yu; Oba, Fumiyasu; Fujita, Koji; Murakami, Hideo; Tanaka, Katsuhisa; Tanaka, Isao
2011-06-01
A superexchange mechanism between Eu2+ 4f spins via the 3d states of nonmagnetic Ti4+ ions is proposed through first-principles calculations based on a hybrid Hartree-Fock density functional approach to explain G-type antiferromagnetism in EuTiO3. This mechanism is supported by systematic calculations for related Eu2+-based perovskite oxides. In EuTiO3, the competition between the antiferromagnetic superexchange and an indirect ferromagnetic exchange via the Eu 5d states leads to a delicate balance between antiferromagnetic and ferromagnetic phases. The superexchange mechanism involving the Ti 3d states hints at the microscopic origin of the strong spin-lattice coupling in EuTiO3.
Local Hubble Expansion: Current State of the Problem
Dumin, Yurii V
2016-01-01
We present a brief qualitative overview of the current state of the problem of Hubble expansion at the sufficiently small scales (e.g., in planetary systems or local intergalactic volume). The crucial drawbacks of the available theoretical treatments are emphasized, and the possible ways to avoid them are outlined. Attention is drawn to a number of observable astronomical phenomena that could be naturally explained by the local Hubble expansion.
Accardi, Luigi
2009-01-01
We construct the quadratic analogue of the boson Fock functor. While in the first order case all contractions on the 1--particle space can be second quantized, the semigroup of contractions that admit a quadratic second quantization is much smaller due to the nonlinearity. Within this semigroup we characterize the unitary and the isometric elements.
Cluster expansion for ground states of local Hamiltonians
Bastianello, Alvise; Sotiriadis, Spyros
2016-08-01
A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates physical requirements inherited by locality as conditions on its cluster amplitudes. Applying a diagrammatic technique we derive the relation of these amplitudes to thermodynamic quantities and local observables. Moreover we derive a set of functional equations that determine the cluster amplitudes for a general Hamiltonian, verify the consistency with perturbation theory and discuss non-perturbative approaches. Lastly we verify the persistence of locality features of the cluster expansion under unitary evolution with a local Hamiltonian and provide applications to out-of-equilibrium problems: a simplified proof of equilibration to the GGE and a cumulant expansion for the statistics of work, for an interacting-to-free quantum quench.
Cluster expansion for ground states of local Hamiltonians
Directory of Open Access Journals (Sweden)
Alvise Bastianello
2016-08-01
Full Text Available A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates physical requirements inherited by locality as conditions on its cluster amplitudes. Applying a diagrammatic technique we derive the relation of these amplitudes to thermodynamic quantities and local observables. Moreover we derive a set of functional equations that determine the cluster amplitudes for a general Hamiltonian, verify the consistency with perturbation theory and discuss non-perturbative approaches. Lastly we verify the persistence of locality features of the cluster expansion under unitary evolution with a local Hamiltonian and provide applications to out-of-equilibrium problems: a simplified proof of equilibration to the GGE and a cumulant expansion for the statistics of work, for an interacting-to-free quantum quench.
Cluster expansion for ground states of local Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Bastianello, Alvise, E-mail: abastia@sissa.it [SISSA, via Bonomea 265, 34136 Trieste (Italy); INFN, Sezione di Trieste (Italy); Sotiriadis, Spyros [SISSA, via Bonomea 265, 34136 Trieste (Italy); INFN, Sezione di Trieste (Italy); Institut de Mathématiques de Marseille (I2M), Aix Marseille Université, CNRS, Centrale Marseille, UMR 7373, 39, rue F. Joliot Curie, 13453, Marseille (France); University of Roma Tre, Department of Mathematics and Physics, L.go S.L. Murialdo 1, 00146 Roma (Italy)
2016-08-15
A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates physical requirements inherited by locality as conditions on its cluster amplitudes. Applying a diagrammatic technique we derive the relation of these amplitudes to thermodynamic quantities and local observables. Moreover we derive a set of functional equations that determine the cluster amplitudes for a general Hamiltonian, verify the consistency with perturbation theory and discuss non-perturbative approaches. Lastly we verify the persistence of locality features of the cluster expansion under unitary evolution with a local Hamiltonian and provide applications to out-of-equilibrium problems: a simplified proof of equilibration to the GGE and a cumulant expansion for the statistics of work, for an interacting-to-free quantum quench.
Optimized $\\delta$ expansion for relativistic nuclear models
Krein, G I; Peres-Menezes, D; Nielsen, M; Pinto, M B
1998-01-01
The optimized $\\delta$-expansion is a nonperturbative approach for field theoretic models which combines the techniques of perturbation theory and the variational principle. This technique is discussed in the $\\lambda \\phi^4$ model and then implemented in the Walecka model for the equation of state of nuclear matter. The results obtained with the $\\delta$ expansion are compared with those obtained with the traditional mean field, relativistic Hartree and Hartree-Fock approximations.
Health-Related Outcomes among the Poor: Medicaid Expansion vs. Non-Expansion States.
Directory of Open Access Journals (Sweden)
Xuesong Han
Full Text Available States' decisions not to expand Medicaid under the Affordable Care Act (ACA could potentially affect access to care and health status among their low-income residents.The 2010-2012 nationally representative Medical Expenditure Panel Survey data were analyzed in 2015 to compare 9755 low-income adults aged 18-64 years from Medicaid-expanding states with 7455 adults from nonexpanding states. Multivariate logistic regression models were fitted to evaluate the differences in access to care, receipt of preventive services, quality of care, attitudes about health and self-reported health status by Medicaid expansion status. The differences in care utilization and medical expenditures between the two groups were examined using a 2-part modeling approach.Compared to their counterparts in Medicaid expansion states, low income adults in the nonexpanding states were more likely to be black and reside in rural areas and were less likely to have a usual source of care (prevalence ratio[PR] 0.86, 95% confidence interval[CI] 0.82-0.91 and recommended preventive services such as dental checkups (PR = 0.86; CI = 0.79-0.94, routine checks (PR = 0.89; CI = 0.83-0.95, flu vaccinations (PR = 0.89; CI = 0.81-0.98, and blood pressure checks (PR = 0.96; CI = 0.94-0.99. They also had less care utilization, fewer prescriptions, and less medical expenditures, but more out-of-pocket expenditures (all p-value <0.05.Low-income adults in Medicaid nonexpanding states, who are disproportionately represented by blacks and rural residents, were worse off for multiple health-related outcomes compared to their counterparts in Medicaid expanding states at the baseline of ACA implementation, suggesting that low income adults residing in nonexpanding states may benefit markedly from the expansion of Medicaid.
Institute of Scientific and Technical Information of China (English)
G(U)M(U)(S), Sedat; (O)ZDO(G)AN, Telhat
2004-01-01
Hartree-Fock-Roothaan (HFR) calculations for ground states of some atoms, i.e. He, Be, Ne, Ar, and Kr have been performed using minimal basis sets of Slater type orbitals (STOs) with integer and noninteger principal quantum numbers (integer n-STOs and noninteger n-STOs). The obtained total energies for these atoms using minimal basis sets of integer n-STOs are in good agreement with those in the previous literature. On the other hand, for the case of minimal basis sets of noninteger n-STOs, although the calculated total energies of these atoms agree well with the results in literature, some striking results have been obtained for atoms Ar and Kr. Our computational results for the energies of atoms Ar and Kr are slightly better than those in literature, by amount of 0.00222 and 0.000054 a.u., respectively. The improvement in the energies of atoms Ar and Kr may result from the efficient calculations of one-center two-electron integrals over noninteger n-STOs. For some atomic ions in their ground state,HFR calculations have been carried out using minimal basis sets of noninteger n-STOs. The obtained total energies for these atomic ions are substantially lower than those available in literature.
Resonant state expansion applied to planar open optical systems
Doost, M B; Muljarov, E A
2011-01-01
The resonant state expansion (RSE), a novel perturbation theory of Brillouin-Wigner type developed in electrodynamics [Muljarov, Langbein, and Zimmermann, Europhys. Lett., 92, 50010(2010)], is applied to planar, effectively one-dimensional optical systems, such as layered dielectric slabs and Bragg reflector microcavities. It is demonstrated that the RSE converges with a power law in the basis size. Algorithms for error estimation and their reduction by extrapolation are presented and evaluated. Complex eigenfrequencies, electro-magnetic fields, and the Green's function of a selection of optical systems are calculated, as well as the observable transmission spectra. In particular we find that for a Bragg-mirror microcavity, which has sharp resonances in the spectrum, the transmission calculated using the resonant state expansion reproduces the result of the transfer/scattering matrix method.
White noise calculus and Fock space
Obata, Nobuaki
1994-01-01
White Noise Calculus is a distribution theory on Gaussian space, proposed by T. Hida in 1975. This approach enables us to use pointwise defined creation and annihilation operators as well as the well-established theory of nuclear space.This self-contained monograph presents, for the first time, a systematic introduction to operator theory on fock space by means of white noise calculus. The goal is a comprehensive account of general expansion theory of Fock space operators and its applications. In particular,first order differential operators, Laplacians, rotation group, Fourier transform and their interrelations are discussed in detail w.r.t. harmonic analysis on Gaussian space. The mathematical formalism used here is based on distribution theory and functional analysis , prior knowledge of white noise calculus is not required.
Ground state energies from converging and diverging power series expansions
Lisowski, C.; Norris, S.; Pelphrey, R.; Stefanovich, E.; Su, Q.; Grobe, R.
2016-10-01
It is often assumed that bound states of quantum mechanical systems are intrinsically non-perturbative in nature and therefore any power series expansion methods should be inapplicable to predict the energies for attractive potentials. However, if the spatial domain of the Schrödinger Hamiltonian for attractive one-dimensional potentials is confined to a finite length L, the usual Rayleigh-Schrödinger perturbation theory can converge rapidly and is perfectly accurate in the weak-binding region where the ground state's spatial extension is comparable to L. Once the binding strength is so strong that the ground state's extension is less than L, the power expansion becomes divergent, consistent with the expectation that bound states are non-perturbative. However, we propose a new truncated Borel-like summation technique that can recover the bound state energy from the diverging sum. We also show that perturbation theory becomes divergent in the vicinity of an avoided-level crossing. Here the same numerical summation technique can be applied to reproduce the energies from the diverging perturbative sums.
Weaving commutators: beyond Fock space
Arzano, Michele
2012-01-01
The symmetrization postulate and the associated Bose/Fermi (anti)-commutators for field mode operators are among the pillars on which local quantum field theory lays its foundations. They ultimately determine the structure of Fock space and are closely connected with the local properties of the fields and with the action of symmetry generators on observables and states. We here show that the quantum field theory describing relativistic particles coupled to three dimensional Einstein gravity as a topological defect must be constructed using a deformed algebra of creation and annihilation operators. This reflects a non-trivial group manifold structure of the classical momentum space and a modification of the Leibniz rule for the action of symmetry generators governed by Newton's constant. We outline various arguments suggesting that, at least at the qualitative level, these three-dimensional results could also apply to real four-dimensional world thus forcing us to re-think the ordinary multiparticle structure ...
DiGiulio, Anne; Haddix, Meredith; Jump, Zach; Babb, Stephen; Schecter, Anna; Williams, Kisha-Ann S; Asman, Kat; Armour, Brian S
2016-12-09
In 2015, 27.8% of adult Medicaid enrollees were current cigarette smokers, compared with 11.1% of adults with private health insurance, placing Medicaid enrollees at increased risk for smoking-related disease and death (1). In addition, smoking-related diseases are a major contributor to Medicaid costs, accounting for about 15% (>$39 billion) of annual Medicaid spending during 2006-2010 (2). Individual, group, and telephone counseling and seven Food and Drug Administration (FDA)-approved medications are effective treatments for helping tobacco users quit (3). Insurance coverage for tobacco cessation treatments is associated with increased quit attempts, use of cessation treatments, and successful smoking cessation (3); this coverage has the potential to reduce Medicaid costs (4). However, barriers such as requiring copayments and prior authorization for treatment can impede access to cessation treatments (3,5). As of July 1, 2016, 32 states (including the District of Columbia) have expanded Medicaid eligibility through the Patient Protection and Affordable Care Act (ACA),*(,†) which has increased access to health care services, including cessation treatments (5). CDC used data from the Centers for Medicare and Medicaid Services (CMS) Medicaid Budget and Expenditure System (MBES) and the Behavioral Risk Factor Surveillance System (BRFSS) to estimate the number of adult smokers enrolled in Medicaid expansion coverage. To assess cessation coverage among Medicaid expansion enrollees, the American Lung Association collected data on coverage of, and barriers to accessing, evidence-based cessation treatments. As of December 2015, approximately 2.3 million adult smokers were newly enrolled in Medicaid because of Medicaid expansion. As of July 1, 2016, all 32 states that have expanded Medicaid eligibility under ACA covered some cessation treatments for all Medicaid expansion enrollees, with nine states covering all nine cessation treatments for all Medicaid expansion
Curiosities on free Fock spaces
Minic, D
1995-01-01
We consider some curious aspects of single-species free Fock spaces, such as novel bosonization and fermionization formulae and relations to various physical properties of bosonic particles. We comment on generalizations of these properties to physically more interesting many-species free Fock spaces.
Functional Representations for Fock Superalgebras
Kupsch, J; Kupsch, Joachim; Smolyanov, Oleg G.
1997-01-01
The Fock space of bosons and fermions and its underlying superalgebra are represented by algebras of functions on a superspace. We define Gaussian integration on infinite dimensional superspaces, and construct superanalogs of the classical function spaces with a reproducing kernel -- including the Bargmann-Fock representation -- and of the Wiener-Segal representation. The latter representation requires the investigation of Wick ordering on Z2-graded algebras. As application we derive a Mehler formula for the Ornstein-Uhlenbeck semigroup on the Fock space.
Twisted Fock representations of noncommutative Kähler manifolds
Sako, Akifumi; Umetsu, Hiroshi
2016-09-01
We introduce twisted Fock representations of noncommutative Kähler manifolds and give their explicit expressions. The twisted Fock representation is a representation of the Heisenberg like algebra whose states are constructed by applying creation operators to a vacuum state. "Twisted" means that creation operators are not Hermitian conjugate of annihilation operators in this representation. In deformation quantization of Kähler manifolds with separation of variables formulated by Karabegov, local complex coordinates and partial derivatives of the Kähler potential with respect to coordinates satisfy the commutation relations between the creation and annihilation operators. Based on these relations, we construct the twisted Fock representation of noncommutative Kähler manifolds and give a dictionary to translate between the twisted Fock representations and functions on noncommutative Kähler manifolds concretely.
Twisted Fock Representations of Noncommutative K\\"ahler Manifolds
Sako, Akifumi
2016-01-01
We introduce twisted Fock representations of noncommutative K\\"ahler manifolds and give their explicit expressions. The twisted Fock representation is a representation of the Heisenberg like algebra whose states are constructed by acting creation operators on a vacuum state. "Twisted" means that creation operators are not hermitian conjugate of annihilation operators in this representation. In deformation quantization of K\\"ahler manifolds with separation of variables formulated by Karabegov, local complex coordinates and partial derivatives of the K\\"ahler potential with respect to coordinates satisfy the commutation relations between the creation and annihilation operators. Based on these relations, we construct the twisted Fock representation of noncommutative K\\"ahler manifolds and give a dictionary to translate between the twisted Fock representations and functions on noncommutative K\\"ahler manifolds concretely.
Courtemanche, Charles; Marton, James; Ukert, Benjamin; Yelowitz, Aaron; Zapata, Daniela
2017-01-01
The Affordable Care Act (ACA) aimed to achieve nearly universal health insurance coverage in the United States through a combination of insurance market reforms, mandates, subsidies, health insurance exchanges, and Medicaid expansions, most of which took effect in 2014. This paper estimates the causal effects of the ACA on health insurance coverage in 2014 using data from the American Community Survey. We utilize difference-in-difference-in-differences models that exploit cross-sectional variation in the intensity of treatment arising from state participation in the Medicaid expansion and local area pre-ACA uninsured rates. This strategy allows us to identify the effects of the ACA in both Medicaid expansion and non-expansion states. Our preferred specification suggests that, at the average pre-treatment uninsured rate, the full ACA increased the proportion of residents with insurance by 5.9 percentage points compared to 2.8 percentage points in states that did not expand Medicaid. Private insurance expansions from the ACA were due to increases in both employer-provided and non-group coverage. The coverage gains from the full ACA were largest for those without a college degree, non-whites, young adults, unmarried individuals, and those without children in the home. We find no evidence that the Medicaid expansion crowded out private coverage.
Resonant-state expansion for a simple dispersive medium
Doost, M B; Muljarov, E A
2015-01-01
The resonant-state expansion (RSE), a rigorous perturbative method developed in electrodynamics for non-dispersive optical systems is applied to media with an Ohm's law dispersion, in which the frequency dependent part of the permittivity scales inversely with the frequency, corresponding to a frequency-independent conductivity. This dispersion has only a single pole at zero frequency, which is already present in the non-dispersive RSE, allowing to maintain not only the linearity of the eigenvalue problem of the RSE but also its size. Media which can be described by this dispersion over the relevant frequency range, such as optical glass or doped semiconductors, can be treated in the RSE without additional complexity. Results are presented using analytically solvable homogeneous spheres, for doped silicon and BK7 glass, both for a perturbation of the system going from non-dispersive to dispersive media and the reverse, from dispersive to non-dispersive media.
Indian Academy of Sciences (India)
Sudhanshu S Jha; S D Mahanti
2007-05-01
We use different determinantal Hartree–Fock (HF) wave functions to calculate true variational upper bounds for the ground state energy of spin-half fermions in volume 0, with mass , electric charge zero, and magnetic moment , interacting through magnetic dipole–dipole interaction. We ﬁnd that at high densities when the average interparticle distance 0 becomes small compared to the magnetic length m ≡ 22/ħ2, a ferromagnetic state with spheroidal occupation function ↑ $(\\vec{k})$, involving quadrupolar deformation, gives a lower upper bound compared to the variational energy for the uniform paramagnetic state or for the state with dipolar deformation. This system is unstable towards inﬁnite density collapse, but we show explicitly that a suitable short-range repulsive (hard core) interaction of strength 0 and range a can stop this collapse. The existence of a stable equilibrium high density ferromagnetic state with spheroidal occupation function is possible as long as the ratio of coupling constants cm ≡ (03/2) is not very smallcompared to 1.
Potential Energy Surface in Hartree-Fock Theory:Adiabatic or Configuration-Constrained?
Institute of Scientific and Technical Information of China (English)
GUO Lu; Sakata Fumihiko; ZHAO En-Guang
2004-01-01
Validity of adiabatic assumption is discussed within the constrained Hartree-Fock theory for self-conjugate nucleus 72Kr. It is shown that the adiabatic assumption does not provide a correct description for the nature of nucleus when a configuration change is involved. The excited Hartree-Fock states and the continuously-connected constrained Hartree-Fock states are given for the first time by applying the configuration dictated constrained Hartree-Fock theory with Gogny force. The importance of self-consistency between the mean-field and the single particle wave functions is emphasized even when a small number of nucleons are involved in the configuration change.
Projected Hartree Fock Theory as a Polynomial Similarity Transformation Theory of Single Excitations
Qiu, Yiheng; Scuseria, Gustavo E
2016-01-01
Spin-projected Hartree-Fock is introduced as a particle-hole excitation ansatz over a symmetry-adapted reference determinant. Remarkably, this expansion has an analytic expression that we were able to decipher. While the form of the polynomial expansion is universal, the excitation amplitudes need to be optimized. This is equivalent to the optimization of orbitals in the conventional projected Hartree-Fock framework of non-orthogonal determinants. Using the inverse of the particle-hole expansion, we similarity transform the Hamiltonian in a coupled-cluster style theory. The left eigenvector of the non-hermitian Hamiltonian is constructed in a similar particle-hole expansion fashion, and we show that to numerically reproduce variational projected Hartree-Fock results, one needs as many pair excitations in the bra as the number of strongly correlated entangled pairs in the system. This single-excitation polynomial similarity transformation theory is an alternative to our recently presented double excitation the...
Relativistic Brueckner-Hartree-Fock theory for finite nuclei
Shen, Shihang; Liang, Haozhao; Meng, Jie; Ring, Peter; Zhang, Shuangquan
2016-01-01
Starting with a bare nucleon-nucleon interaction, for the first time the full relativistic Brueckner-Hartree-Fock equations are solved for finite nuclei in a Dirac-Woods-Saxon basis. No free parameters are introduced to calculate the ground-state properties of finite nuclei. The nucleus $^{16}$O is investigated as an example. The resulting ground-state properties, such as binding energy and charge radius, are considerably improved as compared with the non-relativistic Brueckner-Hartree-Fock results and much closer to the experimental data. This opens the door for \\emph{ab initio} covariant investigations of heavy nuclei.
Series Expansions for Finite-State Markov Chains
Heidergott, Bernd; Hordijk, Arie; Uitert, van Miranda
2005-01-01
This paper provides series expansions of the stationary distribution of a finite Markov chain. This leads to an efficient numerical algorithm for computing the stationary distribution of a finite Markov chain. Numerical examples are given to illustrate the performance of the algorithm.
Resonant-state expansion of light propagation in non-uniform waveguides
Lobanov, S. V.; Zoriniants, G.; Langbein, W.; Muljarov, E. A.
2016-01-01
A new rigorous approach for precise and efficient calculation of light propagation along non-uniform waveguides is presented. Resonant states of a uniform waveguide, which satisfy outgoing-wave boundary conditions, form a natural basis for expansion of the local electromagnetic field. Using such an expansion at fixed frequency, we convert the light propagation along a non-uniform waveguide into an ordinary second-order matrix differential equation for the expansion coefficients along the wave...
Comparison among Magnus/Floquet/Fer expansion schemes in solid-state NMR
Takegoshi, K.; Miyazawa, Norihiro; Sharma, Kshama; Madhu, P. K.
2015-04-01
We here revisit expansion schemes used in nuclear magnetic resonance (NMR) for the calculation of effective Hamiltonians and propagators, namely, Magnus, Floquet, and Fer expansions. While all the expansion schemes are powerful methods there are subtle differences among them. To understand the differences, we performed explicit calculation for heteronuclear dipolar decoupling, cross-polarization, and rotary-resonance experiments in solid-state NMR. As the propagator from the Fer expansion takes the form of a product of sub-propagators, it enables us to appreciate effects of time-evolution under Hamiltonians with different orders separately. While 0th-order average Hamiltonian is the same for the three expansion schemes with the three cases examined, there is a case that the 2nd-order term for the Magnus/Floquet expansion is different from that obtained with the Fer expansion. The difference arises due to the separation of the 0th-order term in the Fer expansion. The separation enables us to appreciate time-evolution under the 0th-order average Hamiltonian, however, for that purpose, we use a so-called left-running Fer expansion. Comparison between the left-running Fer expansion and the Magnus expansion indicates that the sign of the odd orders in Magnus may better be reversed if one would like to consider its effect in order.
Comparison among Magnus/Floquet/Fer expansion schemes in solid-state NMR
Energy Technology Data Exchange (ETDEWEB)
Takegoshi, K., E-mail: takeyan@kuchem.kyoto-u.ac.jp; Miyazawa, Norihiro [Division of Chemistry, Graduate School of Science, Kyoto University, 606-8502 Kyoto (Japan); Sharma, Kshama [TIFR Centre for Interdisciplinary Sciences, 21 Brundavan Colony, Narsingi, Hyderabad 500 075 (India); Madhu, P. K. [TIFR Centre for Interdisciplinary Sciences, 21 Brundavan Colony, Narsingi, Hyderabad 500 075 (India); Department of Chemical Sciences, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400 005 (India)
2015-04-07
We here revisit expansion schemes used in nuclear magnetic resonance (NMR) for the calculation of effective Hamiltonians and propagators, namely, Magnus, Floquet, and Fer expansions. While all the expansion schemes are powerful methods there are subtle differences among them. To understand the differences, we performed explicit calculation for heteronuclear dipolar decoupling, cross-polarization, and rotary-resonance experiments in solid-state NMR. As the propagator from the Fer expansion takes the form of a product of sub-propagators, it enables us to appreciate effects of time-evolution under Hamiltonians with different orders separately. While 0th-order average Hamiltonian is the same for the three expansion schemes with the three cases examined, there is a case that the 2nd-order term for the Magnus/Floquet expansion is different from that obtained with the Fer expansion. The difference arises due to the separation of the 0th-order term in the Fer expansion. The separation enables us to appreciate time-evolution under the 0th-order average Hamiltonian, however, for that purpose, we use a so-called left-running Fer expansion. Comparison between the left-running Fer expansion and the Magnus expansion indicates that the sign of the odd orders in Magnus may better be reversed if one would like to consider its effect in order.
Construction of the Fock-like Space for Quons
Institute of Scientific and Technical Information of China (English)
于挺; 吴兆颜
1994-01-01
The necessary and sufficient condition of the existence of the Fock-like space for quons with a fixed number q is proven, and the uniqueness theorem of the Fock-like space is given. The general-q operators, which satisfy the q-mutation relation a_ja_k - qa_ka_j =δ_jk, areconstructed by using the q = 0 operators as standard building blocks. The Fock-like spaces for quons with q∈(-1,1) prove to be the same as the one with q = 0, which manifestly is the direct sum of all the tensor product powers of the single particle state subspace, hence allow only the Boltzmann statistics .
Superintegrability of the Fock-Darwin system
Drigho-Filho, E.; Kuru, Ş.; Negro, J.; Nieto, L. M.
2017-08-01
The Fock-Darwin system is analyzed from the point of view of its symmetry properties in the quantum and classical frameworks. The quantum Fock-Darwin system is known to have two sets of ladder operators, a fact which guarantees its solvability. We show that for rational values of the quotient of two relevant frequencies, this system is superintegrable, the quantum symmetries being responsible for the degeneracy of the energy levels. These symmetries are of higher order and close a polynomial algebra. In the classical case, the ladder operators are replaced by ladder functions and the symmetries by constants of motion. We also prove that the rational classical system is superintegrable and its trajectories are closed. The constants of motion are also generators of symmetry transformations in the phase space that have been integrated for some special cases. These transformations connect different trajectories with the same energy. The coherent states of the quantum superintegrable system are found and they reproduce the closed trajectories of the classical one.
Modeling electron fractionalization with unconventional Fock spaces
Cobanera, Emilio
2017-08-01
It is shown that certain fractionally-charged quasiparticles can be modeled on D-dimensional lattices in terms of unconventional yet simple Fock algebras of creation and annihilation operators. These unconventional Fock algebras are derived from the usual fermionic algebra by taking roots (the square root, cubic root, etc) of the usual fermionic creation and annihilation operators. If the fermions carry non-Abelian charges, then this approach fractionalizes the Abelian charges only. In particular, the mth-root of a spinful fermion carries charge e/m and spin 1/2. Just like taking a root of a complex number, taking a root of a fermion yields a mildly non-unique result. As a consequence, there are several possible choices of quantum exchange statistics for fermion-root quasiparticles. These choices are tied to the dimensionality D=1,2,3,\\ldots of the lattice by basic physical considerations. One particular family of fermion-root quasiparticles is directly connected to the parafermion zero-energy modes expected to emerge in certain mesoscopic devices involving fractional quantum Hall states. Hence, as an application of potential mesoscopic interest, I investigate numerically the hybridization of Majorana and parafermion zero-energy edge modes caused by fractionalizing but charge-conserving tunneling.
Strongdeco: Expansion of analytical, strongly correlated quantum states into a many-body basis
Juliá-Díaz, Bruno; Graß, Tobias
2012-03-01
We provide a Mathematica code for decomposing strongly correlated quantum states described by a first-quantized, analytical wave function into many-body Fock states. Within them, the single-particle occupations refer to the subset of Fock-Darwin functions with no nodes. Such states, commonly appearing in two-dimensional systems subjected to gauge fields, were first discussed in the context of quantum Hall physics and are nowadays very relevant in the field of ultracold quantum gases. As important examples, we explicitly apply our decomposition scheme to the prominent Laughlin and Pfaffian states. This allows for easily calculating the overlap between arbitrary states with these highly correlated test states, and thus provides a useful tool to classify correlated quantum systems. Furthermore, we can directly read off the angular momentum distribution of a state from its decomposition. Finally we make use of our code to calculate the normalization factors for Laughlin's famous quasi-particle/quasi-hole excitations, from which we gain insight into the intriguing fractional behavior of these excitations. Program summaryProgram title: Strongdeco Catalogue identifier: AELA_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELA_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5475 No. of bytes in distributed program, including test data, etc.: 31 071 Distribution format: tar.gz Programming language: Mathematica Computer: Any computer on which Mathematica can be installed Operating system: Linux, Windows, Mac Classification: 2.9 Nature of problem: Analysis of strongly correlated quantum states. Solution method: The program makes use of the tools developed in Mathematica to deal with multivariate polynomials to decompose analytical strongly correlated states of bosons
Sundholm, Dage; Olsen, Jeppe
1993-04-01
The atomic quadrupole moments Qzz of Be(2s2p;3P2), Al(3p;2P3/2), In(5p;2P3/2), Ne(2p53s3P2), Ar(3p54s;3P2), Kr(4p55s;3P2), and Xe(5p56s;3P2) have been calculated using a finite-element multiconfiguration Hartree-Fock method. The obtained Qzz(Be) of 2.265 a.u. agrees with previously calculated values. The calculated Qzz(Al) and Qzz(In) of 2.579 and 3.165 a.u. are in good agreement with the experimental values of 2.53(15) a.u. and 2.94(10) a.u. A large s-d polarization contribution to the Qzz of the rare gases is found in the present calculations. The correlation contributions from double (D), triple (T), and quadruple (Q) excitations to the Qzz of the rare gases alternate; the total DTQ correlation contribution is negligibly small for Ne, Ar, and Kr, while the DTQ correlation contribution to the Qzz(Xe) is 25% of the final Qzz. The final values are Qzz(Ne)=-0.0506 a.u., Qzz(Ar)=-0.0553 a.u., Qzz(Kr)=+0.0601 a.u., and Qzz(Xe)=+0.4505 a.u., as compared to the experimental values of -0.048(5) a.u., -0.042(4) a.u., +0.046(5) a.u., and +0.30(3) a.u. for Ne, Ar, Kr, and Xe, respectively.
Monitoring the expansion of built-up areas in Seberang Perai region, Penang State, Malaysia
Samat, N.
2014-02-01
Rapid urbanization has caused land use transformation and encroachment of built environment into arable agriculture land. Uncontrolled expansion could bring negative impacts to society, space and the environment. Therefore, information on expansion and future spatial pattern of built-up areas would be useful for planners and decision makers in formulating policies towards managing and planning for sustainable urban development. This study demonstrates the usage of Geographic Information System in monitoring the expansion of built-up area in Seberang Perai region, Penang State, Malaysia. Built-up area has increased by approximately 20% between 1990 and 2001 and further increased by 12% between 2001 and 2007. New development is expected to continue encroach into existing open space and agriculture area since those are the only available land in this study area. The information on statistics of the expansion of built-up area and future spatial pattern of urban expansion were useful in planning and managing urban spatial growth.
Marketized State Ownership and Foreign Expansion of Emerging Market Multinationals
DEFF Research Database (Denmark)
Li, Ming Hua; Cui, Lin; Lu, Jiangyong
2017-01-01
direct investment. We argue that firms with marketized state ownership may derive institutional competitive advantages from their dual responsiveness to shifting global market conditions and home government expectations which has a positive impact on their foreign investment decisions. However......The emergence of marketized shareholders through corporate ownership reform and their impact on the foreign entry of emerging market firms is a critical but understudied issue. Our study investigates the effect of marketized state ownership on emerging market firms' propensity to engage in foreign......, such advantages are likely to vary in magnitude for firms with marketized state ownership at central and local levels of government due to different patterns of corporate restructuring. We predict that such ownership effects are contingent on firms' affiliation to meso-level institutional structures such as state...
Resonant-state expansion Born Approximation applied to Schrodinger's Equation
Doost, M B
2015-01-01
The RSE Born Approximation is a new scattering formula in Physics, it allows the calculation of strong scattering via the Fourier transform of the scattering potential and Resonant-states. In this paper I apply the RSE Born Approximation to Schr\\"odinger's Equation. The resonant-states of the system can be calculated using the recently discovered RSE perturbation theory and normalised correctly to appear in spectral Green's functions via the flux volume normalisation.
Mananga, Eugene Stephane
2013-01-01
This work presents the possibility of applying the Floquet-Magnus expansion and the Fer expansion approaches to the most useful interactions known in solid-state nuclear magnetic resonance using the magic-echo scheme. The results of the effective Hamiltonians of these theories and average Hamiltonian theory are presented.
Data on burden of comorbidities in the united states and medicaid expansion status
Directory of Open Access Journals (Sweden)
Tomi Akinyemiju
2016-09-01
Full Text Available The high prevalence of comorbidities among US adults is a major public health problem. However, there is limited data on the geographic distribution of comorbidities. In addition, recent changes to health insurance programs in the US through the Affordable Care Act, and the Medicaid expansion program specifically, has the potential to significantly improve the prevention and management of comorbid conditions in the US. In a recent analysis, we examined disparities in the burden of comorbidities among US adults by state Medicaid expansion status, (Akinyemiju et al., 2016 [1]. Here, we provide additional data showing the state level mean number of comorbidities in all 50 US states for African–Americans and whites, stratified by Medicaid expansion status. In addition, we provide a map of the US states showing the geographic distribution of comorbidities and stratified by race/ethnicity and gender.
Virial Expansion of the Nuclear Equation of State
Maganaa, Ruslan; Bonasera, Aldo
2010-01-01
We study the equation of state (EOS) of nuclear matter as function of density. We expand the energy per particle (E/A) of symmetric infinite nuclear matter in powers of the density to take into account 2,3,. . .,N-body forces. New EOS are proposed by fitting ground state properties of nuclear matter (binding energy, compressibility and pressure) and assuming that at high densities a second order phase transition to the Quark Gluon Plasma (QGP) occurs. The latter phase transition is due to symmetry breaking at high density from nuclear matter (locally color white) to the QGP (globally color white). In the simplest implementation of a second order phase transition we calculate the critical exponent ? by using Landau's theory of phase transition. We find ? = 3. Refining the properties of the EOS near the critical point gives ? = 5 in agreement with experimental results. We also discuss some scenarios for the EOS at finite temperatures.
Virial Expansion of the Nuclear Equation of State
Magana, Ruslan; Zheng, Hua; Bonasera, Aldo
We study the equation of state (EOS) of nuclear matter as function of density. We expand the energy per particle (E/A) of symmetric infinite nuclear matter in powers of the density to take into account 2, 3, …, N-body forces. New EOS are proposed by fitting ground state properties of nuclear matter (binding energy, compressibility and pressure) and assuming that at high densities a second-order phase transition to the quark-gluon plasma (QGP) occurs. The latter phase transition is due to symmetry breaking at high density from nuclear matter (locally color white) to the QGP (globally color white). In the simplest implementation of a second-order phase transition we calculate the critical exponent δ by using Landau's theory of phase transition. We find δ = 3. Refining the properties of the EOS near the critical point gives δ = 5 in agreement with experimental results. We also discuss some scenarios for the EOS at finite temperatures.
Particle unstable nuclei in the Hartree-Fock theory
Energy Technology Data Exchange (ETDEWEB)
Kruppa, A.T. [Magyar Tudomanyos Akademia, Debrecen (Hungary). Atommag Kutato Intezete; Heenen, P.H. [Brussels Univ. (Belgium). Service de Physique Nucleaire Theorique; Flocard, H. [Paris-11 Univ., 91 - Orsay (France). Inst. de Physique Nucleaire; Liotta, R.J. [Manne Siegbahn Inst. of Physics, Stockholm (Sweden)
1997-12-31
Ground state energies and decay widths of particle unstable nuclei are calculated within the Hartree-Fock approximation by performing a complex scaling of the many-body Hamiltonian. Through this transformation, the wave functions of the resonant state become square integrable. The method is implemented with Skyrme effective interactions. Several Skyrme parametrizations are tested on four unstable nuclei: {sup 10}He, {sup 12}O, {sup 26}O and {sup 28}O. (author). 24 refs.
Ragot, Sébastien
2008-04-01
The ground-state Hartree-Fock (HF) wavefunction of Hooke's atom is not known in closed form, contrary to the exact solution. The single HF orbital involved has thus far been studied using expansion techniques only, leading to slightly disparate energies. Therefore, the present letter aims at proposing alternative definitions of the HF wavefunction. First, the HF limit is ascertained using a simple expansion, which makes it possible to formulate explicit expressions of HF properties. The resulting energy, 2.038 438 871 8 Eh, is found stable at the tenth digit. Second and more instructive, an analysis of the Hartree equation makes it possible to infer a remarkably simple and accurate HF orbital, i.e., φHF(r)=nHFe-αr2√r2+β2, leading to an energy exceeding by 5.76×10-7 Eh only the above HF limit. This orbital makes it possible to obtain (near) Hartree-Fock properties in closed form, which in turn enables handy comparisons with exact quantities.
Relativistic Hartree-Fock-Bogoliubov model for deformed nuclei
Ebran, J -P; Arteaga, D Pena; Vretenar, D
2010-01-01
The Relativistic Hartree-Fock-Bogoliubov model for axially deformed nuclei (RHFBz) is introduced. The model is based on an effective Lagrangian with density-dependent meson-nucleon couplings in the particle-hole channel, and the pairing part of the Gogny force is used in the pairing channel. The RHFBz quasiparticle equations are solved by expansion in the basis of a deformed harmonic oscillator. Illustrative RHFBz calculations are performed for Carbon, Neon and Magnesium isotopes. The effect of the explicitly including the pion field is investigated for binding energies, deformation parameters, and charge radii.
Qiu, Yiheng; Henderson, Thomas M.; Scuseria, Gustavo E.
2016-09-01
Spin-projected Hartree-Fock is written as a particle-hole excitation ansatz over a symmetry-adapted reference determinant. Remarkably, this expansion has an analytic expression that we were able to decipher. While the form of the polynomial expansion is universal, the excitation amplitudes need to be optimized. This is equivalent to the optimization of orbitals in the conventional projected Hartree-Fock framework of non-orthogonal determinants. Using the inverse of the particle-hole expansion, we similarity transform the Hamiltonian in a coupled-cluster style theory. The left eigenvector of the non-Hermitian Hamiltonian is constructed in a similar particle-hole expansion fashion, and we show that to numerically reproduce variational projected Hartree-Fock results, one needs as many pair excitations in the bra as the number of strongly correlated entangled pairs in the system. This single-excitation polynomial similarity transformation theory is an alternative to our recently presented double excitation theory, but supports projected Hartree-Fock and coupled cluster simultaneously rather than interpolating between them.
The $\\hbar$ Expansion in Quantum Field Theory
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins; Hoyer, Paul; /Southern Denmark U., CP3-Origins /Helsinki U. /Helsinki Inst. of Phys.
2010-10-27
We show how expansions in powers of Planck's constant {h_bar} = h = 2{pi} can give new insights into perturbative and nonperturbative properties of quantum field theories. Since {h_bar} is a fundamental parameter, exact Lorentz invariance and gauge invariance are maintained at each order of the expansion. The physics of the {h_bar} expansion depends on the scheme; i.e., different expansions are obtained depending on which quantities (momenta, couplings and masses) are assumed to be independent of {h_bar}. We show that if the coupling and mass parameters appearing in the Lagrangian density are taken to be independent of {h_bar}, then each loop in perturbation theory brings a factor of {h_bar}. In the case of quantum electrodynamics, this scheme implies that the classical charge e, as well as the fine structure constant are linear in {h_bar}. The connection between the number of loops and factors of {h_bar} is more subtle for bound states since the binding energies and bound-state momenta themselves scale with {h_bar}. The {h_bar} expansion allows one to identify equal-time relativistic bound states in QED and QCD which are of lowest order in {h_bar} and transform dynamically under Lorentz boosts. The possibility to use retarded propagators at the Born level gives valence-like wave-functions which implicitly describe the sea constituents of the bound states normally present in its Fock state representation.
Directory of Open Access Journals (Sweden)
Petrosyan G.L.
2012-09-01
Full Text Available The peculiarities for determining the current interconnected geometrical parameters of large diameter ring expansion process are revealed. Based on ring stress state studies the universal system of equations is obtained. It is shown that in case of step-by-step increase of ring diameter the changes of geometrical parameters allow to obtain the equations of plane stripe rolling.
Nonperturbative solution of scalar Yukawa model in two- and three-body Fock space truncations
Karmanov, Vladimir A; Smirnov, Alexander V; Vary, James P
2016-01-01
The Light-Front Tamm-Dancoff method of finding the nonperturbative solutions in field theory is based on the Fock decomposition of the state vector, complemented with the sector-dependent nonperturbative renormalization scheme. We show in detail how to implement the renormalization procedure and to solve the simplest nontrivial example of the scalar Yukawa model in the two- and three-body Fock space truncations incorporating scalar "nucleon" and one or two scalar "pions".
Claudino, D; Gargano, R; Carvalho-Silva, Valter H; E Silva, Geraldo M; da Cunha, W F
2016-07-21
The present paper concludes our series of kinetics studies on the reactions involved in the complex mechanism of nitrogen trifluoride decomposition. Two other related reactions that, along with this mechanism, take part in an efficient boron nitride growth process are also investigated. We report results concerning two abstraction reactions, namely NF2 + N ⇄ 2NF and NF3 + NF ⇄ 2NF2, and two dissociations, N2F4 ⇄ 2NF2 and N2F3 ⇄ NF2 + NF. State-of-the-art electronic structure calculations at the CCSD(T)/cc-pVTZ level of theory were considered to determine geometries and frequencies of reactants, products, and transition states. Extrapolation of the energies to the complete basis set limit was used to obtain energies of all the species. We applied transition state theory to compute thermal rate constants including Wigner, Eckart, Bell, and deformed theory corrections in order to take tunneling effects into account. The obtained results are in good agreement with the experimental data available in the literature and are expected to provide a better phenomenological understanding of the NF3 decomposition role in the boron nitride growth for a wide range of temperature values.
Schmehr, J L; Whitley, W; Huxley, A D
2016-12-01
A new solid-state electrotransport (SSE) apparatus for refining ultra-pure single crystals of metallic compounds under ultra-high vacuum is described. The setup employs a novel thermal expansion compensation mechanism to minimize mechanical stress on the sample during refinement with cold clamps for contamination-less purification at elevated temperatures. The apparatus is designed to tune the composition of initially slightly off-stoichiometric samples. The expansion compensation and stress-free operation were tested by recording the thermal expansion of elemental cerium in a treatment up to 655 °C. SSE refinement was then performed on a high-quality single crystal of U6Fe resulting in a 50% increase of its residual resistivity ratio to the highest value obtained for a single crystal to date.
Schmehr, J. L.; Whitley, W.; Huxley, A. D.
2016-12-01
A new solid-state electrotransport (SSE) apparatus for refining ultra-pure single crystals of metallic compounds under ultra-high vacuum is described. The setup employs a novel thermal expansion compensation mechanism to minimize mechanical stress on the sample during refinement with cold clamps for contamination-less purification at elevated temperatures. The apparatus is designed to tune the composition of initially slightly off-stoichiometric samples. The expansion compensation and stress-free operation were tested by recording the thermal expansion of elemental cerium in a treatment up to 655 °C. SSE refinement was then performed on a high-quality single crystal of U6Fe resulting in a 50% increase of its residual resistivity ratio to the highest value obtained for a single crystal to date.
Resonant-state expansion of light propagation in non-uniform waveguides
Lobanov, S V; Langbein, W; Muljarov, E A
2016-01-01
A new rigorous approach for precise and efficient calculation of light propagation along non-uniform waveguides is presented. Resonant states of a uniform waveguide, which satisfy outgoing-wave boundary conditions, form a natural basis for expansion of the local electromagnetic field. Using such an expansion at fixed frequency, we convert the light propagation along a non-uniform waveguide into an ordinary second-order matrix differential equation for the expansion coefficients along the waveguide. We illustrate the method on examples of planar waveguides with rectangular holes and evaluate its efficiency compared to the aperiodic Fourier modal method and the finite element method, showing improvements of one to two orders of magnitude. A similar improvement can be expected also for applications in other fields of physics showing wave phenomena, such as acoustics and quantum mechanics.
The Extended Fock Basis of Clifford Algebra
Budinich, Marco
2010-01-01
We investigate the properties of the Extended Fock Basis (EFB) of Clifford algebras introduced in [1]. We show that a Clifford algebra can be seen as a direct sum of multiple spinor subspaces that are characterized as being left eigenvectors of $\\Gamma$. We also show that a simple spinor, expressed in Fock basis, can have a maximum number of non zero coordinates that equals the size of the maximal totally null plane (with the notable exception of vectorial spaces with 6 dimensions).
The Extended Fock Basis of Clifford Algebra
2010-01-01
We investigate the properties of the Extended Fock Basis (EFB) of Clifford algebras introduced in [1]. We show that a Clifford algebra can be seen as a direct sum of multiple spinor subspaces that are characterized as being left eigenvectors of \\Gamma. We also show that a simple spinor, expressed in Fock basis, can have a maximum number of non zero coordinates that equals the size of the maximal totally null plane (with the notable exception of vectorial spaces with 6 dimensions).
On the Floquet–Magnus expansion: Applications in solid-state nuclear magnetic resonance and physics
Energy Technology Data Exchange (ETDEWEB)
Mananga, Eugene Stephane, E-mail: emananga@gradcenter.cuny.edu [Harvard Medical School and Massachusetts General Hospital, Center for Advanced Medical Imaging Sciences, Division of Nuclear Medicine and Molecular Imaging Physics, Department of Radiology, 55 Fruit Street, Boston, Massachusetts 02114 (United States); Charpentier, Thibault, E-mail: thibault.charpentier@cea.fr [Commissariat à l’Energie Atomique, IRAMIS, Service interdisciplinaire sur les systèmes moléculaires et matériaux, CEA/CNRS UMR 3299, 91191, Gif-sur-Yvette (France)
2016-01-22
Theoretical approaches are useful and powerful tools for more accurate and efficient spin dynamics simulation to understand experiments and devising new RF pulse sequence in nuclear magnetic resonance. Solid-state NMR is definitely a timely topic or area of research, and not many papers on the respective theories are available in the literature of nuclear magnetic resonance or physics reports. This report presents the power and the salient features of the promising theoretical approach called Floquet–Magnus expansion that is helpful to describe the time evolution of the spin system at all times in nuclear magnetic resonance. The report presents a broad view of algorithms of spin dynamics, based on promising and useful theory of Floquet–Magnus expansion. This theory provides procedures to control and describe the spin dynamics in solid-state NMR. Major applications of the Floquet–Magnus expansion are illustrated by simple solid-state NMR and physical applications such as in nuclear, atomic, molecular physics, and quantum mechanics, NMR, quantum field theory and high energy physics, electromagnetism, optics, general relativity, search of periodic orbits, and geometric control of mechanical systems. The aim of this report is to bring to the attention of the spin dynamics community, the bridge that exists between solid-state NMR and other related fields of physics and applied mathematics. This review article also discusses future potential theoretical directions in solid-state NMR.
Quantum Computing in Fock Space Systems
Berezin, Alexander A.
1997-04-01
Fock space system (FSS) has unfixed number (N) of particles and/or degrees of freedom. In quantum computing (QC) main requirement is sustainability of coherent Q-superpositions. This normally favoured by low noise environment. High excitation/high temperature (T) limit is hence discarded as unfeasible for QC. Conversely, if N is itself a quantized variable, the dimensionality of Hilbert basis for qubits may increase faster (say, N-exponentially) than thermal noise (likely, in powers of N and T). Hence coherency may win over T-randomization. For this type of QC speed (S) of factorization of long integers (with D digits) may increase with D (for 'ordinary' QC speed polynomially decreases with D). This (apparent) paradox rests on non-monotonic bijectivity (cf. Georg Cantor's diagonal counting of rational numbers). This brings entire aleph-null structurality ("Babylonian Library" of infinite informational content of integer field) to superposition determining state of quantum analogue of Turing machine head. Structure of integer infinititude (e.g. distribution of primes) results in direct "Platonic pressure" resembling semi-virtual Casimir efect (presure of cut-off vibrational modes). This "effect", the embodiment of Pythagorean "Number is everything", renders Godelian barrier arbitrary thin and hence FSS-based QC can in principle be unlimitedly efficient (e.g. D/S may tend to zero when D tends to infinity).
Introduction of the Floquet-Magnus expansion in solid-state nuclear magnetic resonance spectroscopy.
Mananga, Eugène S; Charpentier, Thibault
2011-07-28
In this article, we present an alternative expansion scheme called Floquet-Magnus expansion (FME) used to solve a time-dependent linear differential equation which is a central problem in quantum physics in general and solid-state nuclear magnetic resonance (NMR) in particular. The commonly used methods to treat theoretical problems in solid-state NMR are the average Hamiltonian theory (AHT) and the Floquet theory (FT), which have been successful for designing sophisticated pulse sequences and understanding of different experiments. To the best of our knowledge, this is the first report of the FME scheme in the context of solid state NMR and we compare this approach with other series expansions. We present a modified FME scheme highlighting the importance of the (time-periodic) boundary conditions. This modified scheme greatly simplifies the calculation of higher order terms and shown to be equivalent to the Floquet theory (single or multimode time-dependence) but allows one to derive the effective Hamiltonian in the Hilbert space. Basic applications of the FME scheme are described and compared to previous treatments based on AHT, FT, and static perturbation theory. We discuss also the convergence aspects of the three schemes (AHT, FT, and FME) and present the relevant references.
Supercritical-state expansions which cross the binodal line before reaching the nozzle throat
Knuth, Eldon L.; Toennies, J. Peter
2012-11-01
Three peaks have been found in time-of-flight distributions for expansions from supercritical states for both He and CO2, with the two slower peaks consisting of condensed-phase particles. It is observed that the presence of the third peak coincides with source conditions for which the expansion crosses the binodal line before reaching the nozzle throat, which crossing leads to the expanding fluid flashing, thereby creating a mixture of vapor and liquid phases. Christen et al. suggest that the two phases expand simultaneously. However, simultaneous expansions of the vapor and liquid phases through the nozzle would not be consistent with (a) the large differences in the velocities of the observed peaks and (b) the appearance of a solute (when added to the CO2) in only one of the condensed-phase peaks. However a model in which the vapor and liquid phases expand alternately, hence independently, through the nozzle is consistent with the observations. The terminal condensed-phase mass fraction in the vapor-phase expansions (both those with flashing and those without flashing) is calculated from conservation of energy and correlated as a function of a dimensionless correlating parameter introduced in earlier studies of condensations in free jets.
2009 recession and expansion from 2010 to 2012 in the states of Mexico
Directory of Open Access Journals (Sweden)
Alfredo Erquizio Espinal
2014-11-01
Full Text Available The article examines the recession and expansion phases for which transited Mexico in the past four years and in particular explains the causes of regional diversity of manifestations of the Great Recession of 2009. It uses regional–sectoral typology, formulated new indices based on Mitchell hypothesis about classic cycles and proposes a regional cycle equation inspired Frish metaphor about cyclical mechanism. This verifies that the sectoral profile of the states determines such differentiation, since most manufacturing states were most affected and characterized mainly by agricultural or mining character, they were less.
Hankel transforms in generalized Fock spaces
Directory of Open Access Journals (Sweden)
John Schmeelk
1994-01-01
Full Text Available A classical Fock space consists of functions of the form,ϕ↔(ϕ0,ϕ1,…,ϕq,where ϕ0∈ℂ and ϕq∈Lp(ℝq, q≥1. We will replace the ϕq, q≥1 with test functions having Hankel transforms. This space is a natural generalization of a classical Fock space as seen by expanding functionals having abstract Taylor Series. The particular coefficients of such series are multilinear functionals having distributions as their domain. Convergence requirements set forth are somewhat in the spirit of ultra differentiable functions and ultra distribution theory. The Hankel transform oftentimes implemented in Cauchy problems will be introduced into this setting. A theorem will be proven relating the convergence of the transform to the inductive limit parameter, s, which sweeps out a scale of generalized Fock spaces.
Fourier transforms in generalized Fock spaces
Directory of Open Access Journals (Sweden)
John Schmeelk
1990-01-01
Full Text Available A classical Fock space consists of functions of the form,Φ↔(ϕ0,ϕ1,…,ϕq,…,where ϕ0∈C and ϕq∈L2(R3q, q≥1. We will replace the ϕq, q≥1 with q-symmetric rapid descent test functions within tempered distribution theory. This space is a natural generalization of a classical Fock space as seen by expanding functionals having generalized Taylor series. The particular coefficients of such series are multilinear functionals having tempered distributions as their domain. The Fourier transform will be introduced into this setting. A theorem will be proven relating the convergence of the transform to the parameter, s, which sweeps out a scale of generalized Fock spaces.
On the Fock Transformation in Nonlinear Relativity
Bouda, A
2012-01-01
In this paper, we propose a new deformed Poisson brackets which leads to the Fock coordinate transformation by using an analogous procedure as in Deformed Special Relativity. We therefore derive the corresponding momentum transformation which is revealed to be different from previous results. Contrary to the earlier version of Fock's nonlinear relativity for which plane waves cannot be described, our resulting algebra keeps invariant for any coordinate and momentum transformations the four dimensional contraction $p_{\\mu} x^{\\mu} $, allowing therefore to associate plane waves for free particles. As in Deformed Special Relativity, we also derive a canonical transformation with which the new coordinates and momentum satisfy the usual Poisson brackets and therefore transform like the usual Lorentz vectors. Finally, we establish the dispersion relation for Fock's nonlinear relativity.
Parallel scalability of Hartree–Fock calculations
Energy Technology Data Exchange (ETDEWEB)
Chow, Edmond, E-mail: echow@cc.gatech.edu; Liu, Xing [School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0765 (United States); Smelyanskiy, Mikhail; Hammond, Jeff R. [Parallel Computing Lab, Intel Corporation, Santa Clara, California 95054-1549 (United States)
2015-03-14
Quantum chemistry is increasingly performed using large cluster computers consisting of multiple interconnected nodes. For a fixed molecular problem, the efficiency of a calculation usually decreases as more nodes are used, due to the cost of communication between the nodes. This paper empirically investigates the parallel scalability of Hartree–Fock calculations. The construction of the Fock matrix and the density matrix calculation are analyzed separately. For the former, we use a parallelization of Fock matrix construction based on a static partitioning of work followed by a work stealing phase. For the latter, we use density matrix purification from the linear scaling methods literature, but without using sparsity. When using large numbers of nodes for moderately sized problems, density matrix computations are network-bandwidth bound, making purification methods potentially faster than eigendecomposition methods.
Energy Technology Data Exchange (ETDEWEB)
Kato, Tsuyoshi; Ide, Yoshihiro; Yamanouchi, Kaoru [Department of Chemistry, School of Science, The University of Tokyo, 7-3-1, Hongo Bunkyo-ku, Tokyo, 113-0033 (Japan)
2015-12-31
We first calculate the ground-state molecular wave function of 1D model H{sub 2} molecule by solving the coupled equations of motion formulated in the extended multi-configuration time-dependent Hartree-Fock (MCTDHF) method by the imaginary time propagation. From the comparisons with the results obtained by the Born-Huang (BH) expansion method as well as with the exact wave function, we observe that the memory size required in the extended MCTDHF method is about two orders of magnitude smaller than in the BH expansion method to achieve the same accuracy for the total energy. Second, in order to provide a theoretical means to understand dynamical behavior of the wave function, we propose to define effective adiabatic potential functions and compare them with the conventional adiabatic electronic potentials, although the notion of the adiabatic potentials is not used in the extended MCTDHF approach. From the comparison, we conclude that by calculating the effective potentials we may be able to predict the energy differences among electronic states even for a time-dependent system, e.g., time-dependent excitation energies, which would be difficult to be estimated within the BH expansion approach.
Expansion and retrenchment of the Swedish welfare state: a long-term approach.
Buendía, Luis
2015-01-01
In this article, we will undertake a long-term analysis of the evolution of the Swedish welfare state, seeking to explain that evolution through the use of a systemic approach. That is, our approach will consider the interrelations between economic growth (EG), the sociopolitical institutional framework (IF), and the welfare state (WS)-understood as a set of institutions embracing the labor market and its regulation, the tax system, and the so-called social wage-in order to find the main variables that elucidate its evolution. We will show that the expansive phase of the Swedish welfare state can be explained by the symbiotic relationships developed in the WS-EG-IF interaction, whereas the period of welfare state retrenchment is one result of changes operating within the sociopolitical IF and EG bases.
Geographic Expansion of Lyme Disease in the Southeastern United States, 2000-2014.
Lantos, Paul M; Nigrovic, Lise E; Auwaerter, Paul G; Fowler, Vance G; Ruffin, Felicia; Brinkerhoff, R Jory; Reber, Jodi; Williams, Carl; Broyhill, James; Pan, William K; Gaines, David N
2015-12-01
Background. The majority of Lyme disease cases in the United States are acquired on the east coast between northern Virginia and New England. In recent years the geographic extent of Lyme disease has been expanding, raising the prospect of Lyme disease becoming endemic in the southeast. Methods. We collected confirmed and probable cases of Lyme disease from 2000 through 2014 from the Virginia Department of Health and North Carolina Department of Public Health and entered them in a geographic information system. We performed spatial and spatiotemporal cluster analyses to characterize Lyme disease expansion. Results. There was a marked increase in Lyme disease cases in Virginia, particularly from 2007 onwards. Northern Virginia experienced intensification and geographic expansion of Lyme disease cases. The most notable area of expansion was to the southwest along the Appalachian Mountains with development of a new disease cluster in the southern Virginia mountain region. Conclusions. The geographic distribution of Lyme disease cases significantly expanded in Virginia between 2000 and 2014, particularly southward in the Virginia mountain ranges. If these trends continue, North Carolina can expect autochthonous Lyme disease transmission in its mountain region in the coming years.
Convergence of the partial wave expansion of the He ground state
Bromley, M W J
2006-01-01
The Configuration Interaction (CI) method using a very large Laguerre orbital basis is applied to the calculation of the He ground state. A minimum of 35 radial orbitals for each partial wave ranging from 0 to 12 are included resulting in a basis with a total of 465 orbitals. The convergence of the energy and electron-electron $\\delta$-function with respect to J (the maximum angular momenta of the orbitals included in the CI expansion) are investigated in detail. It is seen that the convergence properties of some previous very large calculations show irregularities. The J to infinity limit of the energy was obtained by fitting to expansions of the type Delta E_J = A_E/(J+1/2)^4 + B_E/(J+1/2)^5 + ..., giving an energy about 10^-7 hartree from the exact energy. Convergence issues caused problems when trying to determine the J to infinity limit of using a similar asymptotic expansion and the biggest calculations achieved accuracies between 0.2 and 0.5%.
Tian, Jianxiang; Mulero, A
2016-01-01
Despite the fact that more that more than 30 analytical expressions for the equation of state of hard-disk fluids have been proposed in the literature, none of them is capable of reproducing the currently accepted numeric or estimated values for the first eighteen virial coefficients. Using the asymptotic expansion method, extended to the first ten virial coefficients for hard-disk fluids, fifty-seven new expressions for the equation of state have been studied. Of these, a new equation of state is selected which reproduces accurately all the first eighteen virial coefficients. Comparisons for the compressibility factor with computer simulations show that this new equation is as accurate as other similar expressions with the same number of parameters. Finally, the location of the poles of the 57 new equations shows that there are some particular configurations which could give both the accurate virial coefficients and the correct closest packing fraction in the future when higher virial coefficients than the t...
GEOGRAPHICAL EXPANSION OF CANINE VISCERAL LEISHMANIASIS IN RIO DE JANEIRO STATE, BRAZIL
da SILVA, Denise Amaro; MADEIRA, Maria de Fátima; FIGUEIREDO, Fabiano Borges
2015-01-01
SUMMARY Visceral Leishmaniasis (VL) is a vector-borne disease that affects humans, and domestic and wild animals. It is caused by the protozoan Leishmania (Leishmania) infantum (syn = Leishmania chagasi). The domestic dog (Canis familiaris) is considered the main reservoir of the etiologic agent of VL in domestic and peridomestic environments. In the past three years, although control actions involving domestic dogs are routinely performed in endemic areas of the Rio de Janeiro State, new cases of canine visceral leishmaniasis (CVL) have been reported in several municipalities. The objective of this short communication was to describe the geographical expansion of CVL in the Rio de Janeiro State, Brazil, through its reports in the scientific literature and studies performed by our group. From 2010 to 2013, autochthonous and allochthonous cases of CVL were reported in the municipalities of Mangaratiba, Marica, Niteroi, Barra Mansa, Cachoeiras de Macacu, Volta Redonda, Resende and Rio de Janeiro. These reports demonstrate that CVL is in intense geographical expansion around the state; therefore, a joint effort by public agencies, veterinarians and researchers is needed in order to minimize and/or even prevent the dispersion of this disease. PMID:26603233
Energy Technology Data Exchange (ETDEWEB)
Kano, Naokazu; O' Brien, Nathan J. [Department of Chemistry, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033 (Japan); Uematsu, Ryohei; Ramozzi, Romain; Morokuma, Keiji [Fukui Institute for Fundamental Chemistry, Kyoto University, Takano-Nishihiraki-cho 34-4, Sakyou-ku, Kyoto, 606-8103 (Japan)
2017-05-15
The first trihydroborate bearing a pentacoordinated phosphorus atom was synthesized as a new P-B bonded compound. Hydride abstraction of the trihydroborate gave an intermediary dihydroborane, which showed hydroboration reactivity and was trapped with pyridine whilst maintaining the P-B bond. The dihydroborane underwent a rearrangement, which involved a double ring expansion to compensate for the unbalanced coordination states of the phosphorus and boron atoms, to give a new fused bicyclic phosphine-boronate. (copyright 2017 Wiley-VCH Verlag GmbH and Co. KGaA, Weinheim)
The Fock-Kemmer approach to precursor shock waves in relativistic field theory
Abdullah, Rawand H
2016-01-01
We use distribution theory (generalized functions) to extend and justify the Fock-Kemmer approach to the propagation of precursor shock wave discontinuities in classical and quantum field theory. We apply lightcone causality arguments to propose that shock wave singularities in non-linear classical field theories and in Maxwell's equations for responsive media require a form of classical renormalization analogous to Wilson operator product expansions in quantum field theories.
Loop Quantization Versus Fock Quantization Of P-form Electromagnetism On Static Spacetimes
Carrion Alvarez, M
2004-01-01
As a warmup for studying dynamics and gravitons in loop quantum gravity. Varadajan showed that Wilson loops give operators on the Fock space for electromagnetism in Minkowski spacetime—but only after regularizing the loops by smearing them with a Gaussian. Unregularized Wilson loops are too singular to give densely defined operators. Here we present a rigorous treatment of unsmeared Wilson loops for vacuum electromagnetism on an arbitrary globally hyperbolic static spacetime. Our Wilson loops are not operators, but “quasioperators”: sesquilinear forms on the dense subspace of Fock space spanned by coherent states corresponding to smooth classical solutions. To obtain this result we begin by carefully treating electromagnetism on globally hyperbolic static spacetimes, addressing various issues that are usually ignored, such as the definition of Aharonov-Bohm modes when space is noncompact. We then use a new construction of Fock space based on coherent states to define Wilson loop ...
Coherent states, 6j symbols and properties of the next to leading order asymptotic expansions
Kamiński, Wojciech; Steinhaus, Sebastian
2013-12-01
We present the first complete derivation of the well-known asymptotic expansion of the SU(2) 6j symbol using a coherent state approach, in particular we succeed in computing the determinant of the Hessian matrix. To do so, we smear the coherent states and perform a partial stationary point analysis with respect to the smearing parameters. This allows us to transform the variables from group elements to dihedral angles of a tetrahedron resulting in an effective action, which coincides with the action of first order Regge calculus associated to a tetrahedron. To perform the remaining stationary point analysis, we compute its Hessian matrix and obtain the correct measure factor. Furthermore, we expand the discussion of the asymptotic formula to next to leading order terms, prove some of their properties and derive a recursion relation for the full 6j symbol.
Coherent states, 6j symbols and properties of the next to leading order asymptotic expansions
Energy Technology Data Exchange (ETDEWEB)
Kamiński, Wojciech, E-mail: wkaminsk@fuw.edu.pl [Wydział Fizyki, Uniwersytet Warszawski, Hoża 69, 00-681, Warsaw (Poland); Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada); Max Planck Institute for Gravitational Physics, Am Mühlenberg 1, D-14476 Potsdam (Germany); Steinhaus, Sebastian, E-mail: steinhaus.sebastian@gmail.com [Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada); Max Planck Institute for Gravitational Physics, Am Mühlenberg 1, D-14476 Potsdam (Germany)
2013-12-15
We present the first complete derivation of the well-known asymptotic expansion of the SU(2) 6j symbol using a coherent state approach, in particular we succeed in computing the determinant of the Hessian matrix. To do so, we smear the coherent states and perform a partial stationary point analysis with respect to the smearing parameters. This allows us to transform the variables from group elements to dihedral angles of a tetrahedron resulting in an effective action, which coincides with the action of first order Regge calculus associated to a tetrahedron. To perform the remaining stationary point analysis, we compute its Hessian matrix and obtain the correct measure factor. Furthermore, we expand the discussion of the asymptotic formula to next to leading order terms, prove some of their properties and derive a recursion relation for the full 6j symbol.
Coherent states, 6j symbols and properties of the next to leading order asymptotic expansions
Kaminski, Wojciech
2013-01-01
We present the first complete derivation of the well-known asymptotic expansion of the SU(2) 6j symbol using a coherent state approach, in particular we succeed in computing the determinant of the Hessian matrix. To do so, we smear the coherent states and perform a partial stationary point analysis with respect to the smearing parameters. This allows us to transform the variables from group elements to dihedral angles of a tetrahedron resulting in an effective action, which coincides with the action of first order Regge calculus associated to a tetrahedron. To perform the remaining stationary point analysis, we compute its Hessian matrix and obtain the correct measure factor. Furthermore, we expand the discussion of the asymptotic formula to next to leading order terms, prove some of their properties and derive a recursion relation for the full 6j symbol.
Resonant state expansion applied to two-dimensional open optical systems
Doost, M B; Muljarov, E A
2013-01-01
The resonant state expansion (RSE), a rigorous perturbative method in electrodynamics, is applied to two-dimensional open optical systems. The analytically solvable homogeneous dielectric cylinder is used as unperturbed system, and its Green's function is shown to contain a cut in the complex frequency plane, which is included in the RSE basis. The complex eigenfrequencies of modes are calculated using the RSE for a selection of perturbations which mix unperturbed modes of different orbital momentum, such as half-cylinder, thin-film and thin-wire perturbation, demonstrating the accuracy and convergency of the method. The resonant states for the thin-wire perturbation are shown to reproduce an approximative analytical solution.
Resonant state expansion applied to three-dimensional open optical systems
Doost, M B; Muljarov, E A
2014-01-01
The resonant state expansion (RSE), a rigorous perturbative method in electrodynamics, is developed for three-dimensional open optical systems. Results are presented using the analytically solvable homogeneous dielectric sphere as unperturbed system. Since any perturbation which breaks the spherical symmetry mixes transverse electric (TE) and transverse magnetic (TM) modes, the RSE is extended here to include TM modes and a zero-frequency pole of the Green's function. We demonstrate the validity of the RSE for TM modes by verifying its convergence towards the exact result for a homogeneous perturbation of the sphere. We then apply the RSE to calculate the modes for a selection of perturbations sequentially reducing the remaining symmetry, given by a change of the dielectric constant of half-sphere and quarter-sphere shape. Since no exact solutions are known for these perturbations, we verify the RSE results by comparing them with the results of state of the art finite element method (FEM) and finite differenc...
Caswell, Kyle J; Waidmann, Timothy; Blumberg, Linda J
2013-08-01
This study is the first to offer a detailed look at the burden of medical out-of-pocket spending, defined as total family medical out-of-pocket spending as a proportion of income, for each state. It further investigates which states have greater shares of individuals with high burden levels and no Medicaid coverage but would be Medicaid eligible under the 2014 rules of the Affordable Care Act should their state choose to participate in the expansion. This work suggests which states have the largest populations likely to benefit, in terms of lowering medical spending burden, from participating in the 2014 adult Medicaid expansions.
Szybisz, L.; Zabolitzky, John G.
We describe a Monte-Carlo algorithm to solve exactly the ground-state problem for a system of up to four nucleons interacting via a scalar neutral meson field. The mesonic degrees of freedom are treated exactly without recourse to the potential approximation.
GAUSSIAN WHITE NOISE CALCULUS OF GENERALIZED EXPANSION
Institute of Scientific and Technical Information of China (English)
陈泽乾
2002-01-01
A new framework of Gaussian white noise calculus is established, in line with generalized expansion in [3, 4, 7]. A suitable frame of Fock expansion is presented on Gaussian generalized expansion functionals being introduced here, which provides the integral kernel operator decomposition of the second quantization of Koopman operators for chaotic dynamical systems, in terms of annihilation operators (e)t and its dual, creation operators (e)*t.
Exclusive Processes in Quantum Chromodynamics and the Light-Cone Fock Representation
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.
2000-12-07
Exclusive processes provide a window into the bound state structure of hadrons in QCD as well as the fundamental processes which control hadron dynamics at the amplitude level. The natural calculus for describing bound state structure of relativistic composite systems needed for describing exclusive amplitudes is the light-cone Fock expansion which encodes the multi-quark, gluonic, and color correlations of a hadron in terms of frame-independent wavefunctions. In hard exclusive processes in which hadrons receive a large momentum transfer, perturbative QCD leads to factorization theorems which separate the physics of bound state structure from that of the relevant quark and gluonic hard-scattering reactions which underlie these reactions. At leading twist, the bound state physics is encoded in terms of universal ''distribution amplitudes,'' the fundamental theoretical quantities which describe the valence quark substructure of hadrons as well as nuclei. The combination of discretized light-cone quantization and transverse lattice methods are now providing nonperturbative predictions for the pion distribution amplitude. A basic feature of the gauge theory formalism is ''color transparency,'' the absence of initial and final state interactions of rapidly-moving compact color-singlet states. Other applications of the factorization formalism are briefly discussed, including semileptonic B decays, deeply virtual Compton scattering, and dynamical higher twist effects in inclusive reactions. A new type of jet production reaction, ''self-resolving diffractive interactions'' provide empirical constraints on the light-cone wavefunctions of hadrons in terms of their quark and gluon degrees of freedom as well as the composition of nuclei in terms of their nucleon and mesonic degrees of freedom.
Photons in Fock space and beyond
Honegger, Reinhard
2015-01-01
The three-volume major reference "Photons in Fock Space and Beyond" undertakes a new mathematical and conceptual foundation of the theory of light emphasizing mesoscopic radiation systems. The quantum optical notions are generalized beyond Fock representations where the richness of an infinite dimensional quantum field system, with its mathematical difficulties and theoretical possibilities, is fully taken into account. It aims at a microscopic formulation of a mesoscopic model class which covers in principle all stages of the generation and propagation of light within a unified and well-defined conceptual frame. The dynamics of the interacting systems is founded — according to original works of the authors — on convergent perturbation series and describes the developments of the quantized microscopic as well as the classical collective degrees of freedom at the same time. The achieved theoretical unification fits especially to laser and microwave applications inheriting objective information over quantu...
Institute of Scientific and Technical Information of China (English)
陈媚; 谢琼涛
2011-01-01
The new method proposed recently by Friedberg, Lee, and Zhao is extended to obtain an analytic expansion for the ground-state wavefunction of a time-dependent strong-coupling Schroedinger equation. Two different types of the time-dependent harmonic oscillators are considered as examples for application of the time-dependent expansion. It is show that the time-dependent strong-coupling expansion is applicable to the time-dependent harmonic oscillators with a slowly varying time-dependent parameter.
Adaptive multi-resolution 3D Hartree-Fock-Bogoliubov solver for nuclear structure
Pei, J. C.; Fann, G. I.; Harrison, R. J.; Nazarewicz, W.; Shi, Yue; Thornton, S.
2014-08-01
Background: Complex many-body systems, such as triaxial and reflection-asymmetric nuclei, weakly bound halo states, cluster configurations, nuclear fragments produced in heavy-ion fusion reactions, cold Fermi gases, and pasta phases in neutron star crust, are all characterized by large sizes and complex topologies in which many geometrical symmetries characteristic of ground-state configurations are broken. A tool of choice to study such complex forms of matter is an adaptive multi-resolution wavelet analysis. This method has generated much excitement since it provides a common framework linking many diversified methodologies across different fields, including signal processing, data compression, harmonic analysis and operator theory, fractals, and quantum field theory. Purpose: To describe complex superfluid many-fermion systems, we introduce an adaptive pseudospectral method for solving self-consistent equations of nuclear density functional theory in three dimensions, without symmetry restrictions. Methods: The numerical method is based on the multi-resolution and computational harmonic analysis techniques with a multi-wavelet basis. The application of state-of-the-art parallel programming techniques include sophisticated object-oriented templates which parse the high-level code into distributed parallel tasks with a multi-thread task queue scheduler for each multi-core node. The internode communications are asynchronous. The algorithm is variational and is capable of solving coupled complex-geometric systems of equations adaptively, with functional and boundary constraints, in a finite spatial domain of very large size, limited by existing parallel computer memory. For smooth functions, user-defined finite precision is guaranteed. Results: The new adaptive multi-resolution Hartree-Fock-Bogoliubov (HFB) solver madness-hfb is benchmarked against a two-dimensional coordinate-space solver hfb-ax that is based on the B-spline technique and a three-dimensional solver
Matrices related to some Fock space operators
Directory of Open Access Journals (Sweden)
Krzysztof Rudol
2011-01-01
Full Text Available Matrices of operators with respect to frames are sometimes more natural and easier to compute than the ones related to bases. The present work investigates such operators on the Segal-Bargmann space, known also as the Fock space. We consider in particular some properties of matrices related to Toeplitz and Hankel operators. The underlying frame is provided by normalised reproducing kernel functions at some lattice points.
Multi-Configuration Dirac–Hartree–Fock (MCDHF Calculations for B-Like Ions
Directory of Open Access Journals (Sweden)
Indu Khatri
2016-05-01
Full Text Available Relativistic configuration interaction results are presented for several B-like ions (Ge XXVIII, Rb XXXIII, Sr XXXIV, Ru XL, Sn XLVI, and Ba LII using the multi-configuration Dirac–Hartree–Fock (MCDHF method. The calculations are carried out in the active space approximation with the inclusion of the Breit interaction, the finite nuclear size effect, and quantum electrodynamic corrections. Results for fine structure energy levels for 1s22s22p and 2s2p2 configurations relative to the ground state are reported. The transition wavelengths, transition probabilities, line strengths, and absorption oscillator strengths for 2s22p–2s2p2 electric dipole (E1 transitions are calculated. Both valence and core-valence correlation effects were accounted for through single-double multireference (SD-MR expansions to increasing sets of active orbitals. Comparisons are made with the available data and good agreement is achieved. The values calculated using core–valence correlation are found to be very close to other theoretical and experimental values. The behavior of oscillator strengths as a function of nuclear charge is studied. We believe that our results can guide experimentalists in identifying the fine-structure levels in their future work.
Validation of the activity expansion method with ultrahigh pressure shock equations of state
Rogers, Forrest J.; Young, David A.
1997-11-01
Laser shock experiments have recently been used to measure the equation of state (EOS) of matter in the ultrahigh pressure region between condensed matter and a weakly coupled plasma. Some ultrahigh pressure data from nuclear-generated shocks are also available. Matter at these conditions has proven very difficult to treat theoretically. The many-body activity expansion method (ACTEX) has been used for some time to calculate EOS and opacity data in this region, for use in modeling inertial confinement fusion and stellar interior plasmas. In the present work, we carry out a detailed comparison with the available experimental data in order to validate the method. The agreement is good, showing that ACTEX adequately describes strongly shocked matter.
Validation of the activity expansion method with ultrahigh pressure shock equations of state
Energy Technology Data Exchange (ETDEWEB)
Rogers, F.J.; Young, D.A. [Physics Department, Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, California 94550 (United States)
1997-11-01
Laser shock experiments have recently been used to measure the equation of state (EOS) of matter in the ultrahigh pressure region between condensed matter and a weakly coupled plasma. Some ultrahigh pressure data from nuclear-generated shocks are also available. Matter at these conditions has proven very difficult to treat theoretically. The many-body activity expansion method (ACTEX) has been used for some time to calculate EOS and opacity data in this region, for use in modeling inertial confinement fusion and stellar interior plasmas. In the present work, we carry out a detailed comparison with the available experimental data in order to validate the method. The agreement is good, showing that ACTEX adequately describes strongly shocked matter. {copyright} {ital 1997} {ital The American Physical Society}
Approximate semi-analytical solutions for the steady-state expansion of a contactor plasma
Camporeale, E; MacDonald, E A
2015-01-01
We study the steady-state expansion of a collisionless, electrostatic, quasi-neutral plasma plume into vacuum, with a fluid model. We analyze approximate semi-analytical solutions, that can be used in lieu of much more expensive numerical solutions. In particular, we focus on the earlier studies presented in Parks and Katz (1979), Korsun and Tverdokhlebova (1997), and Ashkenazy and Fruchtman (2001). By calculating the error with respect to the numerical solution, we can judge the range of validity for each solution. Moreover, we introduce a generalization of earlier models that has a wider range of applicability, in terms of plasma injection profiles. We conclude by showing a straightforward way to extend the discussed solutions to the case of a plasma plume injected with non-null azimuthal velocity.
Resonant-state expansion for wave guides with a Sellmeier dispersion
Doost, M B
2015-01-01
The resonant-state expansion (RSE), a rigorous perturbative method developed in electrodynamics for non-dispersive optical systems is further developed to treat wave guides with a Sellmeier dispersion. For media which can be described by these types of dispersion over the relevant frequency range, such as optical glass, the perturbed problem can be solved by diagonalising a second-order eigenvalue problem. In the case of a single resonance at zero frequency, this is simplified to a generalised eigenvalue problem. Results are presented using analytically solvable planar waveguides and parameters of BK7 glass, for a perturbation in the waveguide width. The efficiency of using either an exact dispersion over all frequencies or an approximate dispersion over a narrow frequency range is compared.
Resonant-state-expansion Born approximation with a correct eigen-mode normalisation
Doost, M. B.
2016-08-01
The Born approximation (Born 1926 Z. Phys. 38 802) is a fundamental result in physics, it allows the calculation of weak scattering via the Fourier transform of the scattering potential. As was done by previous authors (Ge et al 2014 New J. Phys. 16 113048) the Born approximation is extended by including in the formula the resonant-states (RSs) of the scatterer. However in this study unlike previous studies the included eigen-modes are correctly normalised with dramatic positive consequences for the accuracy of the method. The normalisation of RSs used in the previous RS expansion Born approximation or resonant-state expansion (RSE) Born approximation made in Ge et al (2014 New J. Phys. 16 113048) has been shown to be numerically unstable in Muljarov et al (2014 arXiv:1409.6877) and by analytics here. The RSs of the system can be calculated using my recently discovered RSE perturbation theory for dispersive electrodynamic scatterers (Muljarov et al 2010 Europhys. Lett. 92 50010; Doost et al 2012 Phys. Rev. A 85 023835; Doost et al 2013 Phys. Rev. A 87 043827; Armitage et al 2014 Phys. Rev. A 89; Doost et al 2014 Phys. Rev. A 90 013834) and normalised correctly to appear in spectral Green's functions and hence the RSE Born approximation via the flux-volume normalisation which I recently rigorously derived in Armitage et al (2014 Phys. Rev. A 89), Doost et al (2014 Phys. Rev. A 90 013834), Doost (2016 Phys. Rev. A 93 023835). In the case of effectively one-dimensional systems I find a RSE Born approximation alternative to the scattering matrix method.
Tischer, Alexander; Auton, Matthew
2013-09-01
We have analyzed the thermodynamic properties of the von Willebrand factor (VWF) A3 domain using urea-induced unfolding at variable temperature and thermal unfolding at variable urea concentrations to generate a phase diagram that quantitatively describes the equilibrium between native and denatured states. From this analysis, we were able to determine consistent thermodynamic parameters with various spectroscopic and calorimetric methods that define the urea-temperature parameter plane from cold denaturation to heat denaturation. Urea and thermal denaturation are experimentally reversible and independent of the thermal scan rate indicating that all transitions are at equilibrium and the van't Hoff and calorimetric enthalpies obtained from analysis of individual thermal transitions are equivalent demonstrating two-state character. Global analysis of the urea-temperature phase diagram results in a significantly higher enthalpy of unfolding than obtained from analysis of individual thermal transitions and significant cross correlations describing the urea dependence of ΔH0 and ΔCP0 that define a complex temperature dependence of the m-value. Circular dichroism (CD) spectroscopy illustrates a large increase in secondary structure content of the urea-denatured state as temperature increases and a loss of secondary structure in the thermally denatured state upon addition of urea. These structural changes in the denatured ensemble make up ∼40% of the total ellipticity change indicating a highly compact thermally denatured state. The difference between the thermodynamic parameters obtained from phase diagram analysis and those obtained from analysis of individual thermal transitions illustrates that phase diagrams capture both contributions to unfolding and denatured state expansion and by comparison are able to decipher these contributions.
Relativistic Dirac-Fock atom properties for Z = 121 to Z = 138
Zhou, Z.; Kas, J. J.; Rehr, J. J.; Ermler, W. C.
2017-03-01
We present relativistic Dirac-Fock calculations of atomic properties for atomic numbers Z = 121- 138, extending a previous tabulation of Desclaux. The calculations assume a single LS ground state configuration and include a correction for finite nuclear size, with an approximation for the mean nuclear mass A(Z) based on the liquid-drop model.
Perturbative calculation of the Sternheimer anti-shielding factor with Hartree-Fock atomic orbitals
2012-01-01
We report a calculation of the Sternheimer anti-shielding factor, \\gamma, by means of first order perturbation theory. In quality of basis functions, we use Hartree-Fock electronic orbitals, expanded on hydrogenic atomic states. The computed \\gamma(r) for Fe^{3+} and Cu^{1+} inner electronic cores are reported and compared with literature values, obtained from alternative methodologies.
Boblest, S.; Meyer, D.; Wunner, G.
2014-11-01
calculations. The guiding functions are created from single-electron orbitals ψi which are either products of a wave function in the z-direction (the direction of the magnetic field) and an expansion of the wave function perpendicular to the direction of the magnetic field in terms of Landau states, ψi(ρ,φ,z)=Pi(z)∑n=0NLtinϕni(ρ,φ), or a full two-dimensional expansion using separate z-wave functions for each Landau level, i.e. ψi(ρ,φ,z)=∑n=0NLPni(z)ϕni(ρ,φ). In the first form, the tin are expansion coefficients, and the expansion is cut off at some maximum Landau level quantum number NL. In the second form, the expansion coefficients are contained in the respective Pni. Restrictions: The method itself is very flexible and not restricted to a certain interval of magnetic field strengths. However, it is only variational for the lowest-lying state in each symmetry subspace and the accompanying Hartree-Fock method can only obtain guiding functions in the regime of strong magnetic fields. Unusual features: The program needs approximate wave functions computed with another method as input. Running time: 1 min-several days. The example provided takes approximately 50 min to run on 1 processor.
Mori, Takashi
2015-02-01
The Floquet eigenvalue problem is analyzed for periodically driven Friedrichs models on discrete and continuous space. In the high-frequency regime, there exists a Floquet bound state consistent with the Floquet-Magnus expansion in the discrete Friedrichs model, while it is not the case in the continuous model. In the latter case, however, the bound state predicted by the Floquet-Magnus expansion appears as a metastable state whose lifetime diverges in the limit of large frequencies. We obtain the lifetime by evaluating the imaginary part of the quasienergy of the Floquet resonant state. In the low-frequency regime, there is no Floquet bound state and instead the Floquet resonant state with exponentially small imaginary part of the quasienergy appears, which is understood as the quantum tunneling in the energy space.
Resonant-state expansion applied to three-dimensional open optical systems
Doost, M. Â. B.; Langbein, W.; Muljarov, E. Â. A.
2014-07-01
The resonant-state expansion (RSE), a rigorous perturbative method in electrodynamics, is developed for three-dimensional open optical systems. Results are presented using the analytically solvable homogeneous dielectric sphere as unperturbed system. Since any perturbation which breaks the spherical symmetry mixes transverse electric (TE) and transverse magnetic (TM) modes, the RSE is extended here to include TM modes and a zero-frequency pole of the Green's function. We demonstrate the validity of the RSE for TM modes by verifying its convergence towards the exact result for a homogeneous perturbation of the sphere. We then apply the RSE to calculate the modes for a selection of perturbations sequentially reducing the remaining symmetry, given by a change of the dielectric constant of half-sphere and quarter-sphere shape. Since no exact solutions are known for these perturbations, we verify the RSE results by comparing them with the results of state of the art finite element method (FEM) and finite difference in time domain (FDTD) solvers. We find that for the selected perturbations, the RSE provides a significantly higher accuracy than the FEM and FDTD for a given computational effort, demonstrating its potential to supersede presently used methods. We furthermore show that in contrast to presently used methods, the RSE is able to determine the perturbation of a selected group of modes by using a limited basis local to these modes, which can further reduce the computational effort by orders of magnitude.
Misfits in Skyrme-Hartree-Fock
Erler, J; Reinhard, P -G
2010-01-01
We address very briefly five critical points in the context of the Skyrme-Hartree-Fock (SHF) scheme: 1) the impossibility to consider it as an interaction, 2) a possible inconsistency of correlation corrections as, e.g., the center-of-mass correction, 3) problems to describe the giant dipole resonance (GDR) simultaneously in light and heavy nuclei, 4) deficiencies in the extrapolation of binding energies to super-heavy elements (SHE), and 5) a yet inappropriate trend in fission life-times when going to the heaviest SHE. While the first two points have more a formal bias, the other three points have practical implications and wait for solution.
Semi-infinite $q$-wedge construction of the level 2 Fock Space of $U_q(\\widehat{sl}_2)$
Petersen, J U H
1997-01-01
In this proceedings a particular example from \\cite{KMPY} (q-alg/9603025) is presented: the construction of the level 2 Fock space of $\\U_q(\\affsl{2})$. The generating ideal of the wedge relations is given and the wedge space defined. Normal ordering of wedges is defined in terms of the energy function. Normally ordered wedges form a base of the wedge space. The q-deformed Fock space is defined as the space of semi-infinite wedges with a finite number of vectors in the wedge product differing from a ground state sequence, and endowed with a separated q-adic topology . Normally ordered wedges form a base of the Fock space. The action of $\\U_q(\\affsl{2})$ on the Fock space converges in the q-adic topology. On the Fock space the action of bosons, which commute with the $\\U_q(\\affsl{2})$-action, also converges in the q-adic topology. Hence follows the decomposition of the Fock space into irreducible $\\U_q(\\affsl{2})$-modules.
Saddlepoint expansions for sums of Markov dependent variables on a continuous state space
DEFF Research Database (Denmark)
Jensen, J.L.
1991-01-01
here very similar to the classical results for i.i.d. variables. In particular we establish also conditions under which the expansions hold uniformly over the range of the saddlepoint. Expansions are also derived for sums of the form f(X1, X0)+f(X2, X1)+...+f(Xn, Xn-1) although the uniformity result...
Polymer and Fock representations for a Scalar field
Ashtekar, Abhay; Sahlmann, H; Ashtekar, Abhay; Lewandowski, Jerzy; Sahlmann, Hanno
2003-01-01
In loop quantum gravity, matter fields can have support only on the `polymer-like' excitations of quantum geometry, and their algebras of observables and Hilbert spaces of states can not refer to a classical, background geometry. Therefore, to adequately handle the matter sector, one has to address two issues already at the kinematic level. First, one has to construct the appropriate background independent operator algebras and Hilbert spaces. Second, to make contact with low energy physics, one has to relate this `polymer description' of matter fields to the standard Fock description in Minkowski space. While this task has been completed for gauge fields, important gaps remained in the treatment of scalar fields. The purpose of this letter is to fill these gaps.
Semiempirical Hartree-Fock calculations for $KNbO_{3}$
Eglitis, R I; Borstel, G
1996-01-01
In applying the semiempirical intermediate neglect of differential overlap (INDO) method based on the Hartree-Fock formalism to a cubic perovskite-based ferroelectric material KNbO3, it was demonstrated that the accuracy of the method is sufficient for adequately describing the small energy differences related to the ferroelectric instability. The choice of INDO parameters has been done for a system containing Nb. Based on the parametrization proposed, the electronic structure, equilibrium ground state structure of the orthorhombic and rhombohedral phases, and Gamma-TO phonon frequencies in cubic and rhombohedral phases of KNbO3 were calculated and found to be in good agreement with the experimental data and with the first-principles calculations available.
Using Hartree-Fock pseudopotentials in GW calculations
Hamann, D. R.; Vanderbilt, David
2010-03-01
The issue of including shallow ``semi-core'' states as valence has recently resurfaced in the context of self-consistent GW calculations.footnotetextF. Bruneval et al., Phys. Rev. Lett. 97, 267601 (2006). Supposing that semi-core-valence exchange is the dominant process necessitating the inclusion of semi-cores, we have investigated whether the use Hartree-Fock pseudopotentialsfootnotetextW. A. Al-Saidi, E. J. Walter, and A. M. Rappe, Phys. Rev. B 77, 075122 (2008). instead of density-functional psp's might obviate the need for semi-cores. The answers to this question appear to be ``yes'' for the case of CuCl (filled d shell), and ``semi-cores don't matter anyway'' for ScN (empty d shell). Opportunity permitting, additional examples will be discussed.
Correlated Electron Calculations with Hartree-Fock Scaling
Gebauer, Ralph; Car, Roberto
2013-01-01
We introduce an energy functional for ground-state electronic structure calculations with fundamental variables the natural spin orbitals and their joint occupation probabilities in an implied many-body trial wave function. We use a controlled approximation for the two-particle density matrix that greatly extends the accuracy compared to current functionals of the one-particle density matrix only. Algebraic scaling of computational cost with electron number is achieved in general, and Hartree-Fock scaling in the seniority-zero version of the theory. We present results obtained with the latter version for saturated small molecular systems for which highly accurate quantum chemical computations are available for comparison. The results are variational, capturing most of the correlation energy from equilibrium to dissociation.
Hwang, Chyi; Guo, Tong-Yi; Shieh, Leang-San
1991-01-01
A canonical state-space realization based on the multipoint Jordan continued-fraction expansion (CFE) is presented for single-input-single-output (SISO) systems. The similarity transformation matrix which relates the new canonical form to the phase-variable canonical form is also derived. The presented canonical state-space representation is particularly attractive for the application of SISO system theory in which a reduced-dimensional time-domain model is necessary.
Robust Periodic Hartree-Fock Exchange for Large-Scale Simulations Using Gaussian Basis Sets.
Guidon, Manuel; Hutter, Jürg; VandeVondele, Joost
2009-11-10
Hartree-Fock exchange with a truncated Coulomb operator has recently been discussed in the context of periodic plane-waves calculations [Spencer, J.; Alavi, A. Phys. Rev. B: Solid State, 2008, 77, 193110]. In this work, this approach is extended to Gaussian basis sets, leading to a stable and accurate procedure for evaluating Hartree-Fock exchange at the Γ-point. Furthermore, it has been found that standard hybrid functionals can be transformed into short-range functionals without loss of accuracy. The well-defined short-range nature of the truncated exchange operator can naturally be exploited in integral screening procedures and makes this approach interesting for both condensed phase and gas phase systems. The presented Hartree-Fock implementation is massively parallel and scales up to ten thousands of cores. This makes it feasible to perform highly accurate calculations on systems containing thousands of atoms or ten thousands of basis functions. The applicability of this scheme is demonstrated by calculating the cohesive energy of a LiH crystal close to the Hartree-Fock basis set limit and by performing an electronic structure calculation of a complete protein (rubredoxin) in solution with a large and flexible basis set.
Knuth, Eldon L.; Miller, David R.; Even, Uzi
2014-12-01
Data extracted from time-of-flight (TOF) measurements made on steady-state He free jets at Göttingen already in 1986 and for pulsed Ne free jets investigated recently at Tel Aviv have been added to an earlier plot of terminal condensed-phase mass fraction x2∞ as a function of the dimensionless scaling parameter Γ. Γ characterizes the source (fluid species, temperature, pressure and throat diameter); values of x2∞ are extracted from TOF measurements using conservation of energy in the free-jet expansion. For nozzles consisting of an orifice in a thin plate; the extracted data yield 22 data points which are correlated satisfactorily by a single curve. The Ne free jets were expanded from a conical nozzle with a 20° half angle; the three extracted data points stand together but apart from the aforementioned curve, indicating that the presence of the conical wall influences significantly the expansion and hence the condensation. The 22 data points for the expansions via an orifice consist of 15 measurements with expansions from the gas-phase side of the binodal curve which crossed the binodal curve downstream from the sonic point and 7 measurements with expansions of the gas-phase product of the flashing which occurred after an expansion from the liquid-phase side of the binodal curve crossed the binodal curve upstream from the sonic point. The association of these 22 points with a single curve supports the alternating-phase model for flows with flashing upstream from the sonic point proposed earlier. In order to assess the role of the spinodal curve in such expansions, the spinodal curves for He and Ne were computed using general multi-parameter Helmholtz-free-energy equation-of-state formulations. Then, for the several sets of source-chamber conditions used in the free-jet measurements, thermodynamic states at key locations in the free-jet expansions (binodal curve, sonic point and spinodal curve) were evaluated, with the expansion presumed to be metastable
Energy Technology Data Exchange (ETDEWEB)
Knuth, Eldon L. [Chemical and Biomolecular Engineering Department, University of California at Los Angeles, CA 90095 (United States); Miller, David R. [Department of Mechanical and Aerospace Engineering, University of California at San Diego, La Jolla, CA 92093 (United States); Even, Uzi [Sackler Faculty of Exact Sciences, School of Chemistry, Tel Aviv University, Ramat Aviv, 69978 Tel Aviv (Israel)
2014-12-09
Data extracted from time-of-flight (TOF) measurements made on steady-state He free jets at Göttingen already in 1986 and for pulsed Ne free jets investigated recently at Tel Aviv have been added to an earlier plot of terminal condensed-phase mass fraction x{sub 2∞} as a function of the dimensionless scaling parameter Γ. Γ characterizes the source (fluid species, temperature, pressure and throat diameter); values of x{sub 2∞} are extracted from TOF measurements using conservation of energy in the free-jet expansion. For nozzles consisting of an orifice in a thin plate; the extracted data yield 22 data points which are correlated satisfactorily by a single curve. The Ne free jets were expanded from a conical nozzle with a 20° half angle; the three extracted data points stand together but apart from the aforementioned curve, indicating that the presence of the conical wall influences significantly the expansion and hence the condensation. The 22 data points for the expansions via an orifice consist of 15 measurements with expansions from the gas-phase side of the binodal curve which crossed the binodal curve downstream from the sonic point and 7 measurements with expansions of the gas-phase product of the flashing which occurred after an expansion from the liquid-phase side of the binodal curve crossed the binodal curve upstream from the sonic point. The association of these 22 points with a single curve supports the alternating-phase model for flows with flashing upstream from the sonic point proposed earlier. In order to assess the role of the spinodal curve in such expansions, the spinodal curves for He and Ne were computed using general multi-parameter Helmholtz-free-energy equation-of-state formulations. Then, for the several sets of source-chamber conditions used in the free-jet measurements, thermodynamic states at key locations in the free-jet expansions (binodal curve, sonic point and spinodal curve) were evaluated, with the expansion presumed to be
The Dielectric Permittivity of Crystals in the reduced Hartree-Fock approximation
Cancès, Eric
2009-01-01
In a recent article (Canc\\`es, Deleurence and Lewin, Commun. Math. Phys., 281 (2008), pp. 129-177), we have rigorously derived, by means of bulk limit arguments, a new variational model to describe the electronic ground state of insulating or semiconducting crystals in the presence of local defects. In this so-called reduced Hartree-Fock model, the ground state electronic density matrix is decomposed as $\\gamma = \\gamma^0_{\\rm per} + Q_{\
Goldblatt, Colin
2015-05-01
There are four different stable climate states for pure water atmospheres, as might exist on so-called "waterworlds." I map these as a function of solar constant for planets ranging in size from Mars-sized to 10 Earth-mass. The states are as follows: globally ice covered (Ts ⪅ 245 K), cold and damp (270 ⪅ Ts ⪅ 290 K), hot and moist (350 ⪅ Ts ⪅ 550 K), and very hot and dry (Tsx2A86;900 K). No stable climate exists for 290 ⪅ T s ⪅ 350 K or 550 ⪅ Ts ⪅ 900 K. The union of hot moist and cold damp climates describes the liquid water habitable zone, the width and location of which depends on planet mass. At each solar constant, two or three different climate states are stable. This is a consequence of strong nonlinearities in both thermal emission and the net absorption of sunlight. Across the range of planet sizes, I account for the atmospheres expanding to high altitudes as they warm. The emitting and absorbing surfaces (optical depth of unity) move to high altitude, making their area larger than the planet surface, so more thermal radiation is emitted and more sunlight absorbed (the former dominates). The atmospheres of small planets expand more due to weaker gravity; the effective runaway greenhouse threshold is about 35 W m(-2) higher for Mars, 10 W m(-2) higher for Earth or Venus, but only a few W m(-2) higher for a 10 Earth-mass planet. There is an underlying (expansion-neglected) trend of increasing runaway greenhouse threshold with planetary size (40 W m(-2) higher for a 10 Earth-mass planet than for Mars). Summing these opposing trends means that Venus-sized (or slightly smaller) planets are most susceptible to a runaway greenhouse. The habitable zone for pure water atmospheres is very narrow, with an insolation range of 0.07 times the solar constant. A wider habitable zone requires background gas and greenhouse gas: N2 and CO2 on Earth, which are biologically controlled. Thus, habitability depends on inhabitance.
Fission dynamics within time-dependent Hartree-Fock: boost-induced fission
Goddard, P M; Rios, A
2015-01-01
Background: Nuclear fission is a complex large-amplitude collective decay mode in heavy nuclei. Microscopic density functional studies of fission have previously concentrated on adiabatic approaches based on constrained static calculations ignoring dynamical excitations of the fissioning nucleus, and the daughter products. Purpose: To explore the ability of dynamic mean-field methods to describe induced fission processes, using quadrupole boosts in the nuclide $^{240}$Pu as an example. Methods: Quadrupole constrained Hartree-Fock calculations are used to create a potential energy surface. An isomeric state and a state beyond the second barrier peak are excited by means of instantaneous as well as temporally extended gauge boosts with quadrupole shapes. The subsequent deexcitation is studied in a time-dependent Hartree-Fock simulation, with emphasis on fissioned final states. The corresponding fission fragment mass numbers are studied. Results: In general, the energy deposited by the quadrupole boost is quickl...
The classical limit of the time dependent Hartree-Fock equation. I. The Weyl symbol of the solution
Amour, Laurent; Nourrigat, Jean
2011-01-01
We study the time evolution of the Weyl symbol of a solution of the time dependent Hartree Fock equation, assuming that for t=0, it has a Weyl symbol which is integrable in the phase space, such as all its derivatives. We prove that the solution has the same property for all t, and we give an asymptotic expansion, in L1 sense, of this Weyl symbol.
Pseudonegative thermal expansion and the state of water in graphene oxide layered assemblies.
Zhu, Jian; Andres, Christine M; Xu, Jiadi; Ramamoorthy, Ayyalusamy; Tsotsis, Thomas; Kotov, Nicholas A
2012-09-25
Unraveling the complex interplay between thermal properties and hydration is a part of understanding the fundamental properties of many soft materials and very essential for many applications. Here we show that graphene oxide (GO) demonstrates a highly negative thermal expansion (NTE) coefficient owing to unique thermohydration processes related with fast transport of water between the GO sheets, the amphiphilic nature of nanochannels, and close-to-zero intrinsic thermal expansion of GO. The humidity-dependent NTE of GO layered assemblies, or "pseudonegative thermal expansion" (PNTE), differs from that of other hygroscopic materials due to its relatively fast and highly reversible expansion/contraction cycles and occurrence at low humidity levels while bearing similarities to classic NTE. Thermal expansion of polyvinyl alcohol/GO composites is easily tunable with additional intricacy of thermohydration effects. PNTE combined with isotropy, nontoxicity, and mechanical robustness is an asset for applications of actuators, sensors, MEMS devices, and memory materials and crucial for developing methods of thermal/photopatterning of GO devices.
Fock-space localization of polaritons in the Jaynes-Cummings dimer model
Shapourian, Hassan; Sadri, Darius
2016-01-01
We present a method to study the semiclassical dynamics of the Jaynes-Cummings dimer model, describing two coupled cavities, each containing a two-level system (qubit). We develop a Fock-space WKB approach in the polariton basis where each site is treated exactly while the intersite polariton hopping is treated semiclassically. We show that the self-trapped states can be viewed as Fock-space localized states. We find that this picture yields the correct critical value of interaction strength at which the delocalization-localization transition occurs. Moreover, the validity of our WKB approach is supported by showing that the quantum spectrum can be derived from a set of Bohr-Sommerfeld quantization conditions and by confirming that the quantum eigenstates are consistent with the classical orbital motion in the polariton band picture. The underlying idea of our method is quite general and can be applied to other interacting spin-boson models.
Pairing phase transition: A Finite-Temperature Relativistic Hartree-Fock-Bogoliubov study
Li, Jia Jie; Long, Wen Hui; Van Giai, Nguyen
2015-01-01
Background: The relativistic Hartree-Fock-Bogoliubov (RHFB) theory has recently been developed and it provides a unified and highly predictive description of both nuclear mean field and pairing correlations. Ground state properties of finite nuclei can accurately be reproduced without neglecting exchange (Fock) contributions. Purpose: Finite-temperature RHFB (FT-RHFB) theory has not yet been developed, leaving yet unknown its predictions for phase transitions and thermal excitations in both stable and weakly bound nuclei. Method: FT-RHFB equations are solved in a Dirac Woods-Saxon (DWS) basis considering two kinds of pairing interactions: finite or zero range. Such a model is appropriate for describing stable as well as loosely bound nuclei since the basis states have correct asymptotic behaviour for large spatial distributions. Results: Systematic FT-RH(F)B calculations are performed for several semi-magic isotopic/isotonic chains comparing the predictions of a large number of Lagrangians, among which are PK...
El-Ganainy, Ramy; Christodoulides, Demetrios N
2013-01-01
We investigate the dynamics of nonclassical states of light in coupled optical structures and we demonstrate a number of intriguing features associated with such arrangements. By diagonalizing the system's Hamiltonian, we show that these geometries can support eigenstates having anomalous optical intensity distribution with no classical counterpart. These features may provide new avenues towards manipulating light flow at the quantum level. By projecting the Hamiltonian operator on Hilbert subspaces spanning different numbers of photon excitations, we demonstrate that processes such as coherent transport, state localization and surface Bloch oscillations can take place in Fock space. Furthermore, we show that Hamiltonian representations of Fock space manifolds differing by one photon obey a discrete supersymmetry relation
Partial-wave Coulomb transition matrices for attractive interaction by Fock's method
Kharchenko, V F
2016-01-01
Leaning upon the Fock method of the stereographic projection of the three-dimensional momentum space onto the four-dimensional unit sphere the possibility of the analytical solving of the Lippmann-Schwinger integral equation for the partial wave two-body Coulomb transition matrix at the ground bound state energy has been studied. In this case new expressions for the partial p-, d- and f-wave two-body Coulomb transition matrices have been obtained in the simple analytical form. The developed approach can also be extended to determine analytically the partial wave Coulomb transition matrices at the energies of excited bound states. Keywords: Partial wave Coulomb transition matrix; Lippmann-Schwinger equation; Fock method; Analytical solution PACS Nos. 03.65.-w; 03.65.Nk; 34.20.Cf
On the Fock representation of the q-commutation relations
Dykema, K J; Dykema, Ken; Nica, Alexandru
1993-01-01
The q-commutation relations in the title are those that have recently received much attention, and that for -1Fock space of Bozejko-Speicher, and we find a canonical unitary U_q from the twisted Fock space to usual full Fock space, such that U_q R^q (U_q)^* contains the Cuntz algebra R^0, and such that we have equality for |q|<0.44.
Diffusion, Absorbing States, and Nonequilibrium Phase Transitions in Range Expansions and Evolution
Lavrentovich, Maxim Olegovich
The spatial organization of a population plays a key role in its evolutionary dynamics and growth. In this thesis, we study the dynamics of range expansions, in which populations expand into new territory. Focussing on microbes, we first consider how nutrients diffuse and are absorbed in a population, allowing it to grow. These nutrients may be absorbed before reaching the population interior, and this "nutrient shielding'' can confine the growth to a thin region on the population periphery. A thin population front implies a small local effective population size and enhanced number fluctuations (or genetic drift). We then study evolutionary dynamics under these growth conditions. In particular, we calculate the survival probability of mutations with a selective advantage occurring at the population front for two-dimensional expansions (e.g., along the surface of an agar plate), and three-dimensional expansions (e.g., an avascular tumor). We also consider the effects of irreversible, deleterious mutations which can lead to the loss of the advantageous mutation in the population via a "mutational meltdown,'' or non-equilibrium phase transition. We examine the effects of an inflating population frontier on the phase transition. Finally, we discuss how spatial dimension and frontier roughness influence range expansions of mutualistic, cross-feeding variants. We find here universal features of the phase diagram describing the onset of a mutualistic phase in which the variants remain mixed at long times.
Hartree-Fock and Random Phase Approximation theories in a many-fermion solvable model
Co', Giampaolo
2016-01-01
We present an ideal system of interacting fermions where the solutions of the many-body Schroedinger equation can be obtained without making approximations. These exact solutions are used to test the validity of two many-body effective approaches, the Hartree-Fock and the Random Phase Approximation theories. The description of the ground state done by the effective theories improves with increasing number of particles.
Higher-order Schrödinger and Hartree–Fock equations
Energy Technology Data Exchange (ETDEWEB)
Carles, Rémi, E-mail: Remi.Carles@math.cnrs.fr [IMAG, UMR5149, CNRS and University Montpellier, CC051, 34095 Montpellier (France); Lucha, Wolfgang, E-mail: Wolfgang.Lucha@oeaw.ac.at [Institute for High Energy Physics, Austrian Academy of Sciences, Nikolsdorfergasse 18, A-1050 Vienna (Austria); Moulay, Emmanuel, E-mail: emmanuel.moulay@univ-poitiers.fr [XLIM (UMR-CNRS 7252), University Poitiers, 11 Blvd. Marie et Pierre Curie, BP 30179, 86962 Futuroscope Chasseneuil Cedex (France)
2015-12-15
The domain of validity of the higher-order Schrödinger equations is analyzed for harmonic-oscillator and Coulomb potentials as typical examples. Then, the Cauchy theory for higher-order Hartree–Fock equations with bounded and Coulomb potentials is developed. Finally, the existence of associated ground states for the odd-order equations is proved. This renders these quantum equations relevant for physics.
Rosenbaum, Sara; Westmoreland, Timothy M
2012-08-01
In National Federation of Independent Business v. Sebelius, the US Supreme Court upheld the constitutionality of the requirement that all Americans have affordable health insurance coverage. But in an unprecedented move, seven justices first declared the mandatory Medicaid eligibility expansion unconstitutional. Then five justices, led by Chief Justice John Roberts, prevented the outright elimination of the expansion by fashioning a remedy that simply limited the federal government's enforcement powers over its provisions and allowed states not to proceed with expanding Medicaid without losing all of their federal Medicaid funding. The Court's approach raises two fundamental issues: First, does the Court's holding also affect the existing Medicaid program or numerous other Affordable Care Act Medicaid amendments establishing minimum Medicaid program requirements? And second, does the health and human services secretary have the flexibility to modify the pace or scope of the expansion as a negotiating strategy with the states? The answers to these questions are key because of the foundational role played by Medicaid in health reform.
Koopmans' theorem in statistical Hartree-Fock theory
Pain, Jean-Christophe
2011-01-01
In this short paper, the validity of Koopmans' theorem in the Hartree-Fock theory at non-zero temperature (Hartree-Fock statistical theory) is investigated. It is shown that Koopmans' theorem does not apply in the grand-canonical ensemble, due to a missing contribution to the energy proportional to the interaction between two electrons belonging to the same orbital. Hartree-Fock statistical theory has also been applied in the canonical ensemble [Blenski et al., Phys. Rev. E 55, R4889 (1997)] for the purpose of photo-absorption calculations. In that case, the Hartree-Fock self-consistent-field equations are derived in the super-configuration approximation. It is shown that Koopmans' theorem does not hold in the canonical ensemble, but that a restricted version of the theorem can be obtained, by assuming that a particular quantity multiplying the interaction matrix element in the expression of the energy does not change during the removal of an electron.
A Hartree-Fock-Bogoliubov mass formula
Samyn, M; Heenen, P H; Pearson, J M; Tondeur, F
2002-01-01
In order to have more reliable predictions of nuclear masses at the neutron drip line, we here go beyond the recent mass formula HFBCS-1 and present a new mass formula, HFB-1, based on the Hartree-Fock-Bogoliubov method. As with the HFBCS-1 mass formula, we use a 10-parameter Skyrme force along with a 4-parameter delta-function pairing force and a 2-parameter phenomenological Wigner term. However, with the original HFBCS-1 Skyrme force (MSk7), the rms error becomes unacceptably large and a new force fit is required. With the isoscalar and isovector effective masses constrained to be equal, the remaining 15 degrees of freedom are fitted to the masses of all the 1754 measured nuclei with A>=16, |N-Z|>2 given in the 1995 Audi-Wapstra compilation. The rms error with respect to the masses of all the 1888 measured nuclei with Z,N>=8 is 0.764 MeV. A complete mass table, HFB-1 (available on the Web), has been constructed, giving all nuclei lying between the two drip lines over the range Z,N>=8 and Z<=120. A compar...
Hida, Kazuo
1992-03-01
The quantum disordered state (QDOS) of the spin 1/2 double layer square lattice Heisenberg antiferromagnet is studied. Using the dimer expansion from the limit of the large interlayer coupling J', the staggered susceptibility χ, the antiferromagnetic structure factor Sπ and the antiferromagnetic correlation length ξ are calculated up to the 6-th order in the intralayer coupling J. The ratio analysis shows that the QDOS becomes unstable against the Néel ordering at J'/J≃2.56. The critical exponents are not inconsistent with the universality class of the 3-dimensional classical Heisenberg model, suggesting that our QDOS corresponds to that expected in the 2-dimensional square lattice Heisenberg antiferromagnet with unphysically small spin (<0.276). The results of the projector Monte Carlo simulation also confirms the dimer expansion results.
Self-Adjointness Criterion for Operators in Fock Spaces
Energy Technology Data Exchange (ETDEWEB)
Falconi, Marco, E-mail: marco.falconi@univ-rennes1.fr [Université de Rennes I, IRMAR and Centre Henri Lebesgue (France)
2015-12-15
In this paper we provide a criterion of essential self-adjointness for operators in the tensor product of a separable Hilbert space and a Fock space. The class of operators we consider may contain a self-adjoint part, a part that preserves the number of Fock space particles and a non-diagonal part that is at most quadratic with respect to the creation and annihilation operators. The hypotheses of the criterion are satisfied in several interesting applications.
Brueckner-Hartree-Fock and its renormalized calculations for finite nuclei
Hu, B S; Ma, Y Z; Wu, Q; Sun, Z H
2016-01-01
We have performed self-consistent Brueckner-Hartree-Fock (BHF) and its renormalized theory to the structure calculations of finite nuclei. The $G$-matrix is calculated within the BHF basis, and the exact Pauli exclusion operator is determined by the BHF spectrum. Self-consistent occupation probabilities are included in the renormalized Brueckner-Hartree-Fock (RBHF). Various systematics and convergences are studies. Good results are obtained for the ground-state energy and radius. RBHF can give a more reasonable single-particle spectrum and radius. We present a first benchmark calculation with other {\\it ab initio} methods using the same effective Hamiltonian. We find that the BHF and RBHF results are in good agreement with other $\\it{ab}$ $\\it{initio}$ methods.
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.
Uniqueness of the Fock quantization of scalar fields in a Bianchi I cosmology with unitary dynamics
Cortez, Jerónimo; Martín-Benito, Mercedes; Marugán, Guillermo A Mena; Olmedo, Javier; Velhinho, José M
2016-01-01
The Fock quantization of free scalar fields is subject to an infinite ambiguity when it comes to choosing a set of annihilation and creation operators, choice that is equivalent to the determination of a vacuum state. In highly symmetric situations, this ambiguity can be removed by asking vacuum invariance under the symmetries of the system. Similarly, in stationary backgrounds, one can demand time-translation invariance plus positivity of the energy. However, in more general situations, additional criteria are needed. For the case of free (test) fields minimally coupled to a homogeneous and isotropic cosmology, it has been proven that the ambiguity is resolved by introducing the criterion of unitary implementability of the quantum dynamics, as an endomorphism in Fock space. This condition determines a specific separation of the time dependence of the field, so that this splits into a very precise background dependence and a genuine quantum evolution. Furthermore, together with the condition of vacuum invaria...
Fission dynamics within time-dependent Hartree-Fock: deformation-induced fission
Goddard, P M; Rios, A
2015-01-01
Background: Nuclear fission is a complex large-amplitude collective decay mode in heavy nuclei. Microscopic density functional studies of fission have previously concentrated on adiabatic approaches based on constrained static calculations ignoring dynamical excitations of the fissioning nucleus, and the daughter products. Purpose: To explore the ability of dynamic mean-field methods to describe fast fission processes beyond the fission barrier, using the nuclide $^{240}$Pu as an example. Methods: Time-dependent Hartree-Fock calculations based on the Skyrme interaction are used to calculate non-adiabatic fission paths, beginning from static constrained Hartree-Fock calculations. The properties of the dynamic states are interpreted in terms of the nature of their collective motion. Fission product properties are compared to data. Results: Parent nuclei constrained to begin dynamic evolution with a deformation less than the fission barrier exhibit giant-resonance-type behaviour. Those beginning just beyond the ...
Directory of Open Access Journals (Sweden)
Kênia Barreiro de Souza
2016-05-01
Full Text Available The service sector expansion has shown to be a multiple trend process, producing distinct sectorial compositions. The present paper aims to make a comparison between two large economies in different stages of development with an extensive service sector (Brazil and United States, by focusing on final and intermediary demand changes and sectorial productivity as well. Input–output matrices for Brazil and United States were used and two applications were carried out: structural decomposition analysis and total factor productivity. Main results are as follows. Firstly, the growth in services was fostered by several factors, among which household consumption assumes an important role for both countries. Second, inter-industrial linkages play a major role only for United States. Thirdly, there is now evidence of cost disease for Brazil. Finally, productivity is lower in Brazil, nonetheless labor productivity increased above the average in some service sectors.
The Fock Space of Loopy Spin Networks for Quantum Gravity
Charles, Christoph
2016-01-01
In the context of the coarse-graining of loop quantum gravity, we introduce loopy and tagged spin networks, which generalize the standard spin network states to account explicitly for non-trivial curvature and torsion. Both structures relax the closure constraints imposed at the spin network vertices. While tagged spin networks merely carry an extra spin at every vertex encoding the overall closure defect, loopy spin networks allow for an arbitrary number of loops attached to each vertex. These little loops can be interpreted as local excitations of the quantum gravitational field and we discuss the statistics to endow them with. The resulting Fock space of loopy spin networks realizes new truncation of loop quantum gravity, allowing to formulate its graph-changing dynamics on a fixed background graph plus local degrees of freedom attached to the graph nodes. This provides a framework for re-introducing a non-trivial background quantum geometry around which we would study the effective dynamics of perturbatio...
Uniqueness of the Fock quantization of scalar fields in a Bianchi I cosmology with unitary dynamics
Cortez, Jerónimo; Navascués, Beatriz Elizaga; Martín-Benito, Mercedes; Mena Marugán, Guillermo A.; Olmedo, Javier; Velhinho, José M.
2016-11-01
The Fock quantization of free scalar fields is subject to an infinite ambiguity when it comes to choosing a set of annihilation and creation operators, a choice that is equivalent to the determination of a vacuum state. In highly symmetric situations, this ambiguity can be removed by asking vacuum invariance under the symmetries of the system. Similarly, in stationary backgrounds, one can demand time-translation invariance plus positivity of the energy. However, in more general situations, additional criteria are needed. For the case of free (test) fields minimally coupled to a homogeneous and isotropic cosmology, it has been proven that the ambiguity is resolved by introducing the criterion of unitary implementability of the quantum dynamics, as an endomorphism in Fock space. This condition determines a specific separation of the time dependence of the field, so that this splits into a very precise background dependence and a genuine quantum evolution. Furthermore, together with the condition of vacuum invariance under the spatial Killing symmetries, unitarity of the dynamics selects a unique Fock representation for the canonical commutation relations, up to unitary equivalence. In this work, we generalize these results to anisotropic spacetimes with shear, which are therefore not conformally symmetric, by considering the case of a free scalar field in a Bianchi I cosmology.
Fractional Electron Loss in Approximate DFT and Hartree-Fock Theory.
Peach, Michael J G; Teale, Andrew M; Helgaker, Trygve; Tozer, David J
2015-11-10
Plots of electronic energy vs electron number, determined using approximate density functional theory (DFT) and Hartree-Fock theory, are typically piecewise convex and piecewise concave, respectively. The curves also commonly exhibit a minimum and maximum, respectively, in the neutral → anion segment, which lead to positive DFT anion HOMO energies and positive Hartree-Fock neutral LUMO energies. These minima/maxima are a consequence of using basis sets that are local to the system, preventing fractional electron loss. Ground-state curves are presented that illustrate the idealized behavior that would occur if the basis set were to be modified to enable fractional electron loss without changing the description in the vicinity of the system. The key feature is that the energy cannot increase when the electron number increases, so the slope cannot be anywhere positive, meaning frontier orbital energies cannot be positive. For the convex (DFT) case, the idealized curve is flat beyond a critical electron number such that any additional fraction of an electron added to the system is unbound. The anion HOMO energy is zero. For the concave (Hartree-Fock) case, the idealized curve is flat up to some critical electron number, beyond which it curves down to the anion energy. A minimum fraction of an electron is required before any binding occurs, but beyond that, the full fraction abruptly binds. The neutral LUMO energy is zero. Approximate DFT and Hartree-Fock results are presented for the F → F(-) segment, and results approaching the idealized behavior are recovered for highly diffuse basis sets. It is noted that if a DFT calculation using a highly diffuse basis set yields a negative LUMO energy then a fraction of an electron must bind and the electron affinity must be positive, irrespective of whether an electron binds experimentally. This is illustrated by calculations on Ne → Ne(-).
Oliveira, Agda Maria; Vieira, Carolina Portugal; Dibo, Margareth Regina; Guirado, Marluci Monteiro; Rodas, Lilian Aparecida Colebrusco; Chiaravalloti-Neto, Francisco
2016-12-01
Visceral leishmaniasis (VL), a neglected disease, is a serious public health problem that affects millions of people worldwide. The objectives of the study were to evaluate the sensitivity of Lutzomyia longipalpis and canine VL (CVL) autochthony early detection and describe the spatial and temporal dispersal of vector and expansion of VL in a Brazilian state. We obtained data on the leishmaniasis vector and VL cases in São Paulo State (SP), Brazil, from the Division of Endemic Disease Control and from the Epidemiological Surveillance Center of the São Paulo State Department of Health. Data were analyzed for 645 municipalities and 63 microregions and presented as thematic and flow maps. Following the verified presence of L. longipalpis in Araçatuba in 1997, the first autochthonous cases of canine VL (CVL) (1998) and of human VL (HVL) (1999) in São Paulo were reported, both in Araçatuba. From 1997 to 2014, the urban presence of the leishmaniasis vector was verified in 167 (25.9%) municipalities with cases of CVL reported in 108 (16.7%) and cases of HVL in 84 (13%). The sensitivities for vector presence early detection in relation to the identification of CVL and HVL autochthony were, respectively, equal to 76.4 and 92.5%. The sensitivity for CVL autochthony early detection in relation to the HVL autochthony identification was 75.8%. Vector dispersal and expansion of CVL and HVL were from the northwest to the southeast of the state, primarily flanking the Marechal Rondon highway at a constant rate of progression of 10, seven, and six new municipalities affected per year, respectively. We concluded that the sensitivity for vector presence and CVL autochthony presented reasonable accuracy and most of the time the vector presence and, specially, the CVL and HVL autochthony were identified in the main cities of the microregions of SP. Vector dispersal and expansion of VL started in 1997 near the state border of SP with the state of Mato Grosso do Sul. It has advanced
Anisotropic expansion of a thermal dipolar Bose gas
Tang, Yijun; Burdick, Nathaniel Q; DiSciacca, Jack M; Petrov, Dmitry S; Lev, Benjamin L
2016-01-01
We report on the anisotropic expansion of ultracold bosonic dysprosium gases at temperatures above quantum degeneracy and develop a quantitative theory to describe this behavior. The theory expresses the post-expansion aspect ratio in terms of temperature and microscopic collisional properties by incorporating Hartree-Fock mean-field interactions, hydrodynamic effects, and Bose-enhancement factors. Our results extend the utility of expansion imaging by providing accurate thermometry for dipolar thermal Bose gases, reducing error in expansion thermometry from tens of percent to only a few percent. Furthermore, we present a simple method to determine scattering lengths in dipolar gases, including near a Feshbach resonance, through observation of thermal gas expansion.
Pathman, Donald E.; Morgan, Jennifer Craft; Konrad, Thomas R.; Goldberg, Lynda
2012-01-01
Purpose: The landscape of education loan repayment programs for health care professionals has been turbulent in recent years, with doubling of the funding for the National Health Service Corps (NHSC) and cuts in funding for some states' programs. We sought to understand how this turbulence is being felt within the state offices involved in…
Energy Technology Data Exchange (ETDEWEB)
Barbosa, Rugles Cesar
2002-07-01
The present thesis is divided into two parts. The first part describes the many kind of the formalisms of the Generator Coordinate Hartree-Fock method (GCHFM) and second part describes the computational aspect applied to the GCHFM formalism in its discreet form. The major aim of this work is the development of an alternative method to non-linear parameters optimization (basis set) and later uses these optimized parameters to adjust the weight function into GCHFM method. The study of the weight function when N {yields} {infinity} (or for large N), where N represents the number of mesh, is important since the GCHFM theory in its continuous form depend on understanding of such behavior. In this thesis, a detailed study is carried out about the methodologies of the self-consistent solution of the GCHFM and some methodology aspects of non-linear parameters optimization. This work shows that the Generator Coordinate Hartree-Fock method is general and it has as particular case the Hartree-Fock Roothaan method. Some possible variations or combinations around of the characteristics of the GCHFM and a comparison with conventional SCF procedure are reported in this thesis. The piecewise weight function method developed in this work shows to be very good for collective parameter optimizations of the Generator Coordinate (GC). The GCHFM calculations are necessary restrict (GCM-RHF), especially when the calculated value energies approach of its numerical values or Hartree-Fock limit. In the optimization methods of state functions for atomic electronic systems is very common the application of the gradient method and its efficacy is not contested. However, the method describes above allow us to obtain results as good as the gradient method. The basis set generated using the piecewise weight function method for Gaussian type function were used in the Restrict Hartree-Fock (RHF) calculations to obtain the total energies for some atomic electronic systems, such as neutron atoms and
Representations Of The Super-virasoro Algebra fock Representations
Polychronidis, V J
1999-01-01
In this dissertation the complete classification of the Super- Virasoro modules M (h, c) of the Neveu-Schwarz and Ramond algebras is constructed. A family of representations F p, po of the Neveu- Schwarz and Ramond algebras, which generalize the Fock representations of the Virasoro algebra, is constructed. The Felder's construction of Fock space resolutions for the Virasoro minimal models is generalized in the Super-Virasoro minimal models case. In particular, a two-sided resolution of the irreducible Super-Verma module L( h, c) of the Neveu- Schwarz algebra is provided. --- 8 --- AN
Directory of Open Access Journals (Sweden)
Mattias Magnusson
Full Text Available Lack of HLA-matched hematopoietic stem cells (HSC limits the number of patients with life-threatening blood disorders that can be treated by HSC transplantation. So far, insufficient understanding of the regulatory mechanisms governing human HSC has precluded the development of effective protocols for culturing HSC for therapeutic use and molecular studies. We defined a culture system using OP9M2 mesenchymal stem cell (MSC stroma that protects human hematopoietic stem/progenitor cells (HSPC from differentiation and apoptosis. In addition, it facilitates a dramatic expansion of multipotent progenitors that retain the immunophenotype (CD34+CD38-CD90+ characteristic of human HSPC and proliferative potential over several weeks in culture. In contrast, transplantable HSC could be maintained, but not significantly expanded, during 2-week culture. Temporal analysis of the transcriptome of the ex vivo expanded CD34+CD38-CD90+ cells documented remarkable stability of most transcriptional regulators known to govern the undifferentiated HSC state. Nevertheless, it revealed dynamic fluctuations in transcriptional programs that associate with HSC behavior and may compromise HSC function, such as dysregulation of PBX1 regulated genetic networks. This culture system serves now as a platform for modeling human multilineage hematopoietic stem/progenitor cell hierarchy and studying the complex regulation of HSC identity and function required for successful ex vivo expansion of transplantable HSC.
Negative parity baryons in the $1/N_c$ expansion: the three towers of states revisited
Matagne, N
2012-01-01
We discuss the compatibility between the quark-shell picture and the meson-nucleon scattering picture in large $N_c$ QCD for mixed symmetric $\\ell$ = 1 states previously analyzed by using a simple Hamiltonian including operators up to order $\\mathcal{O}(N^0_c)$ defined in the standard ground state symmetric core + excited quark procedure. Here we introduce a Hamiltonian of order $\\mathcal{O}(N^0_c)$ defined in a new approach where the separation of the system into two parts is not required. Three degenerate sets of states (towers) with the same quantum numbers as in the scattering picture and in the standard procedure are obtained. Thus the 0 is equally achieved. The eigenvalues of the presently chosen Hamiltonian also have simple analytic expressions, depending linearly on the three dynamical coefficients entering the Hamiltonian. This reinforces the validity of the new approach which had already 0 described excited negative parity baryons in a large energy range.
The quark gluon plasma equation of state and the expansion of the early Universe
Energy Technology Data Exchange (ETDEWEB)
Sanches, S.M.; Navarra, F.S.; Fogaça, D.A., E-mail: david@if.usp.br
2015-05-15
Our knowledge of the equation of state of the quark gluon plasma has been continuously growing due to the experimental results from heavy ion collisions, due to recent astrophysical measurements and also due to the advances in lattice QCD calculations. The new findings about this state may have consequences on the time evolution of the early Universe, which can be estimated by solving the Friedmann equations. The solutions of these equations give the time evolution of the energy density and also of the temperature in the beginning of the Universe. In this work we compute the time evolution of the QGP in the early Universe, comparing several equations of state, some of them based on the MIT bag model (and on its variants) and some of them based on lattice QCD calculations. Among other things, we investigate the effects of a finite baryon chemical potential in the evolution of the early Universe.
PROBLEMS AND COSTS OF THE EUROPEAN UNION EXPANSION WITH OVER 27 STATES
Directory of Open Access Journals (Sweden)
Marina Zaharioaie
2010-12-01
Full Text Available Once on his way to enlargement, the European Union has taken a road of no return. History has shown that all candidate countries have become a point of EU Member States. The question thus is not where you go to the European Union enlargement, but how it will look after the enlargement of the Union politically, economically and socially. The objective of this paper is to analyze potential problems and costs of enlargement beyond the 27 states. Thus, we performed an analysis on the implications of enlargement to the Balkans to Asia Minor and even to the former Soviet bloc countries.
Directory of Open Access Journals (Sweden)
Steven M. Valone
2012-06-01
Full Text Available The δ phase of plutonium with the fcc structure exhibits an unusual negative thermal expansion (NTE over its narrow temperature range of stability, 593–736 K. An accurate description of the anomalous high-temperature volume effect of plutonium goes beyond the current capability of electronic-structure calculations. We propose an atomistic scheme to model the thermodynamic properties of δ-Pu based on the two-state model of Weiss for the Invar alloys, inspired by the simple free-energy analysis previously conducted by Lawson et al. The two-state mechanism is incorporated into the atomistic description of a many-body interacting system. Two modified embedded atom method potentials are employed to represent the binding energies of two competing electronic states in δ-Pu. We demonstrate how the NTE takes place in δ-Pu by means of Monte Carlo simulations implemented with the two-state mechanism.
New York State Health Foundation grant helps health centers win federal expansion funds.
Sandman, David; Cozine, Maureen
2012-11-01
With approximately 1.2 million New Yorkers poised to gain health insurance coverage as a result of federal health reform, demand for primary care services is likely to increase greatly. The Affordable Care Act includes $11 billion in funding to enhance primary care access at community health centers. Recognizing a need and an opportunity, in August 2010 the New York State Health Foundation made a grant of nearly $400,000 to the Community Health Care Association of New York State to work with twelve health centers to develop successful proposals for obtaining and using these federal funds. Ultimately, eleven of the twelve sites are expected to receive $25.6 million in federal grants over a five-year period-a sixty-four-fold return on the foundation's investment. This article describes the strategy for investing in community health centers; identifies key project activities, challenges, and lessons; and highlights its next steps for strengthening primary care.
Brightwell, R J; Labadie, P E; Silverman, J
2010-10-01
The invasive Argentine ant, Linepithema humile (Mayr) (Hymenoptera: Formicidae) has been evident in the North Carolina Piedmont, United States for 90 yr but has failed to spread further north. We investigated the mechanisms preventing this expansion. The Argentine ant ceases foraging at temperatures below 5°C and we hypothesized that winter soil temperatures at higher latitudes restricted foraging long enough to cause colony starvation. We tested if the Argentine ant could successfully feed at temperatures below 5°C and found that colonies would starve. We subjected Argentine ant nests to a range of sub- and above-freezing temperatures and measured worker mortality at various time intervals. We found that Argentine ant colonies will collapse after 8.5 d at 5°C. Argentine ants can escape ambient cold temperatures by moving nests into the soil column. We tested how deeply into the soil Argentine ant queens and workers need to move to survive winter in North Carolina. Soil temperatures in the North Carolina Piedmont do not fall below 5°C for longer than nine consecutive days; therefore, Argentine ant colonies need only to retreat a few centimeters into the soil column to escape unsuitable temperatures. Winter soil temperature data from four climate stations situated from latitudes 35°, the current Eastern United States latitudinal limit for Argentine ant population expansion, to 39° were searched for periods where soil temperatures would have led to colony extirpation. North of their current distributions, extended periods of soil temperatures below 5°C regularly occur, preventing Argentine ant colonies from persisting.
Directory of Open Access Journals (Sweden)
Matthew Dornan
2015-09-01
Full Text Available Small island developing states face unique constraints to the provision of electricity services in rural areas, given their geographical features, and the small scale of government bureaucracies and markets. In small island developing states situated in the Pacific Ocean, these factors have resulted in some of the lowest electrification rates in the world. Seventy percent of Pacific islanders are without access to power; a figure that is equivalent to access rates in Sub-Saharan Africa, despite higher income levels in the Pacific. Past efforts by government and aid organizations to expand electricity access in rural areas have achieved negligible success, given regulatory frameworks that do not encourage grid extension, and the absence of effective institutional frameworks for operation and maintenance of decentralized systems. This paper argues that the binding constraint to rural electrification in Pacific small island developing states is the failure of regulatory frameworks to establish a viable business model for investment. Regulatory reform is needed that creates commercial incentives for private and public sector power utilities to provide power in rural areas, both through extension of electricity networks and decentralized power provision. Regulatory reform could also address past problems with the operation and maintenance of decentralized systems.
Goldblatt, Colin
2015-01-01
There are four different stable climate states for pure water atmospheres, as might exist on so-called "waterworlds". I map these as a function of solar constant for planets ranging in size from Mars size to 10 Earth-mass. The states are: globally ice covered (Ts< 245K), cold and damp (270 < Ts< 290K), hot and moist (350< Ts< 550K) and very hot and dry (Ts< 900K). No stable climate exists for 290< Ts < 350K or 550 < Ts < 900K. The union of hot moist and cold damp climates describe the liquid water habitable zone, the width and location of which depends on planet mass. At each solar constant, two or three different climate states are stable. This is a consequence of strong non-linearities in both thermal emission and the net absorption of sunlight. Across the range of planet sizes, I account for the atmospheres expanding to high altitudes as they warm. The emitting and absorbing surfaces (optical depth of unity) move to high altitude, making their area larger than the planet surfa...
Derivation of Klein-Gordon-Fock equation from General relativity in a time-space symmetrical model
Van Thuan, Vo
2016-01-01
Following a bi-cylindrical model of geometrical dynamics, in the present study we show that Einstein gravitational equation leads to bi-geodesic description in an extended symmetrical time-space which fit Hubble expansion in a "microscopic" cosmological model. As a duality, the geodesic solution is mathematically equivalent to the basic Klein-Gordon-Fock equations of free massive elementary particles, in particular, as the squared Dirac equations of leptons and as a sub-solution with pseudo-axion. This result would serve an explicit approach to consistency between quantum mechanics and general relativity.
Anagnostopoulos, Dorothea; Rutledge, Stacey; Bali, Valentina
2013-01-01
This article examines how SEAs in three states designed, installed, and operated statewide, longitudinal student information systems (SLSIS). SLSIS track individual students' progress in K-12 schools, college, and beyond and link it to individual schools and teachers. They are key components of the information infrastructure of test-based…
Constrained Hartree-Fock and quasi-spin projection
Cambiaggio, M. C.; Plastino, A.; Szybisz, L.
1980-08-01
The constrained Hartree-Fock approach of Elliott and Evans is studied in detail with reference to two quasi-spin models, and their predictions compared with those arising from a projection method. It is found that the new approach works fairly well, although limitations to its applicability are encountered.
Asymptotic freedom of gluons in the Fock space
Głazek, Stanisław D
2015-01-01
Asymptotic freedom of gluons is described in terms of a family of scale-dependent renormalized Hamiltonian operators acting in the Fock space. The Hamiltonians are obtained by applying the renormalization group procedure for effective particles to quantum Yang-Mills theory.
Thingna, Juzar; Zhou, Hangbo; Wang, Jian-Sheng
2014-11-21
We present a general theory to calculate the steady-state heat and electronic currents for nonlinear systems using a perturbative expansion in the system-bath coupling. We explicitly demonstrate that using the truncated Dyson-series leads to divergences in the steady-state limit, thus making it impossible to be used for actual applications. In order to resolve the divergences, we propose a unique choice of initial condition for the reduced density matrix, which removes the divergences at each order. Our approach not only allows us to use the truncated Dyson-series, with a reasonable choice of initial condition, but also gives the expected result that the steady-state solutions should be independent of initial preparations. Using our improved Dyson series we evaluate the heat and electronic currents up to fourth-order in system-bath coupling, a considerable improvement over the standard quantum master equation techniques. We then numerically corroborate our theory for archetypal settings of linear systems using the exact nonequilibrium Green's function approach. Finally, to demonstrate the advantage of our approach, we deal with the nonlinear spin-boson model to evaluate heat current up to fourth-order and find signatures of cotunnelling process.
Energy Technology Data Exchange (ETDEWEB)
Thingna, Juzar [Institute of Physics, University of Augsburg, Universitätsstrasse 1 D-86135 Augsburg (Germany); Nanosystems Initiative Munich, Schellingrstrasse 4, D-80799 München (Germany); Zhou, Hangbo [Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore 117551 (Singapore); NUS Graduate School for Integrative Sciences and Engineering, National University of Singapore, Singapore 117456 (Singapore); Wang, Jian-Sheng, E-mail: phywjs@nus.edu.sg [Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore 117551 (Singapore)
2014-11-21
We present a general theory to calculate the steady-state heat and electronic currents for nonlinear systems using a perturbative expansion in the system-bath coupling. We explicitly demonstrate that using the truncated Dyson-series leads to divergences in the steady-state limit, thus making it impossible to be used for actual applications. In order to resolve the divergences, we propose a unique choice of initial condition for the reduced density matrix, which removes the divergences at each order. Our approach not only allows us to use the truncated Dyson-series, with a reasonable choice of initial condition, but also gives the expected result that the steady-state solutions should be independent of initial preparations. Using our improved Dyson series we evaluate the heat and electronic currents up to fourth-order in system-bath coupling, a considerable improvement over the standard quantum master equation techniques. We then numerically corroborate our theory for archetypal settings of linear systems using the exact nonequilibrium Green's function approach. Finally, to demonstrate the advantage of our approach, we deal with the nonlinear spin-boson model to evaluate heat current up to fourth-order and find signatures of cotunnelling process.
Montgomery, Madeline C; Raifman, Julia; Nunn, Amy S; Bertrand, Thomas; Uvin, A Ziggy; Marak, Theodore; Comella, Jaime; Almonte, Alexi; Chan, Philip A
2017-05-01
In Rhode Island, the Patient Protection and Affordable Care Act has led to over 95% of the state's population being insured. We evaluated insurance coverage and barriers to insurance use among patients presenting for services at the Rhode Island sexually transmitted disease (STD) clinic. We analyzed factors associated with insurance coverage and utilization among patients presenting for STD services between July and December 2015. A total of 692 patients had insurance information available; of those, 40% were uninsured. Patients without insurance were more likely than those with insurance to be nonwhite (50% among uninsured, compared with 40% among insured; P = 0.014) and Hispanic or Latino/a (25%, compared with 16%; P = 0.006), and less likely to be men who have sex with men (27%, compared with 39%; P = 0.001). Of those with health insurance, 26% obtained coverage as a result of the Affordable Care Act, and 56% of those were previously uninsured. Among uninsured individuals, barriers to obtaining health insurance included cost and unemployment. Among those with insurance, 43% reported willingness to use insurance for STD services. Barriers to insurance use included concerns about anonymity and out-of-pocket costs. Despite expanded insurance access, many individuals presenting to the Rhode Island STD Clinic were uninsured. Among those who were insured, significant barriers still existed to using insurance. STD clinics continue to play an important role in providing safety-net STD services in states with low uninsured rates. Both public and private insurers are needed to address financial barriers and optimize payment structures for services.
Parsing polarization squeezing into Fock layers
DEFF Research Database (Denmark)
Mueller, Christian R.; Madsen, Lars Skovgaard; Klimov, Andrei B.
2016-01-01
We investigate polarization squeezing in squeezed coherent states with varying coherent amplitudes. In contrast to the traditional characterization based on the full Stokes parameters, we experimentally determine the Stokes vector of each excitation subspace separately. Only for states with a fix...
Urian, Alyson G; Hatle, John D; Gilg, Matthew R
2011-01-01
Cold temperatures are thought to be among the most important determining factors of geographic distribution for tropical and sub-tropical marine invertebrates. The Asian green mussel, Perna viridis, has been introduced into coastal waters of Florida where its current distribution is hypothesized to be limited by low temperatures during winter. Lethal and sub-lethal effects (heat shock protein/Hsp70 expression) of cold water and air temperatures were analyzed in two size classes of P. viridis from Florida in an effort to determine the effects of current and forecasted temperatures on the potential for range expansion. Mussels were exposed to water temperatures of 14, 10, 7 and 3°C for up to 30 days, or to air temperatures of 14, 7, 0 and -10°C for periods of 2 hr. Mortality was significantly increased at all water and air temperatures ≤14°C. No differences in mortality rates were observed between small (15-45 mm) and large (75-105 mm) size classes except after exposure to 7°C air, in which small mussels had higher mortality. Significant increases in Hsp70 expression were observed after a 2-hour exposure to 10°C water, but Hsp70 expression was not significantly increased at any temperatures in which mortality was not also significant. The temperature threshold for survival in this population appears to be between 10 and 14°C, suggesting that under current conditions P. viridis may already be at the northern edge of its potential range in the United States. If water temperatures increase with global climate change, northerly flowing currents may permit range expansion as temperatures allow. Copyright © 2010 Wiley-Liss, Inc., A Wiley Company.
Pinnola, Francesco Paolo
2016-10-01
The statistical characterization of the oscillator response with non-integer order damping under Gaussian noise represents an important challenge in the modern stochastic mechanics. In fact, this kind of problem appears in several issues of different type (wave propagation in viscoelastic media, Brownian motion, fluid dynamics, RLC circuit, etc.). The aim of this paper is to provide a stochastic characterization of the stationary response of linear fractional oscillator forced by normal white noise. In particular, this paper shows a new method to obtain the correlation function by exact complex spectral moments. These complex quantities contain all the information to describe the random processes but in the considered case their analytical evaluation needs some mathematical manipulations. For this reason such complex spectral moment characterization is used in conjunction with a fractional-order state variable analysis. This kind of analysis permits to find the exact expression of complex spectral moments, and the correlation function by using the Mellin transform. Moreover, the proposed approach provides an analytical expression of the response variance of the fractional oscillator. Capability and efficiency of the present method are shown in the numerical examples in which correlation and variance of fractional oscillator response are found and compared with those obtained by Monte Carlo simulations.
Energy Technology Data Exchange (ETDEWEB)
Coelho, Suani Teixeira [Centro Nacional de Referencia em Biomassa (CENBIO), Sao Paulo, SP (Brazil); Lora, Beatriz Acquaro; Monteiro, Maria Beatriz C.A.
2008-07-01
The present work aimed at analyze the sugar cane culture expansion in substitution to the other cultures in the Sao Paulo state from available georeferred and statistical data. The results had evidenced clear expansion of the sugar cane culture in the state, having totalized a growth of 26.04% in the period from 2003 to 2006, with expressive increase in the regions of President Prudente, Sao Jose do Rio Preto, Barretos and Marilia that had, each one, more than 40% of increase in the period. Concomitantly it had reduction of the maize areas in the studied region and pasture areas stability, followed of a small increase of the cattle heads number. (author)
Accurate Hartree-Fock energy of extended systems using large Gaussian basis sets
Paier, Joachim; Diaconu, Cristian V.; Scuseria, Gustavo E.; Guidon, Manuel; Vandevondele, Joost; Hutter, Jürg
2009-11-01
Calculating highly accurate thermochemical properties of condensed matter via wave-function-based approaches (such as, e.g., Hartree-Fock or hybrid functionals) has recently attracted much interest. We here present two strategies providing accurate Hartree-Fock energies for solid LiH in a large Gaussian basis set and applying periodic boundary conditions. The total energies were obtained using two different approaches, namely, a supercell evaluation of Hartree-Fock exchange using a truncated Coulomb operator and an extrapolation toward the full-range Hartree-Fock limit of a Padé fit to a series of short-range screened Hartree-Fock calculations. These two techniques agreed to significant precision. We also present the Hartree-Fock cohesive energy of LiH (converged to within sub-millielectron volt) at the experimental equilibrium volume as well as the Hartree-Fock equilibrium lattice constant and bulk modulus.
Qualitative breakdown of the unrestricted Hartree-Fock energy
Energy Technology Data Exchange (ETDEWEB)
Mori-Sánchez, Paula, E-mail: paula.mori@uam.es [Departamento de Química and Instituto de Física de la Materia Condensada (IFIMAC), Universidad Autónoma de Madrid, 28049 Madrid (Spain); Cohen, Aron J., E-mail: ajc54@cam.ac.uk [Department of Chemistry, Lensfield Road, University of Cambridge, Cambridge CB2 1EW (United Kingdom)
2014-10-28
The stretching of closed-shell molecules is a qualitative problem for restricted Hartree-Fock that is usually circumvented by the use of unrestricted Hartree-Fock (UHF). UHF is well known to break the spin symmetry at the Coulson-Fischer point, leading to a discontinuous derivative in the potential energy surface and incorrect spin density. However, this is generally not considered as a major drawback. In this work, we present a set of two electron molecules which magnify the problem of symmetry breaking and lead to drastically incorrect potential energy surfaces with UHF. These molecules also fail with unrestricted density-functional calculations where a functional such as B3LYP gives both symmetry breaking and an unphysically low energy due to the delocalization error. The implications for density functional theory are also discussed.
Madeira, Ana Isabel
2005-01-01
This article draws a comparison between the Portuguese in relation to British and French discourses on overseas educational policies at the turn of the nineteenth to the twentieth century until the 1930s. It focuses on three main colonial educational dynamics: school expansion (comparing the public and private sectors); State-Church relations…
Tseitlin, Mark; Eaton, Gareth R; Eaton, Sandra S
2013-12-01
Rapid-scan EPR has been shown to improve the signal-to-noise ratio relative to conventional continuous wave spectroscopy. Equations are derived for the steady-state solution to the Bloch equations as a Fourier expansion in the harmonics of the scan frequency. This simulation method is about two orders of magnitude faster than time-domain numerical integration.
Analytic Characterization for Hilbert-Schmidt Operators on Fock Space
Institute of Scientific and Technical Information of China (English)
Cai Shi WANG; Zhi Yuan HUANG; Xiang Jun WANG
2005-01-01
In this paper we first introduce and investigate some special classes of nonlinear maps and get several useful results. Then, by using these results, we obtain analytic criteria for checking whether or not an operator defined only on the exponential vectors of a symmetric Fock space becomes a Hilbert-Schmidt operator on the whole space. Additionally, as an application, we also get an analytic criterion for Hilbert-Schmidt operators on a Gaussian probability space through the Wiener-Ito-Segal isomorphism.
Energy Spectrum Symmetry of Heisenberg Model in Fock Space
Institute of Scientific and Technical Information of China (English)
WANG An-Min; ZHU Ren-Gui
2006-01-01
@@ We extend the BCS paring model with equally spaced energy levels to a general one-dimensional spin-l/2 Heisenberg model. The two well-known symmetries of the Heisenberg model, i.e. permutational and spin-inversion symmetries, no longer exist. However, when jointing these two operations together, we find a new symmetry of energy spectrum between its subspace n and subspace L - n of the Fock space. A rigorous proof is presented.
Quasi-particle Continuum and Resonances in the Hartree-Fock-Bogoliubov Theory
Energy Technology Data Exchange (ETDEWEB)
Pei, J. C. [University of Tennessee, Knoxville (UTK) & Oak Ridge National Laboratory (ORNL); Kruppa, Andras Tibor [ORNL; Nazarewicz, Witold [ORNL
2011-01-01
The quasi-particle energy spectrum of the Hartree-Fock-Bogoliubov (HFB) equations contains discrete bound states, resonances, and non-resonant continuum states. We study the structure of the unbound quasi-particle spectrum of weakly bound nuclei within several methods that do not rely on imposing scattering or outgoing boundary conditions. Various approximations are examined to estimate resonance widths. It is shown that the stabilization method works well for all HFB resonances except for very narrow ones. The Thomas-Fermi approximation to the non-resonant continuum has been shown to be very effective, especially for coordinate-space HFB calculations in large boxes that involve huge amounts of discretized quasi-particle continuum states.
Quasiparticle continuum and resonances in the Hartree-Fock-Bogoliubov theory
Energy Technology Data Exchange (ETDEWEB)
Pei, Junchen [ORNL; Kruppa, A. T. [Joint Institute for Heavy Ion Research, Oak Ridge; Nazarewicz, W. [University of Tennessee, Knoxville (UTK) & Oak Ridge National Laboratory (ORNL)
2011-01-01
The quasi-particle energy spectrum of the Hartree-Fock-Bogoliubov (HFB) equations contains discrete bound states, resonances, and non-resonant continuum states. We study the structure of the unbound quasi-particle spectrum of weakly bound nuclei within several methods that do not rely on imposing scattering or outgoing boundary conditions. Various approximations are examined to estimate resonance widths. It is shown that the stabilization method works well for all HFB resonances except for very narrow ones. The Thomas-Fermi approximation to the non-resonant continuum has been shown to be very effective, especially for coordinate-space HFB calculations in large boxes that involve huge amounts of discretized quasi-particle continuum states.
Linker, Gerrit-Jan; Loosdrecht , van Paul H.M.; van Duijnen, Piet Th.; Broer, Ria
2015-01-01
The insulating and conducting phases of (EDO-TTF)(2)PF6 were studied by all electron, periodic Hartre-Fock and hybrid density functional calculations. Electronic properties, such as the electronic band structure, the density of states and the Fermi surface are discussed in relation to the metal-insu
Δ (1232 ) effects in density-dependent relativistic Hartree-Fock theory and neutron stars
Zhu, Zhen-Yu; Li, Ang; Hu, Jin-Niu; Sagawa, Hiroyuki
2016-10-01
The density-dependent relativistic Hartree-Fock (DDRHF) theory is extended to include Δ isobars for the study of dense nuclear matter and neutron stars. To this end, we solve the Rarita-Schwinger equation for spin-3/2 particle. Both the direct and exchange terms of the Δ isobars' self-energies are evaluated in detail. In comparison with the relativistic mean field theory (Hartree approximation), a weaker parameter dependence is found for DDRHF. An early appearance of Δ isobars is recognized at ρB˜0.28 fm-3, comparable with that of hyperons. Also, we find that the Δ isobars' softening of the equation of state is mainly due to the reduced Fock contributions from the coupling of the isoscalar mesons, while the pion contributions are negligibly small. We finally conclude that with typical parameter sets, neutron stars with Δ isobars in their interiors could be as heavy as the two massive pulsars whose masses are precisely measured, with slightly smaller radii than normal neutron stars.
$\\Delta$ (1232) effects in density-dependent relativistic Hartree-Fock theory and neutron stars
Zhu, Zhen-Yu; Hu, Jin-Niu; Sagawa, Hiroyuki
2016-01-01
The density-dependent relativistic Hartree-Fock (DDRHF) theory is extended to include $\\Delta$-isobars for the study of dense nuclear matter and neutron stars. To this end, we solve the Rarita-Schwinger equation for spin-3/2 particle. Both the direct and exchange terms of the $\\Delta$-isobars' self-energies are evaluated in details. In comparison with the relativistic mean field theory (Hartree approximation), a weaker parameter dependence is found for DDRHF. An early appearance of $\\Delta$-isobars is recognized at $\\rho_B\\sim0.27$fm$^{-3}$, comparable with that of hyperons. Also, we find that the $\\Delta$-isobars' softening of the equation of state is found to be mainly due to the reduced Fock contributions from the coupling of the isoscalar mesons, while the pion contributions are found negligibly small. We finally conclude that with typical parameter sets, neutron stars with $\\Delta$-isobars in their interiors could be as heavy as the two massive pulsars whose masses are precisely measured, with slightly s...
General Quantum Modeling of Combining Concepts: A Quantum Field Model in Fock Space
Aerts, Diederik
2007-01-01
We extend a quantum model in Hilbert space developed in Aerts (2007a) into a quantum field theoric model in Fock space for the modeling of the combination of concepts. Items and concepts are represented by vectors in Fock space and membership weights of items are modeled by quantum probabilities. We apply this theory to model the disjunction of concepts and show that the predictions of our theory for the membership weights of items regarding the disjunction of concepts match with great accuracy the complete set of results of an experiment conducted by Hampton (1988b). It are the quantum effects of interference and superposition of that are at the origin of the effects of overextension and underextension observed by Hampton as deviations from a classical use of the disjunction. It is essential for the perfect matches we obtain between the predictions of the quantum field model and Hampton's experimental data that items can be in superpositions of `different numbers states' which proves that the genuine structu...
Dayang Norwana, A.A.B.; Kanjappan, R.; Chin, M.; Schoneveld, G.C.; Potter, L; Andriani, R.
2011-01-01
This study is part of a broader research process assessing the local economic, social and environmental impacts from feedstock expansion for the growing biofuel sector (see German et al. 2011). Nonetheless, in the Malaysian context, biofuel production volumes are negligible despite government interest in promoting sector expansion. Since Malaysia is the second largest palm oil producer in the world, palm oil is slated to become the primary feedstock for biofuel production in the country. Sinc...
Anisotropic Expansion of a Thermal Dipolar Bose Gas.
Tang, Y; Sykes, A G; Burdick, N Q; DiSciacca, J M; Petrov, D S; Lev, B L
2016-10-07
We report on the anisotropic expansion of ultracold bosonic dysprosium gases at temperatures above quantum degeneracy and develop a quantitative theory to describe this behavior. The theory expresses the postexpansion aspect ratio in terms of temperature and microscopic collisional properties by incorporating Hartree-Fock mean-field interactions, hydrodynamic effects, and Bose-enhancement factors. Our results extend the utility of expansion imaging by providing accurate thermometry for dipolar thermal Bose gases. Furthermore, we present a simple method to determine scattering lengths in dipolar gases, including near a Feshbach resonance, through observation of thermal gas expansion.
Anisotropic Expansion of a Thermal Dipolar Bose Gas
Tang, Y.; Sykes, A. G.; Burdick, N. Q.; DiSciacca, J. M.; Petrov, D. S.; Lev, B. L.
2016-10-01
We report on the anisotropic expansion of ultracold bosonic dysprosium gases at temperatures above quantum degeneracy and develop a quantitative theory to describe this behavior. The theory expresses the postexpansion aspect ratio in terms of temperature and microscopic collisional properties by incorporating Hartree-Fock mean-field interactions, hydrodynamic effects, and Bose-enhancement factors. Our results extend the utility of expansion imaging by providing accurate thermometry for dipolar thermal Bose gases. Furthermore, we present a simple method to determine scattering lengths in dipolar gases, including near a Feshbach resonance, through observation of thermal gas expansion.
Spiral magnetic phases on the Kondo Lattice Model: A Hartree-Fock approach
Costa, N. C.; Lima, J. P.; dos Santos, Raimundo R.
2017-02-01
We study the Kondo Lattice Model (KLM) on a square lattice through a Hartree-Fock approximation in which the local spins are treated semi-classically, in the sense that their average values are modulated by a magnetic wavevector Q while they couple with the conduction electrons through fermion operators. In this way, we obtain a ground state phase diagram in which spiral magnetic phases (in which the wavevector depends on the coupling constants and on the density) interpolate between the low-density ferromagnetic phase and the antiferromagnetic phase at half filling; within small regions of the phase diagram commensurate magnetic phases can coexist with Kondo screening. We have also obtained 'Doniach-like' diagrams, showing the effect of temperature on the ground state phases, and established that for some ranges of the model parameters (the exchange coupling and conduction electron density) the magnetic wavevector changes with temperature, either continuously or abruptly (e.g., from spiral to ferromagnetic).
The planar spectrum in U(N)-invariant quantum mechanics by Fock space methods: I. The bosonic case
De Pietri, R; Onofri, E
2007-01-01
Prompted by recent results on Susy-U(N)-invariant quantum mechanics in the large N limit by Veneziano and Wosiek, we have examined the planar spectrum in the full Hilbert space of U(N)-invariant states built on the Fock vacuum by applying any U(N)-invariant combinations of creation-operators. We present results about 1) the supersymmetric model in the bosonic sector, 2) the standard quartic Hamiltonian. This latter is useful to check our techniques against the exact result of Brezin et al. The SuSy case is where Fock space methods prove to be the most efficient: it turns out that the problem is separable and the exact planar spectrum can be expressed in terms of the single-trace spectrum. In the case of the anharmonic oscillator, on the other hand, the Fock space analysis is quite cumbersome due to the presence of large off-diagonal O(N) terms coupling subspaces with different number of traces; these terms should be absorbed before taking the planar limit and recovering the known planar spectrum. We give anal...
THE CODIMENSION FORMULA ON QUASI-INVARIANT SUBSPACES OF THE FOCK SPACE
Institute of Scientific and Technical Information of China (English)
侯绳照; 胡俊云
2003-01-01
Let M be an approximately finite codimensional quasi-invariant subspace of the Fock space.This paper gives a formula to calculate the codimension of such spaces and uses this formulato study the structure of quasi-invariant subspaces of the Fock space. Especially, as one ofapplications, it is showed that the analogue of Beurling's theorem is not true for the Fock spaceL2a (Cn ) in the case of n ≥ 2.
Polarizability of supported metal nanoparticles: Mehler-Fock approach
Jung, Jesper; Pedersen, Thomas G.
2012-09-01
Using toroidal coordinates and the Mehler-Fock transform, we present an analysis of the polarizability of a complex structure allowing for the study of arbitrarily truncated metal spheres including a dielectric substrate. Our analysis is based on an electrostatic approach, i.e., we are in the quasi-static limit, where we solve the Laplace equation for the potential. The derived method is used to analyze the behavior of localized surface plasmon resonances of truncated metal nanospheres including substrate effects. The method is fast, simple, easy to implement, and useful for analysis of experimental work on supported metal nanoparticles, e.g., within the area of plasmonic photovoltaics.
Quantum turing machine and brain model represented by Fock space
Iriyama, Satoshi; Ohya, Masanori
2016-05-01
The adaptive dynamics is known as a new mathematics to treat with a complex phenomena, for example, chaos, quantum algorithm and psychological phenomena. In this paper, we briefly review the notion of the adaptive dynamics, and explain the definition of the generalized Turing machine (GTM) and recognition process represented by the Fock space. Moreover, we show that there exists the quantum channel which is described by the GKSL master equation to achieve the Chaos Amplifier used in [M. Ohya and I. V. Volovich, J. Opt. B 5(6) (2003) 639., M. Ohya and I. V. Volovich, Rep. Math. Phys. 52(1) (2003) 25.
Properties of the periodic Hartree-Fock minimizer
Ghimenti, Marco
2008-01-01
We study the periodic Hartree-Fock model used for the description of electrons in a crystal. The existence of a minimizer was previously shown by Catto, Le Bris and Lions (Ann. Inst. H. Poincare Anal. Non Lineaire} 18 (2001), no.6, 687--760). We prove in this paper that any minimizer is necessarily a projector and that it solves a certain nonlinear equation, similarly to the atomic case. In particular we show that the Fermi level is either empty or totally filled.
Mananga, Eugene Stephane
2013-01-01
The purpose of this article is to present an historical overview of theoretical approaches used for describing spin dynamics under static or rotating experiments in solid state nuclear magnetic resonance. The article gives a brief historical overview for major theories in nuclear magnetic resonance and the promising theories. We present the first application of Floquet-Magnus expansion to chemical shift anisotropy when irradiated by BABA pulse sequence.
On the problem of representability and the Bogolyubov-Hartree-Fock theory
Energy Technology Data Exchange (ETDEWEB)
Knoerr, Hans Konrad
2013-11-22
The general topic of this thesis is an approximation of the ground state energy for many-particle quantum systems. In particular the Bogolyubov-Hartree-Fock theory and the representability of one- and two-particle density matrices are studied. After an introductory chapter we specify some basic notation of many-body quantum mechanics in Chapter 2. In Chapter 3 we consider boson, as well as fermion systems. We first tackle the question of representability for bosons, i.e., the question which conditions a one- and a two-particle operator must satisfy to ensure that they are the one- and the two-particle density matrix of a state. For a particle number-conserving system, the representability conditions up to second order for bosons are well-known and called admissibility, P-, and G-conditions. Since, however, most physical systems consisting of bosons are not particle number-conserving, we give an alternative for such systems: Generalizing the two-particle density matrix, we observe that the representability conditions up to second order hold if and only if this generalized two-particle density matrix is positive semi-definite and the one- and the two-particle density matrices fulfill trace class and symmetry conditions. Moreover, we study the Bogolyubov-Hartree-Fock energy of boson and fermion systems. We generalize Lieb's variational principle which in its original formulation holds for purely repulsive particle interactions for fermions only. Our second main result is the following: for bosons, as well as for fermions the infimum of the energy for a variation over pure quasifree states coincides with the one for a variation over all quasifree states under the assumption that the Hamiltonian is bounded below. In the last section of Chapter 3 we specify the relation between centered quasifree states and their corresponding generalized one-particle density matrix, which finds an application in the variational process in the Bogolyubov-Hartree-Fock theory. It is
Dayang Norwana, A.A.B.; Kanjappan, R.; Chin, M.; Schoneveld, G.C.; Potter, L.; Andriani, R.
2011-01-01
This study is part of a broader research process assessing the local economic, social and environmental impacts from feedstock expansion for the growing biofuel sector (see German et al. 2011). Nonetheless, in the Malaysian context, biofuel production volumes are negligible despite government intere
Chan, W Y; Huang, H S; Su, W B; Lin, W H; Jeng, H-T; Wu, M K; Chang, C S
2012-04-06
We use scanning tunneling microscopy and spectroscopy to measure the energy shift of empty quantum-well (QW) states in Pb islands on the Cu(111) surface. It is found that, with an increase of the electric field, the behavior of the energy shift can be grouped into two different modes for most QW states. In the first mode, the state energy moves toward high energy monotonically. In the second mode, the state energy shifts to a lower energy initially and then turns around to a higher energy. Moreover, we have observed that the QW states of higher energy behave in preference to the first mode, but they gradually change to the second mode as the Pb island becomes thicker. This thickness-dependent behavior reflects the existence of local expansion in the Pb islands, due to the electric field, and that the expansion is larger for a thicker island. QW states can thus be used for studying the localized lattice deformation in the nanometer scale.
Constrained Hartree-Fock Theory and Study of Deformed Structures of Closed Shell Nuclei
Praharaj, Choudhury
2016-03-01
We have studied some N or Z = 50 nuclei in a microscopic model with effective interaction in a reasonably large shell model space. Excitation of particles across 50 shell closure leads to well-deformed excited prolate configurations. The potential energy surfaces of nuclei are studied using Hartree-Fock theory with quadrupole constraint to explore the various deformed configurations of N = 50 nuclei 82Ge , 84Se and 86Kr . Energy spectra are calculated from various intrinsic states using Peierls-Yoccoz angular momentum projection technique. Results of spectra and electromagnetic moments and transitions will be presented for N = 50 nuclei and for Z = 50 114Sn nucleus. Supported by Grant No SB/S2/HEP-06/2013 of DST.
On the Discrete Spectrum of a Model Operator in Fermionic Fock Space
Directory of Open Access Journals (Sweden)
Zahriddin Muminov
2013-01-01
Full Text Available We consider a model operator H associated with a system describing three particles in interaction, without conservation of the number of particles. The operator H acts in the direct sum of zero-, one-, and two-particle subspaces of the fermionic Fock space ℱa(L2(3 over L2(3. We admit a general form for the "kinetic" part of the Hamiltonian H, which contains a parameter γ to distinguish the two identical particles from the third one. (i We find a critical value γ* for the parameter γ that allows or forbids the Efimov effect (infinite number of bound states if the associated generalized Friedrichs model has a threshold resonance and we prove that only for γγ*. (ii In the case γ>γ* , we also establish the following asymptotics for the number N(z of eigenvalues of H below z0, for all γ>γ*.
Time-Dependent Hartree-Fock Approach to Nuclear Pasta at Finite Temperature
Schuetrumpf, Bastian; Iida, Kei; Maruhn, Joachim; Mecke, Klaus; Reinhard, Paul-Gerhard
2013-01-01
We present simulations of neutron-rich matter at subnuclear densities, like supernova matter, with the time-dependent Hartree-Fock approximation at temperatures of several MeV. The initial state consists of $\\alpha$ particles randomly distributed in space that have a Maxwell-Boltzmann distribution in momentum space. Adding a neutron background initialized with Fermi distributed plane waves the calculations reflect a reasonable approximation of astrophysical matter. This matter evolves into spherical, rod-like, and slab-like shapes and mixtures thereof. The simulations employ a full Skyrme interaction in a periodic three-dimensional grid. By an improved morphological analysis based on Minkowski functionals, all eight pasta shapes can be uniquely identified by the sign of only two valuations, namely the Euler characteristic and the integral mean curvature.
Self-consistent Hartree-Fock RPA calculations in 208Pb
Taqi, Ali H.; Ali, Mohammed S.
2017-07-01
The nuclear structure of 208Pb is studied in the framework of the self-consistent random phase approximation (SCRPA). The Hartree-Fock mean field and single particle states are used to implement a completely SCRPA with Skyrme-type interactions. The Hamiltonian is diagonalised within a model space using five Skyrme parameter sets, namely LNS, SkI3, SkO, SkP and SLy4. In view of the huge number of the existing Skyrme-force parameterizations, the question remains which of them provide the best description of data. The approach attempts to accurately describe the structure of the spherical even-even nucleus 208Pb. To illustrate our approach, we compared the binding energy, charge density distribution, excitation energy levels scheme with the available experimental data. Moreover, we calculated isoscalar and isovector monopole, dipole, and quadrupole transition densities and strength functions.
Angular-momentum projection for Hartree-Fock and RPA with realistic interactions
Energy Technology Data Exchange (ETDEWEB)
Erler, Bastian; Roth, Robert [Institut fuer Kernphysik, TU Darmstadt (Germany)
2012-07-01
Hartree-Fock (HF) with a Hamiltonian constructed from similarity transformed realistic NN potentials plus 3N contact interactions provides a good starting point for the description of closed shell nuclei. In conjunction with Many-Body-Perturbation-Theory, experimental ground-state energies and radii are well reproduced. To describe collective excitations, the Random-Phase-Approximation (RPA) is the method of choice. Beyond closed shells, e.g. in the sd-shell region, ground-states might exhibit intrinsic deformation, resulting in HF states where angular-momentum ceases to be a good quantum number. Lab-frame observables, like ground-state energies or rotational bands can be recovered from the intrinsic states via angular-momentum projection. We study axially deformed even-even sd-shell nuclei, namely {sup 20}Ne, {sup 28}Si and {sup 32}S. Starting from a HF ground state obtained by exact angular-momentum projection, we use the RPA to study collective excitations. The transition strengths obtained from the RPA are projected to good angular momentum in an exact formalism, without resorting to popular approximations. We investigate the effect of deformed intrinsic states on giant resonances.
Rogers, Christopher K; Zhang, Ning Jackie
2017-02-13
Cardiovascular disease (CVD) is one of the most prevalent chronic diseases nationally and disproportionately affects low-income individuals. There are substantial disparities on CVD outcomes that stem from the lack of health insurance among low-income populations. The Affordable Care Act expands Medicaid health insurance to low-income populations, and aims to increase the utilization of health, social, and economic preventive services to reduce health disparities and prevent chronic diseases. The authors analyzed data from the 2014 Behavioral Risk Factor Surveillance System to understand the potential impact of Medicaid expansion on disparities in CVD among low-income populations. Logistic regression models examined the association between CVD self-reported outcomes among low-income adults with incomes at or below 138% of the federal poverty level in states that have chosen to expand Medicaid and those states choosing not to expand, controlling for socioeconomic, demographic, behavioral, social, and health variables that affect CVD. Overall, the results show that adults in Medicaid expansion states have significantly lower odds of experiencing poor heart health compared to those in non-Medicaid expansion states (odds ratio = 0.767, 95% confidence interval 0.667-0.882). Additionally, significant findings were found between the association of CVD and demographic, socioeconomic, health, and health behavioral covariates. Policy makers should consider policies, systems, and interventions that increase access to a comprehensive set of preventive, population health, and socioeconomic services targeting the key determinants of CVD and other outcomes when expanding Medicaid and designing state plans and waivers.
Discrete Parametric Oscillation and Nondiffracting Beams in a Glauber-Fock Oscillator
Oztas, Z
2016-01-01
We consider a Glauber-Fock oscillator and show that diffraction can be managed. We show how to design arrays of waveguides where light beams experience zero diffraction. We find an exact analytical family of nondiffracting localized solution. We predict discrete parametric oscillation in the Glauber-Fock oscillator.
Hellweg, Arnim
2016-01-01
Hartree--Fock theory is one of the most ancient methods of computational chemistry, but up to the present day quantum chemical calculations on Hartree--Fock level or with hybrid density functional theory can be excessively time consuming. We compare three currently available techniques to reduce the computational demands of such calculations in terms of timing and accuracy.
Restricted Closed Shell Hartree Fock Roothaan Matrix Method Applied to Helium Atom Using Mathematica
Acosta, César R.; Tapia, J. Alejandro; Cab, César
2014-01-01
Slater type orbitals were used to construct the overlap and the Hamiltonian core matrices; we also found the values of the bi-electron repulsion integrals. The Hartree Fock Roothaan approximation process starts with setting an initial guess value for the elements of the density matrix; with these matrices we constructed the initial Fock matrix.…
Giladi, Aviram M; Aliu, Oluseyi; Chung, Kevin C
2014-05-01
Understanding the benefits of Medicaid is crucial as states decide whether to expand Medicaid under the Patient Protection and Affordable Care Act. We used the 2001 Medicaid expansion in New York to evaluate changes in use by Medicaid beneficiaries and the uninsured of breast cancer reconstruction, panniculectomy, and lower-extremity trauma management. Data for all patients 19 to 64 years old having undergone the selected procedures between 1998 and 2006 were obtained from the State Inpatient Database. We used an interrupted time series using variance weighted least squares regression to evaluate the effect of Medicaid expansion on the probability that Medicaid beneficiaries or uninsured patients received the procedures. We also determined the predicted use had there been no expansion. New York Census data were used for population-adjusted case-volume calculations. Likelihood of Medicaid as the primary payer increased significantly after expansion, 0.34% per quarter (95% CI, 0.28-0.40), without a decrease in uninsured patients receiving these procedures. This resulted in a 7.2% increase in the proportion of Medicaid beneficiaries receiving these procedures, an additional 1.9 Medicaid cases per quarter per 100,000 New York residents. In subgroup analysis, the proportion of Medicaid beneficiaries increased for breast reconstruction (0.28% per quarter; 95% CI, 0.21-0.35) and panniculectomy (0.19% per quarter; 95% CI, 0.1-0.28) without a decrease for the uninsured. Lower-extremity trauma procedures had a decreasing trend in use by uninsured patients with a slight increase for Medicaid beneficiaries (not significant). Subspecialty surgeons responded to expansion by increasing volume of procedures for Medicaid beneficiaries. This occurred without decline in care for the uninsured, suggesting that Medicaid expansion resulted in increased access for underserved patients. Although more patients received needed care once they had coverage, subgroup analysis identified
On Blowup for time-dependent generalized Hartree-Fock equations
Hainzl, Christian; Lewin, Mathieu; Schlein, Benjamin
2009-01-01
We prove finite-time blowup for spherically symmetric and negative energy solutions of Hartree-Fock and Hartree-Fock-Bogoliubov type equations, which describe the evolution of attractive fermionic systems (e. g. white dwarfs). Our main results are twofold: First, we extend the recent blowup result of [Hainzl and Schlein, Comm. Math. Phys. \\textbf{287} (2009), 705--714] to Hartree-Fock equations with infinite rank solutions and a general class of Newtonian type interactions. Second, we show the existence of finite-time blowup for spherically symmetric solutions of a Hartree-Fock-Bogoliubov model, where an angular momentum cutoff is introduced. We also explain the key difficulties encountered in the full Hartree-Fock-Bogoliubov theory.
Testing Machine for Expansive Mortar
Silva, Romulo Augusto Ventura
2011-01-01
The correct evaluation of a material property is fundamental to, on their application; they met all expectations that were designed for. In development of an expansive cement for ornamental rocks purpose, was denoted the absence of methodologies and equipments to evaluate the expansive pressure and temperature of expansive cement during their expansive process, having that data collected in a static state of the specimen. In that paper, is described equipment designed for evaluation of pressure and temperature of expansive cements applied to ornamental rocks.
On the problem of representability and the Bogolyubov-Hartree-Fock theory
Energy Technology Data Exchange (ETDEWEB)
Knoerr, Hans Konrad
2013-11-22
The general topic of this thesis is an approximation of the ground state energy for many-particle quantum systems. In particular the Bogolyubov-Hartree-Fock theory and the representability of one- and two-particle density matrices are studied. After an introductory chapter we specify some basic notation of many-body quantum mechanics in Chapter 2. In Chapter 3 we consider boson, as well as fermion systems. We first tackle the question of representability for bosons, i.e., the question which conditions a one- and a two-particle operator must satisfy to ensure that they are the one- and the two-particle density matrix of a state. For a particle number-conserving system, the representability conditions up to second order for bosons are well-known and called admissibility, P-, and G-conditions. Since, however, most physical systems consisting of bosons are not particle number-conserving, we give an alternative for such systems: Generalizing the two-particle density matrix, we observe that the representability conditions up to second order hold if and only if this generalized two-particle density matrix is positive semi-definite and the one- and the two-particle density matrices fulfill trace class and symmetry conditions. Moreover, we study the Bogolyubov-Hartree-Fock energy of boson and fermion systems. We generalize Lieb's variational principle which in its original formulation holds for purely repulsive particle interactions for fermions only. Our second main result is the following: for bosons, as well as for fermions the infimum of the energy for a variation over pure quasifree states coincides with the one for a variation over all quasifree states under the assumption that the Hamiltonian is bounded below. In the last section of Chapter 3 we specify the relation between centered quasifree states and their corresponding generalized one-particle density matrix, which finds an application in the variational process in the Bogolyubov-Hartree-Fock theory. It is
Error estimates for the Skyrme-Hartree-Fock model
Erler, J
2014-01-01
There are many complementing strategies to estimate the extrapolation errors of a model which was calibrated in least-squares fits. We consider the Skyrme-Hartree-Fock model for nuclear structure and dynamics and exemplify the following five strategies: uncertainties from statistical analysis, covariances between observables, trends of residuals, variation of fit data, dedicated variation of model parameters. This gives useful insight into the impact of the key fit data as they are: binding energies, charge r.m.s. radii, and charge formfactor. Amongst others, we check in particular the predictive value for observables in the stable nucleus $^{208}$Pb, the super-heavy element $^{266}$Hs, $r$-process nuclei, and neutron stars.
Computational Nuclear Physics and Post Hartree-Fock Methods
Lietz, Justin; Jansen, Gustav R; Hagen, Gaute; Hjorth-Jensen, Morten
2016-01-01
We present a computational approach to infinite nuclear matter employing Hartree-Fock theory, many-body perturbation theory and coupled cluster theory. These lectures are closely linked with those of chapters 9, 10 and 11 and serve as input for the correlation functions employed in Monte Carlo calculations in chapter 9, the in-medium similarity renormalization group theory of dense fermionic systems of chapter 10 and the Green's function approach in chapter 11. We provide extensive code examples and benchmark calculations, allowing thereby an eventual reader to start writing her/his own codes. We start with an object-oriented serial code and end with discussions on strategies for porting the code to present and planned high-performance computing facilities.
A Quantum Probability Explanation in Fock Space for Borderline Contradictions
Sozzo, Sandro
2013-01-01
The construction of a consistent theory for structuring and representing how concepts combine and interact is one of the main challenges for the scholars involved in cognitive studies. All traditional approaches are still facing serious hindrances when dealing with combinations of concepts and concept vagueness. One of the main consequences of these difficulties is the existence of borderline cases which is hardly explainable from the point of view of classical (fuzzy set) logic and probability theory. Resting on a quantum-theoretic approach which successfully models conjunctions and disjuncions of two concepts, we propound a quantum probability model in Fock space which faithfully reproduces the experimental data collected by Alxatib and Pelletier (2011) on borderline contradictions. Our model allows one to explain the occurrence of the latter contradictions in terms of genuine quantum effects, such as contextuality, superposition, interference and emergence. In particular, we claim that it is the specific m...
The Gogny-Hartree-Fock-Bogoliubov nuclear-mass model
Energy Technology Data Exchange (ETDEWEB)
Goriely, S. [Universite Libre de Bruxelles, Institut d' Astronomie et d' Astrophysique, CP-226, Brussels (Belgium); Hilaire, S.; Girod, M.; Peru, S. [CEA, DAM, DIF, Arpajon (France)
2016-07-15
We present the Gogny-Hartree-Fock-Bogoliubov model which reproduces nuclear masses with an accuracy comparable with the best mass formulas. In contrast to the Skyrme-HFB nuclear-mass models, an explicit and self-consistent account of all the quadrupole correlation energies is included within the 5D collective Hamiltonian approach. The final rms deviation with respect to the 2353 measured masses is 789 keV in the 2012 atomic mass evaluation. In addition, the D1M Gogny force is shown to predict nuclear and neutron matter properties in agreement with microscopic calculations based on realistic two- and three-body forces. The D1M properties and its predictions of various observables are compared with those of D1S and D1N. (orig.)
Emergence of new magic numbers, = 16 and 32 by tensor interaction in Skyrme–Hartree–Fock theory
Indian Academy of Sciences (India)
Rupayan Bhattacharya
2014-10-01
Melting of = 20 shell and development of = 16 and 32 shells for neutronrich nuclei have been studied extensively by including tensor interaction in Skyrme–Hartree–Fock theory optimized to reproduce the splitting $ 1 f$ shells of 40,48Ca and 56Ni nuclei. Evolution of gap generated by the energy difference of single-particle levels $v2s_{1/2}$ and $v1d_{3/2}$ has been found to be responsible for shell closure at = 16. The splitting pattern of spin–orbit partners 2 shell model state in Ca, Ti, Cr, Fe and Ni isotopes indicates the formation of a new shell at = 32 region.
A suggested periodic table up to Z≤ 172, based on Dirac-Fock calculations on atoms and ions.
Pyykkö, Pekka
2011-01-07
Extended Average Level (EAL) Dirac-Fock calculations on atoms and ions agree with earlier work in that a rough shell-filling order for the elements 119-172 is 8s Periodic Table develops further that of Fricke, Greiner and Waber [Theor. Chim. Acta 1971, 21, 235] by formally assigning the elements 121-164 to (nlj) slots on the basis of the electron configurations of their ions. Simple estimates are made for likely maximum oxidation states, i, of these elements M in their MX(i) compounds, such as i = 6 for UF(6). Particularly high i are predicted for the 6f elements.
Fock representations of Q-deformed commutation relations
BoŻejko, Marek; Lytvynov, Eugene; Wysoczański, Janusz
2017-07-01
We consider Fock representations of the Q-deformed commutation relations ∂s∂t†=Q (s ,t ) ∂t†∂s+δ (s ,t ) for s ,t ∈T . Here T :=Rd (or more generally T is a locally compact Polish space), the function Q :T2→C satisfies |Q (s ,t ) |≤1 and Q (s ,t ) =Q (t ,s ) ¯ , and ∫T2h (s ) g (t ) δ (s ,t ) σ (d s ) σ (d t ) :=∫Th (t ) g (t ) σ (d t ) , σ being a fixed reference measure on T. In the case, where |Q (s ,t ) |≡1 , the Q-deformed commutation relations describe a generalized statistics studied by Liguori and Mintchev. These generalized statistics contain anyon statistics as a special case (with T =R2 and a special choice of the function Q). The related Q-deformed Fock space F (H ) over H :=L2(T →C ,σ ) is constructed. An explicit form of the orthogonal projection of H⊗n onto the n-particle space Fn(H ) is derived. A scalar product in Fn(H ) is given by an operator Pn≥0 in H⊗n which is strictly positive on Fn(H ) . We realize the smeared operators ∂t† and ∂t as creation and annihilation operators in F (H ) , respectively. Additional Q-commutation relations are obtained between the creation operators and between the annihilation operators. They are of the form ∂s†∂t†=Q (t ,s ) ∂t†∂s†, ∂s∂t=Q (t ,s ) ∂t∂s, valid for those s ,t ∈T for which |Q(s, t)| = 1.
Fourier-Legendre expansion of the one-electron density-matrix of ground-state two-electron atoms
Ragot, Sebastien; Ruiz, Maria Belen
2009-01-01
The density-matrix rho(r, r') of a spherically symmetric system can be expanded as a Fourier-Legendre series of Legendre polynomials Pl(cos(theta) = r.r'/rr'). Application is here made to harmonically trapped electron pairs (i.e. Moshinsky's and Hooke's atoms), for which exact wavefunctions are known, and to the helium atom, using a near-exact wavefunction. In the present approach, generic closed form expressions are derived for the series coefficients of rho(r, r'). The series expansions are...
Barreto, Larissa; Schoorl, Jeroen M; Kok, Kasper; Veldkamp, Tom; Hass, Adriani
2013-01-30
In Brazil, agriculture expansion is taking place primarily in the Cerrado ecosystems. With the aim of supporting policy development and protecting the natural environment at relevant hotspots, a scenario study was conducted that concerned not only land-use change, but also the resulting effects on erosion and deposition. This coupled approach helped to evaluate potential landscape impacts of the land-use scenarios. In the study area, the Balsas sub-basin in Maranhão State, a model chain was used to model plausible future soybean expansion locations (CLUE-S model) and resulting sediment mobilization patterns (LAPSUS model) for a business-as-usual scenario. In the scenario, more erosion occurred in areas where the conversion of natural vegetation into soybean cultivation is likely to take place, but the generated sediments tended to accumulate mainly within the conversion areas, thus limiting the offsite effects of the increased erosion. These results indicated that when agricultural expansion is kept away from rivers, Cerrado conversion will have only a limited impact on the sediment loads of local rivers. Where land-use changes are most concentrated are coincident with areas where more new sediments are generated (higher erosion) and where more sediments are re-deposited.
1970-10-01
sale: is disributici is unlimited = F’)RIWRD Seior Ignacio Soto, Rrecutive President, Instituto Mexicano del Cementc y Concreto , invited Mr. Bryant... Concreto , a.c., Kwidco, D. F., Mexico. Based on info.mation largely obtained from ACT Committee 223, Expansive ’ement. Concretes, ACI Journal, August 1Q70
Energy Technology Data Exchange (ETDEWEB)
Chenoweth, D R
1983-06-01
An ideal-gas, quasi-steady, duct-flow model previously formulated for small scale gas-transfer problems is extended to real gases via the van der Waals equation of state as well as general virial expansions. The model is applicable for an arbitrary series of ducting components where each is described empirically by total pressure and total temperature change correlations. The adequacy of the van der Waals model for gas-transfer calculations is verified by comparisons with: (1) real gas PVT data; (2) the magnitudes of the controlling effects; and (3) approximate limiting case solutions with numerical results using more accurate real-gas modeling. 25 figures.
Fock model and Segal-Bargmann transform for minimal representations of Hermitian Lie groups
DEFF Research Database (Denmark)
Hilgert, Joachim; Kobayashi, Toshiyuki; Möllers, Jan;
2012-01-01
For any Hermitian Lie group G of tube type we construct a Fock model of its minimal representation. The Fock space is defined on the minimal nilpotent K_C-orbit X in p_C and the L^2-inner product involves a K-Bessel function as density. Here K is a maximal compact subgroup of G, and g_C=k_C+p_C i...... intertwines the Schroedinger and Fock model. Its kernel involves the same I-Bessel function. Using the Segal--Bargmann transform we also determine the integral kernel of the unitary inversion operator in the Schroedinger model which is given by a J-Bessel function....
2-D Hartee-Fock-Bogoliubov Calculations For Exotic Deformed Nuclei
Blazkiewicz, Artur; Oberacker, Volker E.; Umar, Sait A.; Teran, Edgar
2003-10-01
We solve the Hartree-Fock-Bogoliubov (HFB) equations in coordinate space; the computational method has been specifically designed to study ground state properties of nuclei near the neutron and proton drip lines teref1. The unique feature of our code is that it takes into account the strong coupling to high-energy continuum states, up to an equivalent single-particle energy of 60 MeV or higher. We solve the HFB equations for deformed, axially symmetric even-even nuclei in coordinate space on a 2-D lattice with Basis-Spline methods. For the p-h channel, the Skyrme (SLy4) effective N-N interaction is utilized, and for the p-p and h-h channel we use a delta interaction. Results teref2,ref3 are presented for binding energies, deformations, normal densities and pairing densities, Fermi levels, and pairing gaps. In particular, we calculate the properties of two light isotope chains up to the two-neutron dripline: oxygen (^22-28O) and sulfur (^40-52S). For some of the sulfur isotopes we found the "shape coexistence" what was also confirmed by RMF calculations of P. Ring and G.A. Lalazissis teref4. Furthermore, we study the strongly deformed heavy systems zirconium (^102,104Zr), cerium (^152Ce), and samarium (^158Sm).We are also planning to study other isotopes by running our new parallel MPI version of HFB code. Comparison with relativistic mean field theory and with experimental data is given whenever available. This work has been supported by the U.S. Department of Energy under grant No. DE-FG02-96ER40963 with Vanderbilt University. The numerical calculations were carried out on the IBM-RS/6000 SP supercomputer at NERSC in Berkeley and on our local "Beowulf" Vampire computer at Vanderbilt University. 99 ref1 Axially Symmetric Hartee-Fock-Bogoliubov calculations for nuclei near the drip lines,E. Teran, V.E. Oberacker and A.S. Umar, Phys. Rev. C 67, (June 2003) ref2 Half lives of isomeric states from SF of ^252Cf and large deformations in ^104Zr and ^158Sm, J.K. Hwang, A
Dobaczewski, J.; Olbratowski, P.
2005-05-01
-range interaction, allows for a simple implementation of pairing effects within the Hartree-Fock-Bogolyubov method. Solution method: The program uses the Cartesian harmonic-oscillator basis to expand single-particle or single-quasiparticle wave functions of neutrons and protons interacting by means of the Skyrme effective interaction and zero-range pairing interaction. The expansion coefficients are determined by the iterative diagonalization of the mean field Hamiltonians or Routhians which depend non-linearly on the local neutron and proton densities. Suitable constrains are used to obtain states corresponding to a given configuration, deformation or angular momentum. The method of solution has been presented in [J. Dobaczewski, J. Dudek, Comput. Phys. Comm. 102 (1997) 166]. Summary of revisions: 1. Incorrect value of the " t" force parameter for SLY5 has been corrected. 2. Opening of an empty file "FILREC" for IWRIRE=-1 has been removed. 3. Call to subroutine "OLSTOR" has been moved before that to "SPZERO". In this way, correct data transferred to "FLISIG", "FLISIM", "FLISIQ" or "FLISIZ" allow for a correct determination of the candidate states for diabatic blocking. These corrections pertain to the user interface of the code and do not affect results performed for forces other than SLY5. Restrictions on the complexity of the problem: The main restriction is the CPU time required for calculations of heavy deformed nuclei and for a given precision required. Pairing correlations are only included for even-even nuclei and conserved simplex symmetry. Unusual features: The user must have access to the NAGLIB subroutine F02AXE or to the LAPACK subroutines ZHPEV or ZHPEVX, which diagonalize complex Hermitian matrices, or provide another subroutine which can perform such a task. The LAPACK subroutines ZHPEV and ZHPEVX can be obtained from the Netlib Repository at University of Tennessee, Knoxville: http://netlib2.cs.utk.edu/cgi-bin/netlibfiles.pl?filename=/lapack/complex16/zhpev.f and
Uniqueness of the Fock quantization of Dirac fields in 2+1 dimensions
Cortez, Jerónimo; Martín-Benito, Mercedes; Marugán, Guillermo A Mena; Velhinho, José M
2016-01-01
We study the Fock quantization of a free Dirac field in 2+1-dimensional backgrounds which are conformally ultrastatic, with a time-dependent conformal factor. As it is typical for field theories, there is an infinite ambiguity in the Fock representation of the canonical anticommutation relations. Different choices may lead to unitarily inequivalent theories that describe different physics. To remove this ambiguity one usually requires that the vacuum be invariant under the unitary transformations that implement the symmetries of the equations of motion. However, in non-stationary backgrounds, where time translation is not a symmetry transformation, the requirement of vacuum invariance is in general not enough to fix completely the Fock representation. We show that this problem is overcome in the considered scenario by demanding, in addition, a unitarily implementable quantum dynamics. The combined imposition of these conditions selects a unique family of equivalent Fock representations. Moreover, one also obt...
The origin of linear scaling Fock matrix calculation with density prescreening
Energy Technology Data Exchange (ETDEWEB)
Mitin, Alexander V., E-mail: mitin@phys.chem.msu.ru [Chemistry Department, Moscow State University, Moscow, 119991 (Russian Federation)
2015-12-31
A theorem was proven, which reads that the number of nonzero two-electron integrals scales linearly with respect to the number of basis functions for large molecular systems. This permits to show that linear scaling property of the Fock matrix calculation with using density prescreening arises due to linear scaling properties of the number of nonzero two-electron integrals and the number of leading matrix elements of density matrix. This property is reinforced by employing the density prescreening technique. The use of the density difference prescreening further improves the linear scaling property of the Fock matrix calculation method. As a result, the linear scaling regime of the Fock matrix calculation can begin from the number of basis functions of 2000–3000 in dependence on the basis function type in molecular calculations. It was also shown that the conventional algorithm of Fock matrix calculation from stored nonzero two-electron integrals with density prescreening possesses linear scaling property.
Iso-spin Dependent Microscopic Optical Model Potential Based on Dirac Bruckner Haretree Fock Method
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
The microscopic optical model is investigated in the Dirac-Brueckner-Hartree-Fock (DBHF) framework with Bonn B meson exchange potential. Both real and imaginary parts of isospin-dependent self-energies are derived from a strict projection
Fock space resolutions of the Virasoro highest weight modules with c<=1
Bouwknegt, P; Pilch, K; Bouwknegt, Peter; Carthy, Jim Mc; Pilch, Krzysztof
1991-01-01
We extend Felder's construction of Fock space resolutions for the Virasoro minimal models to all irreducible modules with $c\\leq 1$. In particular, we provide resolutions for the representations corresponding to the boundary and exterior of the Kac table.
Heisenberg Algebra in the Bargmann-Fock Space with Natural Cutoffs
Directory of Open Access Journals (Sweden)
Maryam Roushan
2014-01-01
Full Text Available We construct a Heisenberg algebra in Bargmann-Fock space in the presence of natural cutoffs encoded as minimal length, minimal momentum, and maximal momentum through a generalized uncertainty principle.
Quantum stopping times stochastic integral in the interacting Fock space
Energy Technology Data Exchange (ETDEWEB)
Kang, Yuanbao, E-mail: kangyuanb@163.com [College of Mathematics Science, Chong Qing Normal University, Chongqing 400047 (China)
2015-08-15
Following the ideas of Hudson [J. Funct. Anal. 34(2), 266-281 (1979)] and Parthasarathy and Sinha [Probab. Theory Relat. Fields 73, 317-349 (1987)], we define a quantum stopping time (QST, for short) τ in the interacting Fock space (IFS, for short), Γ, over L{sup 2}(ℝ{sup +}), which is actually a spectral measure in [0, ∞] such that τ([0, t]) is an adapted process. Motivated by Parthasarathy and Sinha [Probab. Theory Relat. Fields 73, 317-349 (1987)] and Applebaum [J. Funct. Anal. 65, 273-291 (1986)], we also develop a corresponding quantum stopping time stochastic integral (QSTSI, for abbreviations) on the IFS over a subspace of L{sup 2}(ℝ{sup +}) equipped with a filtration. As an application, such integral provides a useful tool for proving that Γ admits a strong factorisation, i.e., Γ = Γ{sub τ]} ⊗ Γ{sub [τ}, where Γ{sub τ]} and Γ{sub [τ} stand for the part “before τ” and the part “after τ,” respectively. Additionally, this integral also gives rise to a natural composition operation among QST to make the space of all QSTs a semigroup.
Auxiliary Density Matrix Methods for Hartree-Fock Exchange Calculations.
Guidon, Manuel; Hutter, Jürg; VandeVondele, Joost
2010-08-10
The calculation of Hartree-Fock exchange (HFX) is computationally demanding for large systems described with high-quality basis sets. In this work, we show that excellent performance and good accuracy can nevertheless be obtained if an auxiliary density matrix is employed for the HFX calculation. Several schemes to derive an auxiliary density matrix from a high-quality density matrix are discussed. Key to the accuracy of the auxiliary density matrix methods (ADMM) is the use of a correction based on standard generalized gradient approximations for HFX. ADMM integrates seamlessly in existing HFX codes and, in particular, can be employed in linear scaling implementations. Demonstrating the performance of the method, the effect of HFX on the structure of liquid water is investigated in detail using Born-Oppenheimer molecular dynamics simulations (300 ps) of a system of 64 molecules. Representative for large systems are calculations on a solvated protein (Rubredoxin), for which ADMM outperforms the corresponding standard HFX implementation by approximately a factor 20.
A collisional extension of time-dependent Hartree-Fock
Lacombe, L.; Reinhard, P.-G.; Dinh, P. M.; Suraud, E.
2016-12-01
We propose a collisional extension of time-dependent mean-field theories on the basis of a recently proposed stochastic extension of mean-field dynamics (stochastic time-dependent Hartree-Fock, STDHF). The latter theory is unfortunately too involved to envision practical applications in realistic systems in the near future and is thus bound to model systems. It is also hard to explore moderate to low energies with STDHF, because of vanishing transition probabilities that are impossible to sample properly. For such moderately excited situations covering small fluctuations, we compactify sampling by employing the same average mean field for all STDHF trajectories. The new approach, coined average STDHF (ASTDHF), ignores the fluctuations of the mean field but still accounts correctly for the collisional correlations responsible for dissipative features on top of mean-field dynamics. We detail the main features of the new approach in relation to existing equations, in particular quantum kinetic theories. The new theory is directly connected to STDHF, both formally and practically. We thus discuss in detail how the two approaches are related to each other. We apply the new scheme to illustrative examples taking as benchmark STDHF dynamics in 1D. ASTDHF provides results that are in remarkable agreement with the more elaborate STDHF. It makes it a promising approach to deal with dissipative dynamics in finite quantum systems, because of its moderate cost allowing applications in realistic systems and the possibility of exploring any excitation energy range where collisional correlations are expected to play a role.
Spectrum of the [Formula: see text]-Neumann Laplacian on the Fock space.
Haslinger, Friedrich
2013-06-15
The spectrum of the [Formula: see text]-Neumann Laplacian on the Fock space [Formula: see text] is explicitly computed. It turns out that it consists of positive integer eigenvalues, each of which is of infinite multiplicity. Spectral analysis of the [Formula: see text]-Neumann Laplacian on the Fock space is closely related to Schrödinger operators with magnetic fields and to the complex Witten Laplacian.
Fock-exchange for periodic structures in the real-space formalism and the KLI approximation.
Natan, Amir
2015-12-21
The calculation of Fock-exchange interaction is an important task in the computation of molecule and solid properties. In this work we describe how we implement the Fock exchange in the real-space formalism using the KLI approximation for the OEP equation for 3D periodic systems. The implementation is demonstrated within the PARSEC real-space pseudopotential code that uses a discrete uniform grid and norm conserving pseudopotentials for the ionic potentials.
Momentum distribution of relativistic nuclei with Hartree-Fock mesonic correlations
Energy Technology Data Exchange (ETDEWEB)
Amaro, J.E. [Departamento de Fisica Moderna, Universidad de Granada, E-18071 Granada (Spain); Barbaro, M.B. [Dipartimento di Fisica Teorica, Universita di Torino and INFN, Sezione di Torino, Via P. Giuria 1, 10125 Torino (Italy); Departamento de Fisica Atomica, Molecular y Nuclear Universidad de Sevilla, Apdo. 1065, E-41080 Sevilla (Spain); Caballero, J.A. [Departamento de Fisica Atomica, Molecular y Nuclear Universidad de Sevilla, Apdo. 1065, E-41080 Sevilla (Spain); Donnelly, T.W. [Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Molinari, A. [Dipartimento di Fisica Teorica, Universita di Torino and INFN, Sezione di Torino, Via P. Giuria 1, 10125 Torino (Italy)
2002-12-01
The impact of Hartree-Fock correlations on the nuclear momentum distribution is studied in a fully relativistic one-boson-exchange model. Hartree-Fock equations are exactly solved to first order in the coupling constants. The renormalization of the Dirac spinors in the medium is shown to affect the momentum distribution, as opposed to what happens in the non-relativistic case. The unitarity of the model is shown to be preserved by the present renormalization procedure. (orig.)
Generalized Hartree-Fock-Bogoliubov description of the Fröhlich polaron
Kain, Ben; Ling, Hong Y.
2016-07-01
We adapt the generalized Hartree-Fock-Bogoliubov (HFB) method to an interacting many-phonon system free of impurities. The many-phonon system is obtained from applying the Lee-Low-Pine (LLP) transformation to the Fröhlich model which describes a mobile impurity coupled to noninteracting phonons. We specialize our general HFB description of the Fröhlich polaron to Bose polarons in quasi-one-dimensional cold-atom mixtures. The LLP-transformed many-phonon system distinguishes itself with an artificial phonon-phonon interaction which is very different from the usual two-body interaction. We use the quasi-one-dimensional model, which is free of an ultraviolet divergence that exists in higher dimensions, to better understand how this unique interaction affects polaron states and how the density and pair correlations inherent to the HFB method conspire to create a polaron ground state with an energy in good agreement with and far closer to the prediction from Feynman's variational path integral approach than mean-field theory where HFB correlations are absent.
Embedding qubits into fermionic Fock space, peculiarities of the four-qubit case
Lévay, Péter
2015-01-01
We give a fermionic Fock space description of embedded entangled qubits. Within this framework the problem of classification of pure state entanglement boils down to the problem of classifying spinors. The usual notion of separable states turns out to be just a special case of the one of pure spinors. By using the notion of single, double and mixed occupancy representation with intertwiners relating them a natural physical interpretation of embedded qubits is found. As an application of these ideas one can make a physically sound meaning of some of the direct sum structures showing up in the context of the so-called Black-Hole/Qubit Correspondence. We discuss how the usual invariants for qubits serving as measures of entanglement can be obtained from invariants for spinors in an elegant manner. In particular a detailed case study for recovering the invariants for four-qubits within a spinorial framework is presented. We also observe that reality conditions on complex spinors defining Majorana spinors for embe...
Greenman, Loren; Haxton, Daniel J; McCurdy, C William
2016-01-01
We have verified a mechanism for Raman excitation of atoms through continuum levels previously obtained by quantum optimal control using the multi-configurational time-dependent Hartree-Fock (MCTDHF) method. This mechanism, which was obtained at the time-dependent configuration interaction singles (TDCIS) level of theory, involves sequentially exciting an atom from the ground state to an intermediate core-hole state using a long pump pulse, and then transferring this population to the target Raman state with a shorter Stokes pulse. This process represents the first step in a multidimensional x-ray spectroscopy scheme that will provide a local probe of valence electronic correlations. Although at the optimal pulse intensities at the TDCIS level of theory the MCTDHF method predicts multiple ionization of the atom, at slightly lower intensities (reduced by a factor of about 4) the TDCIS mechanism is shown to hold qualitatively. Quantitatively, the MCTDHF populations are reduced from the TDCIS calculations by a f...
Energy Technology Data Exchange (ETDEWEB)
Smeyers, Y.G.; Delgado-Barrio, G.
1976-05-01
The half-projected Hartree--Fock function for singlet states (HPHF) is analyzed in terms of natural electronic configurations. For this purpose the HPHF spinless density matrix and its natural orbitals are first deduced. It is found that the HPHF function does not contain any contribution from odd-times excited configurations. It is seen in addition, in the case of the singlet ground states, this function is approximately equivalent to two closed-shell configurations, although the nature of the excited one depends on the nuclear geometry. An example is given in the case of the LiH ground state. Finally, the application of this model for studying systems of more than two atoms is criticized.
Buica, Gabriela; 10.1016/j.jqsrt.2007.05.004
2013-01-01
We theoretically study multiphoton ionization of Mg in the circularly as well as the linearly polarized laser fields. Specifically two-, three-, and four-photon ionization cross sections from the ground and first excited states are calculated as a function of photon energy. Calculations are performed using the frozen-core Hartree-Fock and also the model potential approaches and the results are compared. We find that the model potential approach provide results as good as or even slightly better than those by the frozen-core Hartree-Fock approach. We also report the relative ratios of the ionization cross sections by the circularly and linearly polarized laser fields as a function of photon energy, which exhibit clear effects of electron correlations.
Energy Technology Data Exchange (ETDEWEB)
Li, Xiaoma; Zhou, Yuyu; Asrar, Ghassem R.; Imhoff, Marc; Li, Xuecao
2017-12-01
Abstract: Urban heat island (UHI), a major concern worldwide, affects human health and energy use. With current and anticipated rapid urbanization, improved understanding of the response of UHI to urbanization is important for impact analysis and developing effective adaptation measures and mitigation strategies. Current studies mainly focus on a single or a few big cities and knowledge on the response of UHI to urbanization for large areas is very limited. Modelling UHI caused by urbanization for large areas that encompass multiple metropolitans remains a major scientific challenge/opportunity. As a major indicator of urbanization, urban area size lends itself well for representation in prognostic models to investigate the impacts of urbanization on UHI and the related socioeconomic and environmental effects. However, we have little knowledge on how UHI responds to the increase of urban area size, namely urban expansion, and its spatial and temporal variation over large areas. In this study, we investigated the relationship between surface UHI (SUHI) and urban area size in the climate and ecological context, and its spatial and temporal variations, based on a panel analysis of about 5000 urban areas of 10 km2 or larger, in the conterminous U.S. We found statistically significant positive relationship between SUHI and urban area size, and doubling the urban area size led to a SUHI increase of higher than 0.7 °C. The response of SUHI to the increase of urban area size shows spatial and temporal variations, with stronger SUHI increase in the Northern region of U.S., and during daytime and summer. Urban area size alone can explain as much as 87% of the variance of SUHI among cities studied, but with large spatial and temporal variations. Urban area size shows higher association with SUHI in regions where the thermal characteristics of land cover surrounding the urban are more homogeneous, such as in Eastern U.S., and in the summer months. This study provides a
Energy Technology Data Exchange (ETDEWEB)
Kupka, T.; Ruscic, B.; Botto, R. E.; Chemistry
2003-05-01
The nuclear shielding anisotropy and shielding tensor components calculated using the hybrid density functional B3PW91 are reported for a model set of compounds comprised of N{sub 2}, NH{sub 3}, CH{sub 4}, C{sub 2}H{sub 4}, HCN and CH{sub 3}CN. An estimation of density functional theory (DFT) and Hartree-Fock complete basis-set limit (CBS) parameters from a 2 (3) point exact fit vs. least-squares fit was obtained with the cc-pVxZ and aug-cc-pVxZ basis sets (x=D, T, Q, 5, 6). Both Hartree-Fock- and DFT-predicted CBS shielding anisotropies and shielding tensor components of the model molecules were in reasonable agreement with available experimental data. The utility of using a limited CBS approach for calculating accurate anisotropic shielding parameters of larger molecules as complementary methods to solid-state NMR is proposed.
Cui, Yao; Bulik, Ireneusz W; Jiménez-Hoyos, Carlos A; Henderson, Thomas M; Scuseria, Gustavo E
2013-10-21
We study the spectra of the molecular orbital Hessian (stability matrix) and random-phase approximation (RPA) Hamiltonian of broken-symmetry Hartree-Fock solutions, focusing on zero eigenvalue modes. After all negative eigenvalues are removed from the Hessian by following their eigenvectors downhill, one is left with only positive and zero eigenvalues. Zero modes correspond to orbital rotations with no restoring force. These rotations determine states in the Goldstone manifold, which originates from a spontaneously broken continuous symmetry in the wave function. Zero modes can be classified as improper or proper according to their different mathematical and physical properties. Improper modes arise from symmetry breaking and their restoration always lowers the energy. Proper modes, on the other hand, correspond to degeneracies of the wave function, and their symmetry restoration does not necessarily lower the energy. We discuss how the RPA Hamiltonian distinguishes between proper and improper modes by doubling the number of zero eigenvalues associated with the latter. Proper modes in the Hessian always appear in pairs which do not double in RPA. We present several pedagogical cases exemplifying the above statements. The relevance of these results for projected Hartree-Fock methods is also addressed.
Balaban, Victor; Marks, Suzanne M; Etkind, Sue C; Katz, Dolly J; Higashi, Julie; Flood, Jennifer; Cronin, Ann; Ho, Christine S; Khan, Awal; Chorba, Terence
2015-01-01
The Patient Protection and Affordable Care Act can enhance ongoing efforts to control tuberculosis (TB) in the United States by bringing millions of currently uninsured Americans into the health-care system. However, much of the legislative and financial framework that provides essential public health services necessary for effective TB control is outside the scope of the law. We identified three key issues that will still need to be addressed after full implementation of the Affordable Care Act: (1) essential TB-related public health functions will still be needed and will remain the responsibility of federal, state, and local health departments; (2) testing and treatment for latent TB infection (LTBI) is not covered explicitly as a recommended preventive service without cost sharing or copayment; and (3) remaining uninsured populations will disproportionately include groups at high risk for TB. To improve and continue TB control efforts, it is important that all populations at risk be tested and treated for LTBI and TB; that testing and treatment services be accessible and affordable; that essential federal, state, and local public health functions be maintained; that private-sector medical/public health linkages for diagnosis and treatment be developed; and that health-care providers be trained in conducting appropriate LTBI and TB clinical care.
Energy Technology Data Exchange (ETDEWEB)
Kuwahara, Riichi [Department of Physics, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501 (Japan); Accelrys K. K., Kasumigaseki Tokyu Building 17F, 3-7-1 Kasumigaseki, Chiyoda-ku, Tokyo 100-0013 (Japan); Tadokoro, Yoichi; Ohno, Kaoru, E-mail: ohno@ynu.ac.jp [Department of Physics, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501 (Japan)
2014-08-28
In this paper, we calculate kinetic and potential energy contributions to the electronic ground-state total energy of several isolated atoms (He, Be, Ne, Mg, Ar, and Ca) by using the local density approximation (LDA) in density functional theory, the Hartree–Fock approximation (HFA), and the self-consistent GW approximation (GWA). To this end, we have implemented self-consistent HFA and GWA routines in our all-electron mixed basis code, TOMBO. We confirm that virial theorem is fairly well satisfied in all of these approximations, although the resulting eigenvalue of the highest occupied molecular orbital level, i.e., the negative of the ionization potential, is in excellent agreement only in the case of the GWA. We find that the wave function of the lowest unoccupied molecular orbital level of noble gas atoms is a resonating virtual bound state, and that of the GWA spreads wider than that of the LDA and thinner than that of the HFA.
Kuwahara, Riichi; Tadokoro, Yoichi; Ohno, Kaoru
2014-08-28
In this paper, we calculate kinetic and potential energy contributions to the electronic ground-state total energy of several isolated atoms (He, Be, Ne, Mg, Ar, and Ca) by using the local density approximation (LDA) in density functional theory, the Hartree-Fock approximation (HFA), and the self-consistent GW approximation (GWA). To this end, we have implemented self-consistent HFA and GWA routines in our all-electron mixed basis code, TOMBO. We confirm that virial theorem is fairly well satisfied in all of these approximations, although the resulting eigenvalue of the highest occupied molecular orbital level, i.e., the negative of the ionization potential, is in excellent agreement only in the case of the GWA. We find that the wave function of the lowest unoccupied molecular orbital level of noble gas atoms is a resonating virtual bound state, and that of the GWA spreads wider than that of the LDA and thinner than that of the HFA.
Nuclear Pasta at Finite Temperature with the Time-Dependent Hartree-Fock Approach
Schuetrumpf, B.; Klatt, M. A.; Iida, K.; Maruhn, J. A.; Mecke, K.; Reinhard, P.-G.
2016-01-01
We present simulations of neutron-rich matter at sub-nuclear densities, like supernova matter. With the time-dependent Hartree-Fock approximation we can study the evolution of the system at temperatures of several MeV employing a full Skyrme interaction in a periodic three-dimensional grid [1]. The initial state consists of α particles randomly distributed in space that have a Maxwell-Boltzmann distribution in momentum space. Adding a neutron background initialized with Fermi distributed plane waves the calculations reflect a reasonable approximation of astrophysical matter. The matter evolves into spherical, rod-like, connected rod-like and slab-like shapes. Further we observe gyroid-like structures, discussed e.g. in [2], which are formed spontaneously choosing a certain value of the simulation box length. The ρ-T-map of pasta shapes is basically consistent with the phase diagrams obtained from QMD calculations [3]. By an improved topological analysis based on Minkowski functionals [4], all observed pasta shapes can be uniquely identified by only two valuations, namely the Euler characteristic and the integral mean curvature. In addition we propose the variance in the cell-density distribution as a measure to distinguish pasta matter from uniform matter.
Qubit and Fermionic Fock Spaces from Type II Superstring Black Holes
Belhaj, A; Benslimane, Z; Sedra, M B; Segui, A
2016-01-01
Using Hodge diagram combinatorial data, we study qubit and fermionic Fock spaces from the point of view of type II superstring black holes based on complex compactifications. Concretely, we establish a one-to-one correspondence between qubits, fermionic spaces and extremal black holes in maximally supersymmetric supergravity obtained from type II superstring on complex toroidal and Calabi-Yau compactifications. We interpret the differential forms of the n-dimensional complex toroidal compactification as states of n-qubits encoding information on extremal black hole charges. We show that there are 2^n copies of n-qubit systems which can be split as 2^n=2^{n-1}+2^{n-1}. More precisely, 2^{n-1} copies are associated with even D-brane charges in type IIA superstring and the other 2^{n-1} ones correspond to odd D-brane charges in IIB superstring. This correspondence is generalized to a class of Calabi-Yau manifolds. In connection with black hole charges in type IIA superstring, an n-qubit system has been obtained ...
Basis set effects on the Hartree-Fock description of confined many-electron atoms
Garza, Jorge; Hernández-Pérez, Julio M.; Ramírez, José-Zeferino; Vargas, Rubicelia
2012-01-01
In this work, the basis sets designed by Clementi, Bunge and Thakkar, for atomic systems, have been used to obtain the electronic structure of confined many-electron atoms by using Roothaan's approach in the Hartree-Fock context with a new code written in C, which uses the message-passing interface library. The confinement was imposed as Ludeña suggested to simulate walls with infinity potential. For closed-shell atoms, the Thakkar basis set functions give the best total energies (TE) as a function of the confinement radius, obtaining the following ordering: TE(Thakkar) Clementi). However, for few open-shell atoms this ordering is not preserved and a trend, for the basis sets, is not observed. Although there are differences between the TE predicted by these basis set functions, the corresponding pressures are similar to each other; it means that changes in the total energy are described almost in the same way by using any of these basis sets. By analysing the total energy as a function of the inverse of the volume we propose an equation of state; for regions of small volumes, this equation predicts that the pressure is inversely proportional to the square of the volume.
A project based on multi-configuration Dirac-Fock calculations for plasma spectroscopy
Comet, M.; Pain, J.-C.; Gilleron, F.; Piron, R.
2017-09-01
We present a project dedicated to hot plasma spectroscopy based on a Multi-Configuration Dirac-Fock (MCDF) code, initially developed by J. Bruneau. The code is briefly described and the use of the transition state method for plasma spectroscopy is detailed. Then an opacity code for local-thermodynamic-equilibrium plasmas using MCDF data, named OPAMCDF, is presented. Transition arrays for which the number of lines is too large to be handled in a Detailed Line Accounting (DLA) calculation can be modeled within the Partially Resolved Transition Array method or using the Unresolved Transition Arrays formalism in jj-coupling. An improvement of the original Partially Resolved Transition Array method is presented which gives a better agreement with DLA computations. Comparisons with some absorption and emission experimental spectra are shown. Finally, the capability of the MCDF code to compute atomic data required for collisional-radiative modeling of plasma at non local thermodynamic equilibrium is illustrated. In addition to photoexcitation, this code can be used to calculate photoionization, electron impact excitation and ionization cross-sections as well as autoionization rates in the Distorted-Wave or Close Coupling approximations. Comparisons with cross-sections and rates available in the literature are discussed.
Brueckner-Hartree-Fock calculations for finite nuclei with renormalized realistic forces
Hu, B. S.; Xu, F. R.; Wu, Q.; Ma, Y. Z.; Sun, Z. H.
2017-03-01
One can adopt two-step G -matrix approximations for the Brueckner-Hartree-Fock (BHF) calculations. The first G matrix is to soften the bare force, and the second one is to include the high-order correlations of the interaction in medium. The first G -matrix calculation for two-nucleon interaction should be done in the center-of-mass coordinate. As another alternative BHF approach, we have adopted the Vlow-k technique to soften the interaction and used the G matrix to include high-order correlations. The Vlow-k renormalization leads to high-momentum and low-momentum components of the interaction decoupled. With the Vlow-k potential, we have performed the BHF calculations for finite nuclei. The G -matrix elements with exact Pauli exclusions are calculated in the self-consistent BHF basis. To see effects from further possible correlations beyond BHF, we have simultaneously performed renormalized BHF (RBHF) calculations with the same potential. In RBHF, the mean field derived from realistic forces is modified by introducing the particle-occupation depletion resulting from many-body correlations. The ground-state energies and radii of the closed-shell nuclei, 4He, 16O, and 40Ca, have been investigated. The convergences of the BHF and RBHF calculations have been discussed and compared with other ab initio calculations with the same potential.
Gellatly, Kyle J; Krim, Sarah; Palenchar, Daniel J; Shepherd, Katie; Yoon, Kyong Sup; Rhodes, Christopher J; Lee, Si Hyeock; Marshall Clark, J
2016-05-01
Pediculosis is a prevalent parasitic infestation of humans, which is increasing due, in part, to the selection of lice resistant to either the pyrethrins or pyrethroid insecticides by the knockdown resistance (kdr) mechanism. To determine the extent and magnitude of the kdr-type mutations responsible for this resistance, lice were collected from 138 collection sites in 48 U.S. states from 22 July 2013 to 11 May 2015 and analyzed by quantitative sequencing. Previously published data were used for comparisons of the changes in the frequency of the kdr-type mutations over time. Mean percent resistance allele frequency (mean % RAF) values across the three mutation loci were determined from each collection site. The overall mean % RAF (±SD) for all analyzed lice was 98.3 ± 10%. 132/138 sites (95.6%) had a mean % RAF of 100%, five sites (3.7%) had intermediate values, and only a single site had no mutations (0.0%). Forty-two states (88%) had a mean % RAF of 100%. The frequencies of kdr-type mutations did not differ regardless of the human population size that the lice were collected from, indicating a uniformly high level of resistant alleles. The loss of efficacy of the Nix formulation (Prestige Brand, Tarrytown, NY) from 1998 to 2013 was correlated to the increase in kdr-type mutations. These data provide a plausible reason for the decrease in the effectiveness of permethrin in the Nix formulation, which is the parallel increase of kdr-type mutations in lice over time. © The Authors 2016. Published by Oxford University Press on behalf of Entomological Society of America.
Level-0 action of $U_{q}(\\widehat{sl}_{n})$ on the q-deformed Fock spaces
Takemura, K; Takemura, Kouichi; Uglov, Denis
1996-01-01
On the level-1 Fock space modules of the algebra $U_q(\\hat{sl_n})$ we define a level-0 action $U_0$ of the $U_q(\\hat{sl_n})$, and an action of an abelian algebra of conserved Hamiltonians commuting with the $U_0$. An irreducible decomposition of the Fock space with respect to the level-0 action is derived by constructing a base of the Fock space in terms of the Non-symmetric Macdonald Polynomials.
Directory of Open Access Journals (Sweden)
CASTRO EUSTÁQUIO V. R. DE
2001-01-01
Full Text Available The generator coordinate Hartree-Fock method is used to generate adapted Gaussian basis sets for the atoms from Li (Z=3 through Xe (Z=54. In this method the Griffin-Hill-Wheeler-Hartree-Fock equations are integrated through the integral discretization technique. The wave functions generated in this work are compared with the widely used Roothaan-Hartree-Fock wave functions of Clementi and Roetti (1974, and with other basis sets reported in the literature. For all atoms studied, the errors in our total energy values relatively to the numerical Hartree-Fock limits are always less than 7.426 mhartree.
Potential Functions of Al2 by the Relativistic Fock-Space Coupled Cluster Method
Directory of Open Access Journals (Sweden)
Uzi Kaldor
2002-05-01
Full Text Available Abstract: Potential functions of the ground and low excited states of Al2 are calculated by the relativistic Fock-space coupled cluster method in the framework of the projected Dirac-Coulomb Hamiltonian. A moderate-size basis [16s11p3d3f/6s6p3d2f] is used. 3ÃŽÂ u is confirmed as the ground state of the system. Its spin orbit splittings are reproduced well, with the ÃŽÂ› = 1, 2 states lying 32.5 and 66.1 cmÃ¢ÂˆÂ’1, respectively, above the ÃŽÂ› = 0 minimum (experimental values are 30.4 and 63.4 cmÃ¢ÂˆÂ’1. The bond is somewhat too weak, with De 0.14 eV below experiment, Re too high by 0.08 Ã‹ÂšA, and ÃÂ‰e 21 cmÃ¢ÂˆÂ’1 too low. It is speculated that the better agreement obtained in earlier calculations may be due to neglect of basis set superposition errors. The description of bonding in the molecule may be improved by the use of a better basis and the inclusion of more correlation by the intermediate Hamiltonian coupled cluster method, which makes it possible to handle larger P spaces and extend the potential functions to the whole range of internuclear separations.
Study of superdeformation at zero spin with Skyrme-Hartree-Fock method
Energy Technology Data Exchange (ETDEWEB)
Takahara, S.; Tajima, N.; Onishi, N. [Tokyo Univ. (Japan)
1998-03-01
Superdeformed (SD) bands have been studied extensively both experimentally and theoretically in the last decade. Since the first observation in {sup 152}Dy in 1986, SD bands have been found in four mass regions, i.e., A {approx} 80, 130, 150 and 190. While these SD bands have been observed only at high spins so far, they may also be present at zero spin like fission isomers in actinide nuclei: The familiar generic argument on the strong shell effect at axis ratio 2:1 does not assume rotations. If non-fissile SD isomers exist at zero spin, they may be utilized to develop new experimental methods to study exotic states, in a similar manner as short-lived high-spin isomers are planned to be utilized as projectiles of fusion reactions in order to populate very high-spin near-yrast states. They will also be useful to test theoretical models whether the models can describe correctly the large deformations of rare-earth nuclei without further complications due to rotations. In this report, we employ the Skyrme-Hartree-Fock method to study the SD states at zero spin. First, we compare various Skyrme force parameter sets to test whether they can reproduce the extrapolated excitation energy of the SD band head of {sup 194}Hg. Second, we systematically search large-deformation solutions with the SkM{sup *} force. The feature of our calculations is that the single-particle wavefunctions are expressed in a three-dimensional-Cartesian-mesh representation. This representation enables one to obtain solutions of various shapes (including SD) without preparing a basis specific to each shape. Solving the mean-field equations in this representation requires, however, a large amount of computation which can be accomplished only with present supercomputers. (author)
Borovikov, Dmitry
2012-01-01
Features and parameters of \\boiling" liquid layer, which arises under conditions of isentropic expansion of warm dense matter (WDM), are stud- ied with the use of simplest van der Waals equation of state (EOS). Advan- tage of this EOS is possibility of demonstrable and semi-analytical descrip- tion of thermo- and hydrodynamics of the process. Idealized self-similar case of behavior of matter on interception of equilibrium (not metastable) isoentropic curve and boundary of gas-liquid coexistence curve (binodal) is analyzed. The possibility of formation of such "liquid layer" was studied previously in [1] during solving the problem of ablation of metal surface under the action of strong laser radiation. Peculiarity of such "freezing" of finite portion of expanding matter in the state, which corresponds to the binodal of gas-liquid or/and other phase transitions|so called "phase freezeout"and prospects of applications of this phenomenon for intended generation of uniform and extensive zone of previously unexplor...
Density of states from mode expansion of the self-dynamic structure factor of a liquid metal
Guarini, E.; Bellissima, S.; Bafile, U.; Farhi, E.; De Francesco, A.; Formisano, F.; Barocchi, F.
2017-01-01
We show that by exploiting multi-Lorentzian fits of the self-dynamic structure factor at various wave vectors it is possible to carefully perform the Q →0 extrapolation required to determine the spectrum Z (ω ) of the velocity autocorrelation function of a liquid. The smooth Q dependence of the fit parameters makes their extrapolation to Q =0 a simple procedure from which Z (ω ) becomes computable, with the great advantage of solving the problems related to resolution broadening of either experimental or simulated self-spectra. Determination of a single-particle property like the spectrum of the velocity autocorrelation function turns out to be crucial to understanding the whole dynamics of the liquid. In fact, we demonstrate a clear link between the collective mode frequencies and the shape of the frequency distribution Z (ω ) . In the specific case considered in this work, i.e., liquid Au, analysis of Z (ω ) revealed the presence, along with propagating sound waves, of lower frequency modes that were not observed before by means of dynamic structure factor measurements. By exploiting ab initio simulations for this liquid metal we could also calculate the transverse current-current correlation spectra and clearly identify the transverse nature of the above mentioned less energetic modes. Evidence of propagating transverse excitations has actually been reported in various works in the recent literature. However, in some cases, like the present one, these modes are difficult to detect in density fluctuation spectra. We show here that the analysis of the single-particle dynamics is able to unveil their presence in a very effective way. The properties here shown to characterize Z (ω ) , and the information in it contained therefore allow us to identify it with the density of states (DoS) of the liquid. We demonstrate that only nonhydrodynamic modes contribute to the DoS, thus establishing its purely microscopic origin. Finally, as a by-product of this work, we
Spectral structure and decompositions of optical states, and their applications
Rohde, P P; Silberhorn, C; Rohde, Peter P.; Mauerer, Wolfgang; Silberhorn, Christine
2006-01-01
We discuss the spectral structure and decomposition of multi-photon states. Ordinarily `multi-photon states' and `Fock states' are regarded as synonymous. However, when the spectral degrees of freedom are included this is not the case, and the class of `multi-photon' states is much broader than the class of `Fock' states. We discuss the criteria for a state to be considered a Fock state. We then address the decomposition of general multi-photon states into bases of orthogonal eigenmodes, building on existing multi-mode theory, and introduce an occupation number representation that provides an elegant description of such states that in many situations simplifies calculations. Finally we apply this technique to several example situations, which are highly relevant for state of the art experiments. These include Hong-Ou-Mandel interference, spectral filtering, finite bandwidth photo-detection, homodyne detection and the conditional preparation of Schr\\"odinger Kitten and Fock states. Our techniques allow for ver...
Zhou, Fuyang; Li, Jiguang; Wang, Jianguo
2015-01-01
The multi-configuration Dirac-Hartree-Fock method was employed to calculate the total and excitation energies, oscillator strengths and hyperfine structure constants for low-lying levels of Sm I. In the first-order perturbation approximation, we systematically analyzed correlation effects from each electrons and electron pairs. It was found that the core correlations are of importance for physical quantities concerned. Based on the analysis, the important configuration state wave functions were selected to constitute atomic state wave functions. By using this computational model, our excitation energies, oscillator strengths, and hyperfine structure constants are in better agreement with experimental values than earlier theoretical works.
Configuration interaction with Kohn Sham orbitals and their relation to excited electronic states
Bouř, Petr
2001-09-01
Kohn-Sham (KS) orbitals in CH 2, formaldehyde and acetone molecules were used as reference states for configuration interaction (CI) instead of the usual Hartree-Fock (HF) orbitals. A little difference in overall accuracy of electronic excitation energies was found between these schemes. However, analysis of the wave functions indicated that Slater determinant with the KS orbitals is more suitable for construction of the electronic states. Typically, the main expansion coefficients for the CI/KS procedure were closer to unity than those for HF. The difference was most pronounced for the lowest-energy transitions, while the two methods provided more comparable results for the higher-energy states. Similar behaviour of singlet and triplet states was observed. The results justify the common practice of using the KS determinant as a wave function, for example in sum-over-states theories.
Langhoff, S. R.; Scott, W. R.; Suzuki, N.; Chong, D. P.
1979-01-01
Ordinary Rayleigh-Schroudinger perturbation theory with Moller-Plesset (RSMP) partitioning is used to calculate second- and third-order correlation corrections to the CHF polarizability and dipole moment of the water molecule by a finite-field procedure. Pade approximants are found to be useful in accelerating the convergence of the property perturbation expansions. Field-induced polarization functions suitable for polarizability calculations are determined. The average polarizability calculated, neglecting vibrational averaging, with Dunning's (9s5p/4s-4s2p/2s) contracted GTO basis set augmented by field-induced lslp2d/lp polarization functions is within 3 per cent of the experimental result. Correlation corrections to the dipole moment and polarizability of the water molecule calculated by the finite-field RSMP and single + double excitation CI(SDCI) methods for the same basis set are found to be in close agreement. The RSMP approach has the advantages of being size-consistent and of being capable of greater efficiency than the SCDI method. Comparative calculations carried out using Epstein-Nesbet partitioning show that through third order RSEN correlation perturbation expansions for the dipole moment and polarizability are less rapidly convergent than RSMP expansions. However, reasonable accord with RSMP results can be achieved by using Pade approximants to accelerate the convergence of RSEN energy perturbation expansions. The convergence of RSMP property correlation expansions based on the zeroth-order uncoupled-Hartree-Fock (UCHF) and coupled-Hartree-Fock (CHF) approximations are compared through third order. Whereas the CHF + RSMP expansions are for practical purposes fully converged, the UCHF + RSMP expansions are not adequately converged.
Localized form of Fock terms in nuclear covariant density functional theory
Liang, Haozhao; Ring, Peter; Roca-Maza, Xavier; Meng, Jie
2012-01-01
In most of the successful versions of covariant density functional theory in nuclei, the Fock terms are not included explicitly, which leads to local functionals and forms the basis of their widespread applicability at present. However, it has serious consequences for the description of Gamow-Teller resonances (GTR) and spin-dipole resonances (SDR) which can only be cured by adding further phenomenological parameters. Relativistic Hartree-Fock models do not suffer from these problems. They can successfully describe the GTR and SDR as well as the isovector part of the Dirac effective mass without any additional parameters. However, they are non-local and require considerable numerical efforts. By the zero-range reduction and the Fierz transformation, a new method is proposed to take into account the Fock terms in local functionals, which retains the simplicity of conventional models and provides proper descriptions of the spin-isospin channels and the Dirac masses.
A finite-temperature Hartree-Fock code for shell-model Hamiltonians
Bertsch, G. F.; Mehlhaff, J. M.
2016-10-01
The codes HFgradZ.py and HFgradT.py find axially symmetric minima of a Hartree-Fock energy functional for a Hamiltonian supplied in a shell model basis. The functional to be minimized is the Hartree-Fock energy for zero-temperature properties or the Hartree-Fock grand potential for finite-temperature properties (thermal energy, entropy). The minimization may be subjected to additional constraints besides axial symmetry and nucleon numbers. A single-particle operator can be used to constrain the minimization by adding it to the single-particle Hamiltonian with a Lagrange multiplier. One can also constrain its expectation value in the zero-temperature code. Also the orbital filling can be constrained in the zero-temperature code, fixing the number of nucleons having given Kπ quantum numbers. This is particularly useful to resolve near-degeneracies among distinct minima.
Kalinowski, Jaroslaw; Wennmohs, Frank; Neese, Frank
2017-07-11
A resolution of identity based implementation of the Hartree-Fock method on graphical processing units (GPUs) is presented that is capable of handling basis functions with arbitrary angular momentum. For practical reasons, only functions up to (ff|f) angular momentum are presently calculated on the GPU, thus leaving the calculation of higher angular momenta integrals on the CPU of the hybrid CPU-GPU environment. Speedups of up to a factor of 30 are demonstrated relative to state-of-the-art serial and parallel CPU implementations. Benchmark calculations with over 3500 contracted basis functions (def2-SVP or def2-TZVP basis sets) are reported. The presented implementation supports all devices with OpenCL support and is capable of utilizing multiple GPU cards over either MPI or OpenCL itself.
Zhang, Ying; Meng, Jie
2010-01-01
The neutron pair correlation in nuclei near the neutron drip-line is investigated using the selfconsistent continuum Skyrme-Hartree-Fock-Bogoliubov theory formulated with the coordinate-space Green's function technique. Numerical analysis is performed for even-even N = 86 isotones in the Mo-Sn region, where the 3p3/2 and 3p1/2 orbits lying near the Fermi energy are either weakly bound or unbound. The quasiparticle states originating from the l = 1 orbits form resonances with large widths, which are due to the low barrier height and the strong continuum coupling caused by the pair potential. Analyzing in detail the pairing properties and roles of the quasiparticle resonances, we found that the l = 1 broad quasiparticle resonances persist to feel the pair potential and contribute to the pair correlation even when their widths are comparable with the resonance energy.
Application of Fourth Order Vibrational Perturbation Theory with Analytic Hartree-Fock Force Fields
Gong, Justin Z.; Matthews, Devin A.; Stanton, John F.
2014-06-01
Fourth-Order Rayleigh-Schrodinger Perturbation Theory (VPT4) is applied to a series of small molecules. The quality of results have been shown to be heavily dependent on the quality of the quintic and sextic force constants used and that numerical sextic force constants converge poorly and are unreliable for VPT4. Using analytic Hartree-Fock force constants, it is shown that these analytic higher-order force constants are comparable to corresponding force constants from numerical calculations at a higher level of theory. Calculations show that analytic Hartree-Fock sextic force constants are reliable and can provide good results with Fourth-Order Rayleigh-Schrodinger Perturbation Theory.
New Multithreaded Hybrid CPU/GPU Approach to Hartree-Fock.
Asadchev, Andrey; Gordon, Mark S
2012-11-13
In this article, a new multithreaded Hartree-Fock CPU/GPU method is presented which utilizes automatically generated code and modern C++ techniques to achieve a significant improvement in memory usage and computer time. In particular, the newly implemented Rys Quadrature and Fock Matrix algorithms, implemented as a stand-alone C++ library, with C and Fortran bindings, provides up to 40% improvement over the traditional Fortran Rys Quadrature. The C++ GPU HF code provides approximately a factor of 17.5 improvement over the corresponding C++ CPU code.
Excess Charge for Pseudo-relativistic Atoms in Hartree-Fock Theory
DEFF Research Database (Denmark)
Dall'Acqua, Anna; Solovej, Jan Philip
2010-01-01
We prove within the Hartree-Fock theory of pseudo-relativistic atoms that the maximal negative ionization charge and the ionization energy of an atom remain bounded independently of the nuclear charge $Z$ and the fine structure constant $\\alpha$ as long as $Z\\alpha$ is bounded.......We prove within the Hartree-Fock theory of pseudo-relativistic atoms that the maximal negative ionization charge and the ionization energy of an atom remain bounded independently of the nuclear charge $Z$ and the fine structure constant $\\alpha$ as long as $Z\\alpha$ is bounded....
Excess Charge for Pseudo-relativistic Atoms in Hartree-Fock Theory
DEFF Research Database (Denmark)
Dall'Acqua, Anna; Solovej, Jan Philip
2010-01-01
We prove within the Hartree-Fock theory of pseudo-relativistic atoms that the maximal negative ionization charge and the ionization energy of an atom remain bounded independently of the nuclear charge $Z$ and the fine structure constant $\\alpha$ as long as $Z\\alpha$ is bounded.......We prove within the Hartree-Fock theory of pseudo-relativistic atoms that the maximal negative ionization charge and the ionization energy of an atom remain bounded independently of the nuclear charge $Z$ and the fine structure constant $\\alpha$ as long as $Z\\alpha$ is bounded....
Energy Technology Data Exchange (ETDEWEB)
Harrach, R.J.; Rogers, F.J.
1981-09-01
Two equation-of-state (EOS) models for multipy ionized matter are evaluated for the case of an aluminum plasma in the temperature range from about one eV to several hundred eV, spanning conditions of weak to strong ionization. Specifically, the simple analytical mode of Zel'dovich and Raizer and the more comprehensive model comprised by Rogers' plasma physics avtivity expansion code (ACTEX) are used to calculate the specific internal energy epsilon and average degree of ionization Z-bar*, as functons of temperature T and density rho. In the absence of experimental data, these results are compared against each other, covering almost five orders-of-magnitude variation in epsilon and the full range of Z-bar* We find generally good agreement between the two sets of results, especially for low densities and for temperatures near the upper end of the rage. Calculated values of epsilon(T) agree to within +- 30% over nearly the full range in T for densities below about 1 g/cm/sup 3/. Similarly, the two models predict values of Z-bar*(T) which track each other fairly well; above 20 eV the discrepancy is less than +- 20% fpr rho< or approx. =1 g/cm/sup 3/. Where the calculations disagree, we expect the ACTEX code to be more accurate than Zel'dovich and Raizer's model, by virtue of its more detailed physics content.
Harrach, Robert J.; Rogers, Forest J.
1981-09-01
Two equation-of-state (EOS) models for multipy ionized matter are evaluated for the case of an aluminum plasma in the temperature range from about one eV to several hundred eV, spanning conditions of weak to strong ionization. Specifically, the simple analytical mode of Zel'dovich and Raizer and the more comprehensive model comprised by Rogers' plasma physics avtivity expansion code (ACTEX) are used to calculate the specific internal energy ɛ and average degree of ionization Z¯*, as functons of temperature T and density ρ. In the absence of experimental data, these results are compared against each other, covering almost five orders-of-magnitude variation in ɛ and the full range of Z¯* We find generally good agreement between the two sets of results, especially for low densities and for temperatures near the upper end of the rage. Calculated values of ɛ(T) agree to within ±30% over nearly the full range in T for densities below about 1 g/cm3. Similarly, the two models predict values of Z¯*(T) which track each other fairly well; above 20 eV the discrepancy is less than ±20% fpr ρ≲1 g/cm3. Where the calculations disagree, we expect the ACTEX code to be more accurate than Zel'dovich and Raizer's model, by virtue of its more detailed physics content.
Shepherd, James J.; Grüneis, Andreas; Booth, George H.; Kresse, Georg; Alavi, Ali
2012-07-01
Using the finite simulation-cell homogeneous electron gas (HEG) as a model, we investigate the convergence of the correlation energy to the complete-basis-set (CBS) limit in methods utilizing plane-wave wave-function expansions. Simple analytic and numerical results from second-order Møller-Plesset theory (MP2) suggest a 1/M decay of the basis-set incompleteness error where M is the number of plane waves used in the calculation, allowing for straightforward extrapolation to the CBS limit. As we shall show, the choice of basis-set truncation when constructing many-electron wave functions is far from obvious, and here we propose several alternatives based on the momentum transfer vector, which greatly improve the rate of convergence. This is demonstrated for a variety of wave-function methods, from MP2 to coupled-cluster doubles theory and the random-phase approximation plus second-order screened exchange. Finite basis-set energies are presented for these methods and compared with exact benchmarks. A transformation can map the orbitals of a general solid state system onto the HEG plane-wave basis and thereby allow application of these methods to more realistic physical problems. We demonstrate this explicitly for solid and molecular lithium hydride.
Szmytkowski, Radosław
2016-01-01
The ground state of the Dirac one-electron atom, placed in a weak, static electric field of definite $2^{L}$-polarity, is studied within the framework of the first-order perturbation theory. The Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30 (1997) 825, erratum: 30 (1997) 2747] is used to derive closed-form analytical expressions for various far-field and near-nucleus static electric multipole susceptibilities of the atom. The far-field multipole susceptibilities --- the polarizabilities $\\alpha_{L}$, electric-to-magnetic cross-susceptibilities $\\alpha_{\\mathrm{E}L\\to\\mathrm{M}(L\\mp1)}$ and electric-to-toroidal-magnetic cross-susceptibilities $\\alpha_{\\mathrm{E}L\\to\\mathrm{T}L}$ --- are found to be expressible in terms of one or two non-terminating generalized hypergeometric functions ${}_{3}F_{2}$ with the unit argument. Counterpart formulas for the near-nucleus multipole susceptibilities --- the electric nuclear shielding constants $\\sigma_{\\mathrm{E}L\\to\\m...
$\\it{Ab}$ $\\it{initio}$ nuclear many-body perturbation calculations in the Hartree-Fock basis
Hu, Baishan; Sun, Zhonghao; Vary, James P; Li, Tong
2016-01-01
Starting from realistic nuclear forces, the chiral N$^3$LO and JISP16, we have applied many-body perturbation theory (MBPT) to the structure of closed-shell nuclei, $^4$He and $^{16}$O. The two-body N$^3$LO interaction is softened by a similarity renormalization group transformation while JISP16 is adopted without renormalization. The MBPT calculations are performed within the Hartree-Fock (HF) bases. The angular momentum coupled scheme is used, which can reduce the computational task. Corrections up to the third order in energy and up to the second order in radius are evaluated. Higher-order corrections in the HF basis are small relative to the leading-order perturbative result. Using the anti-symmetrized Goldstone diagram expansions of the wave function, we directly correct the one-body density for the calculation of the radius, rather than calculate corrections to the occupation propabilities of single-particle orbits as found in other treatments. We compare our results with other methods where available a...
Augspurger, Joseph D.; Dykstra, Clifford E.
1993-08-01
Molecular Sternheimer shielding constants, γ, the proportionality constants relating the electric field gradient at a quadrupolar nucleus to an external electric field gradient are usually introduced phenomenologically. In this report, we take a comprehensive view of the sensitivity of the electric field gradient at a nucleus to arbitrary external electrical potentials and we show how the response can be obtained from analytically determined properties via derivative Hartree-Fock theory. From application of this ab initio technique, values have been obtained for the first and second order changes in nuclear quadrupole coupling with respect to external fields and field gradients, as well as nearby ideal multipole moments, for HCN and HCl. These values have been used to evaluate the change in the nuclear quadrupole coupling for several weakly bound complexes and to provide a nonempirical approach to relative effects on Sternheimer shielding. In weak molecular complexes, the effect of uniform fields can be as sizable as the effect of external field gradients in the overall change in nuclear quadrupole coupling, and so the underlying issue of convergence of multipolar expansions is considered over a range of geometries. This is important for structural interpretations of both nuclear magnetic resonance (NMR) and microwave data, and a simple formula, representing a practical point of truncation, is presented for quadrupole coupling analysis.
Prykarpatski, A. K.; Bogolubov, N. N.
2017-01-01
A quantum fermionic massless charged particle self-intercating with its own self-generated bosonic electromagnetic field is reanalyzed in the framework of the Fock many-temporal and Feynman proper time approaches. The self-interaction phenomenon structure is discussed within the renormalized quantum Fock space. The quantum electromagnetic charged particle mass origin is suggested.
Directory of Open Access Journals (Sweden)
Iago Oliveira Ferreira
2014-12-01
Full Text Available The present article intents to study the tendencies of the criminal legislations of some occidental countries in the last decades, attaining to the political-criminal phenomenon that has been showing a peculiar expansion of punitivism in the central and peripheral countries, by the increasing of severity of criminal repressions and flexibilization of the penal garantism. This study has its justification on the importance of the impacts that these legislative tendencies are causing on the punitive discipline in the occidental States. It has as objective, in synthesis, to investigate the legitimacy of the paradigm of the criminal toughness that has been observed in the present times – named as “Criminal Law of the Enemy” by Gunther Jakobs – and its compatibility with the postulates that build the modern Constitutional State of Law, in compass with the impositions of the minimalist Criminal Law and of the Penal Garantism. To do so, the present study relies on international and national doctrines, aiming to put in terms the major philosophical and juridical bases of the minimalist and garantistic model, defending its close relationship with the rule of law principle. In addition, analyzes the investigated phenomenon of the penal expansionism, seeking, about this last one, to establish its general characteristics in the occidental world, for which we also undertake a research of the pertinent criminal legislation of some countries took as models. By the shown, we conclude that the expansionism of the Criminal Law model observed in the last decades in the Occident is totally incompatible with the juridical limits and guarantees disposed in the occidental constitutions, which build the model of the Penal Garantism, with protection of the citizens’ freedom against the excesses of the punitive power. Indeed, the flexibilization of these limits and guarantees operated by the penal expansionism or “Criminal Law of the Enemy” create an State
Mananga, Eugene S; Reid, Alicia E; Charpentier, Thibault
2012-02-01
This article describes the use of an alternative expansion scheme called Floquet-Magnus expansion (FME) to study the dynamics of spin system in solid-state NMR. The main tool used to describe the effect of time-dependent interactions in NMR is the average Hamiltonian theory (AHT). However, some NMR experiments, such as sample rotation and pulse crafting, seem to be more conveniently described using the Floquet theory (FT). Here, we present the first report highlighting the basics of the Floquet-Magnus expansion (FME) scheme and hint at its application on recoupling sequences that excite more efficiently double-quantum coherences, namely BABA and C7 radiofrequency pulse sequences. The use of Λ(n)(t) functions available only in the FME scheme, allows the comparison of the efficiency of BABA and C7 sequences.
Dirac-Fock atomic electronic structure calculations using different nuclear charge distributions
Visscher, L; Dyall, KG
1997-01-01
Numerical Hartree-Fock calculations based on the Dirac-Coulomb Hamiltonian for the first 109 elements of the periodic table are presented. The results give the total electronic energy, as a function of the nuclear model that is used, for four different models of the nuclear charge distribution. The
Hartree-Fock Cluster Study of Interstitial Transition Metals in Silicon
Broer, R.; Aissing, G.; Nieuwpoort, W.C.; Feiner, L.F.
1986-01-01
Results are presented of a Hartree-Fock cluster study of interstitial Ti, V, Cr, and Mn impurities in silicon. A Si10 cluster models the nearest Si atoms around a tetrahedral interstitial site in crystalline Si. The dangling bonds of the Si atoms are saturated by hydrogens. The effect of the Si core
Flight test report: Focke wulf PIAGGIO P149D-TP
CSIR Research Space (South Africa)
Barker, D
2015-12-01
Full Text Available and subsequently built under licence by Focke Wulf for the German Air Force. After the fleet was retired from Luftwaffe Service, Heiml’s brother bought one and overhauled it. Several years later, while on a visit to Germany, it was ‘love at first sight’ leaving...
Monte Carlo solution of the Schrödinger equation in Fock space representation
Szybisz, L.; Zabolitzky, J. G.
1984-09-01
A new Monte Carlo method to solve the Schrödinger equation when expressed in Fock space is presented. The procedure is applied to two soluble many-body hamiltonians, the quasispin model of Lipkin-Meshkov-Glick and the so-called "static source" limit of the nucleon-scalar-meson interaction in the discrete one-dimensional space.
Monte Carlo solution of the Schroedinger equation in Fock space representation
Energy Technology Data Exchange (ETDEWEB)
Szybisz, L.; Zabolitzky, J.G. (Koeln Univ. (Germany, F.R.). Inst. fuer Theoretische Physik)
1984-09-03
A new Monte Carlo method to solve the Schroedinger equation when expressed in Fock space is presented. The procedure is applied to two soluble many-body hamiltonians, the quasispin model of Lipkin-Meshkov-Glick and the so-called 'static source' limit of the nucleon-scalar-meson interaction in the discrete one-dimensional space.
Group classification and conservation laws of the generalized Klein-Gordon-Fock equation
Muatjetjeja, B.
2016-08-01
In the present paper, we perform Lie and Noether symmetries of the generalized Klein-Gordon-Fock equation. It is shown that the principal Lie algebra, which is one-dimensional, has several possible extensions. It is further shown that several cases arise for which Noether symmetries exist. Exact solutions for some cases are also obtained from the invariant solutions of the investigated equation.
Method of renormalization potential for one model of Hartree-Fock-Slater type
Zasorin, Y V
2002-01-01
A new method of the potential renormalization for the quasiclassical model of the Hartree-Fock-Slater real potential is proposed. The method makes it possible to easily construct the wave functions and contrary to the majority od similar methods it does not require the knowledge of the real-type potential
Zeros of the Bergman kernel of the Fock-Bargmann-Hartogs domain and the interlacing property
Yamamori, Atsushi
2011-01-01
In this paper we consider the zeros of the Bergman kernel of the Fock-Bargmann-Hartogs domain $D_{n,m}$. We describe how the existence of zeros of the Bergman kernel depends on the integers $m$ and $n$ with the help of the interlacing property.
Dirac-Fock atomic electronic structure calculations using different nuclear charge distributions
Visscher, L; Dyall, KG
1997-01-01
Numerical Hartree-Fock calculations based on the Dirac-Coulomb Hamiltonian for the first 109 elements of the periodic table are presented. The results give the total electronic energy, as a function of the nuclear model that is used, for four different models of the nuclear charge distribution. The
Koopmans' theorem in the statistical Hartree-Fock theory
Energy Technology Data Exchange (ETDEWEB)
Pain, Jean-Christophe, E-mail: jean-christophe.pain@cea.fr [CEA, DAM, DIF, F-91297 Arpajon (France)
2011-07-28
In this short paper, the validity of Koopmans' theorem in the Hartree-Fock theory at non-zero temperature (Hartree-Fock statistical theory) is investigated. It is shown that Koopmans' theorem does not apply in the grand-canonical ensemble, due to a missing contribution to the energy proportional to the interaction between two electrons belonging to the same orbital. The Hartree-Fock statistical theory has also been applied in the canonical ensemble (Blenski et al 1997 Phys. Rev. E 55 R4889) for the purpose of photo-absorption calculations. In that case, the Hartree-Fock self-consistent field equations are derived in the super-configuration approximation. It is shown that Koopmans' theorem does not hold in the canonical ensemble, but a restricted version of the theorem can be obtained by assuming that a particular quantity multiplying the interaction matrix element in the expression of the energy does not change during the removal of an electron.
Hartree-Fock Cluster Study of Interstitial Transition Metals in Silicon
Broer, R.; Aissing, G.; Nieuwpoort, W.C.; Feiner, L.F.
Results are presented of a Hartree-Fock cluster study of interstitial Ti, V, Cr, and Mn impurities in silicon. A Si10 cluster models the nearest Si atoms around a tetrahedral interstitial site in crystalline Si. The dangling bonds of the Si atoms are saturated by hydrogens. The effect of the Si core
Energy Technology Data Exchange (ETDEWEB)
Dupuis, M. (ed.)
1981-02-01
Twenty-seven papers are included in four sessions titled: generalized Fock operator methods, annihilation of single excitations methods, second-order MCSCF methods, and applications of MCHF methods. Separate abstracts were prepared for eight papers; one of the remaining had been previously abstracted. (DLC)
PERTURBATION THEORY FOR THE FOCK-DIRAC DENSITY MATRIX
ATOMIC ENERGY LEVELS, *ATOMIC ORBITALS, *QUANTUM THEORY , ATOMIC SPECTROSCOPY, ELECTRONS, EXCITATION, FUNCTIONS(MATHEMATICS), MATHEMATICAL ANALYSIS, NUCLEAR SPINS, PERTURBATION THEORY , SOLID STATE PHYSICS, THEORY
Dielectronic recombination rate coefficients to excited states of Be-like oxygen
Energy Technology Data Exchange (ETDEWEB)
Murakami, Izumi; Safronova, Ulyana I.; Kato, Takako
2001-05-01
We have calculated energy levels, radiative transition probabilities, and autoionization rates for Be-like oxygen (O{sup 4+}) including ls{sup 2}2lnl' (n=2 - 8, l {<=} n - 1) and 1s{sup 2}3l'nl (n=3 - 6, l {<=} n - l) states by multi-configurational Hartree-Fock method (Cowan code) and perturbation theory Z-expansion method (MZ code). The state selective dielectronic recombination rate coefficients to excited states of Be-like O ions are obtained. Configuration mixing plays an important role for the principal quantum number n distribution of the dielectronic recombination rate coefficients for 2snl (n {<=} 5) levels at low electron temperature. The orbital angular momentum quantum number l distribution of the rate coefficients shows a peak at l = 4. The total dielectronic recombination rate coefficient is derived as a function of electron temperature. (author)
Accardi, Luigi
2007-01-01
The identification of the $*$--Lie algebra of the renormalized higher powers of white noise (RHPWN) and the analytic continuation of the second quantized Virasoro--Zamolodchikov--$w_{\\infty}$ $*$--Lie algebra of conformal field theory and high-energy physics, was recently established in \\cite{id} based on results obtained in [1] and [2]. In the present paper we show how the RHPWN Fock kernels must be truncated in order to be positive definite and we obtain a Fock representation of the two algebras. We show that the truncated renormalized higher powers of white noise (TRHPWN) Fock spaces of order $\\geq 2$ host the classical continuous binomial process.
Meng, Qingyong; Meyer, Hans-Dieter
2015-10-28
Molecular-surface studies are often done by assuming a corrugated, static (i.e., rigid) surface. To be able to investigate the effects that vibrations of surface atoms may have on spectra and cross sections, an expansion Hamiltonian model is proposed on the basis of the recently reported [R. Marquardt et al., J. Chem. Phys. 132, 074108 (2010)] SAP potential energy surface (PES), which was built for the CO/Cu(100) system with a rigid surface. In contrast to other molecule-surface coupling models, such as the modified surface oscillator model, the coupling between the adsorbed molecule and the surface atoms is already included in the present expansion SAP-PES model, in which a Taylor expansion around the equilibrium positions of the surface atoms is performed. To test the quality of the Taylor expansion, a direct model, that is avoiding the expansion, is also studied. The latter, however, requests that there is only one movable surface atom included. On the basis of the present expansion and direct models, the effects of a moving top copper atom (the one to which CO is bound) on the energy levels of a bound CO/Cu(100) system are studied. For this purpose, the multiconfiguration time-dependent Hartree calculations are carried out to obtain the vibrational fundamentals and overtones of the CO/Cu(100) system including a movable top copper atom. In order to interpret the results, a simple model consisting of two coupled harmonic oscillators is introduced. From these calculations, the vibrational levels of the CO/Cu(100) system as function of the frequency of the top copper atom are discussed.
Energy Technology Data Exchange (ETDEWEB)
Meng, Qingyong, E-mail: mengqingyong@dicp.ac.cn [State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Zhongshan Road 457, 116023 Dalian (China); Meyer, Hans-Dieter, E-mail: hans-dieter.meyer@pci.uni-heidelberg.de [Theoretische Chemie, Physikalisch-Chemisches Institut, Ruprecht-Karls Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg (Germany)
2015-10-28
Molecular-surface studies are often done by assuming a corrugated, static (i.e., rigid) surface. To be able to investigate the effects that vibrations of surface atoms may have on spectra and cross sections, an expansion Hamiltonian model is proposed on the basis of the recently reported [R. Marquardt et al., J. Chem. Phys. 132, 074108 (2010)] SAP potential energy surface (PES), which was built for the CO/Cu(100) system with a rigid surface. In contrast to other molecule-surface coupling models, such as the modified surface oscillator model, the coupling between the adsorbed molecule and the surface atoms is already included in the present expansion SAP-PES model, in which a Taylor expansion around the equilibrium positions of the surface atoms is performed. To test the quality of the Taylor expansion, a direct model, that is avoiding the expansion, is also studied. The latter, however, requests that there is only one movable surface atom included. On the basis of the present expansion and direct models, the effects of a moving top copper atom (the one to which CO is bound) on the energy levels of a bound CO/Cu(100) system are studied. For this purpose, the multiconfiguration time-dependent Hartree calculations are carried out to obtain the vibrational fundamentals and overtones of the CO/Cu(100) system including a movable top copper atom. In order to interpret the results, a simple model consisting of two coupled harmonic oscillators is introduced. From these calculations, the vibrational levels of the CO/Cu(100) system as function of the frequency of the top copper atom are discussed.
Quantum State Engineering Via Coherent-State Superpositions
Janszky, Jozsef; Adam, P.; Szabo, S.; Domokos, P.
1996-01-01
The quantum interference between the two parts of the optical Schrodinger-cat state makes possible to construct a wide class of quantum states via discrete superpositions of coherent states. Even a small number of coherent states can approximate the given quantum states at a high accuracy when the distance between the coherent states is optimized, e. g. nearly perfect Fock state can be constructed by discrete superpositions of n + 1 coherent states lying in the vicinity of the vacuum state.
A Hartree–Fock study of the confined helium atom: Local and global basis set approaches
Energy Technology Data Exchange (ETDEWEB)
Young, Toby D., E-mail: tyoung@ippt.pan.pl [Zakład Metod Komputerowych, Instytut Podstawowych Prolemów Techniki Polskiej Akademia Nauk, ul. Pawińskiego 5b, 02-106 Warszawa (Poland); Vargas, Rubicelia [Universidad Autónoma Metropolitana Iztapalapa, División de Ciencias Básicas e Ingenierías, Departamento de Química, San Rafael Atlixco 186, Col. Vicentina, Iztapalapa, D.F. C.P. 09340, México (Mexico); Garza, Jorge, E-mail: jgo@xanum.uam.mx [Universidad Autónoma Metropolitana Iztapalapa, División de Ciencias Básicas e Ingenierías, Departamento de Química, San Rafael Atlixco 186, Col. Vicentina, Iztapalapa, D.F. C.P. 09340, México (Mexico)
2016-02-15
Two different basis set methods are used to calculate atomic energy within Hartree–Fock theory. The first is a local basis set approach using high-order real-space finite elements and the second is a global basis set approach using modified Slater-type orbitals. These two approaches are applied to the confined helium atom and are compared by calculating one- and two-electron contributions to the total energy. As a measure of the quality of the electron density, the cusp condition is analyzed. - Highlights: • Two different basis set methods for atomic Hartree–Fock theory. • Galerkin finite element method and modified Slater-type orbitals. • Confined atom model (helium) under small-to-extreme confinement radii. • Detailed analysis of the electron wave-function and the cusp condition.
Multiconfiguration hartree-fock theory for pseudorelativistic systems: The time-dependent case
Hajaiej, Hichem
2014-03-01
In [Setting and analysis of the multi-configuration time-dependent Hartree-Fock equations, Arch. Ration. Mech. Anal. 198 (2010) 273-330] the third author has studied in collaboration with Bardos, Catto and Mauser the nonrelativistic multiconfiguration time-dependent Hartree-Fock system of equations arising in the modeling of molecular dynamics. In this paper, we extend the previous work to the case of pseudorelativistic atoms. We show the existence and the uniqueness of global-in-time solution to the underlying system under technical assumptions on the energy of the initial data and the charge of the nucleus. Moreover, we prove that the result can be extended to the case of neutron stars when the number of electrons is less than a critical number N cr. © 2014 World Scientific Publishing Company.
Dirac fields in flat FLRW cosmology: Uniqueness of the Fock quantization
Cortez, Jerónimo; Martín-Benito, Mercedes; Marugán, Guillermo A Mena; Velhinho, José M
2016-01-01
We address the issue of the infinite ambiguity that affects the construction of a Fock quantization of a Dirac field propagating in a cosmological spacetime with flat compact sections. In particular, we discuss a physical criterion that restricts to a unique possibility (up to unitary equivalence) the infinite set of available vacua. We prove that this desired uniqueness is guaranteed, for any possible choice of spin structure on the spatial sections, if we impose two conditions. The first one is that the symmetries of the classical system must be implemented quantum mechanically, so that the vacuum is invariant under the symmetry transformations. The second and more important condition is that the constructed theory must have a quantum dynamics that is implementable as a (non-trivial) unitary operator in Fock space. Actually, this unitarity of the quantum dynamics leads us to identify as explicitly time dependent some very specific contributions of the Dirac field. In doing that, we essentially characterize ...
Relativity with Respect to Measurement: Collapse and Quantum Events from Fock to Cramer
Directory of Open Access Journals (Sweden)
Leonardo Chiatti
2014-10-01
Full Text Available Some observations are presented starting with the well-known article by Vladimir Fock “Quantum Physics and Philosophical Problems”, published in 1971. In this article, which summarizes for Western readers a long and complicated reflection of the foundations of quantum mechanics (QM, Fock illustrates his “minimal” interpretation of this theory. By minimal, we mean that it only uses concepts related to the operational aspects of the measurement procedures, avoiding any mention of definite quantum ontologies (Bell’s beables. It is argued that, by taking into account the time reversal invariance of the microscopic processes and introducing the notion of irreversibility in an appropriate manner, Fock’s description becomes an anticipation of the “transaction” notion introduced by Cramer a decade later. So, the concept of “collapse” does retain the features of a QM “freak” postulate to become a new way to look at the elementary quantum processes.
Institute of Scientific and Technical Information of China (English)
RONG; Jian; MA; Zhongyu
2004-01-01
The relativistic microscopic optical potential in the asymmetric nuclear matter is studied in the framework of the Dirac Brueckner-Hartree-Fock method. A new decomposition of the Dirac structure of the nuclear self-energy in nuclear matter is adopted. The self-energy of a nucleon with E＞ 0 in nuclear matter is calculated with the G matrix in the Hartree-Fock approach. The optical potential of a nucleon in the nuclear medium is identified with the nucleon self-energy. The energy and asymmetric parameter dependence of the relativistic optical potentials for proton and neutron are discussed. The resulting Schroedinger equivalent potentials have reasonable behaviors of the energy dependence. The asymmetric parameter dependence of relativistic optical potentials and Schroedinger potentials are emphasized.
The Mehler-Fock transform of general order and arbitrary index and its inversion
Directory of Open Access Journals (Sweden)
Cyril Nasim
1984-01-01
Full Text Available An integral transform involving the associated Legendre function of zero order, P−12+iτ(x, x∈[1,∞, as the kernel (considered as a function of τ, is called Mehler-Fock transform. Some generalizations, involving the function P−12+iτμ(x, where the order μ is an arbitrary complex number, including the case when μ=0,1,2,… have been known for some time. In this present note, we define a general Mehler-Fock transform involving, as the kernel, the Legendre function P−12+tμ(x, of general order μ and an arbitrary index −12+t, t=σ+iτ, −∞<τ<∞. Then we develop a symmetric inversion formulae for these transforms. Many well-known results are derived as special cases of this general form. These transforms are widely used for solving many axisymmetric potential problems.
Gomar, Laura Castelló; Blas, Daniel Martín-de; Marugán, Guillermo A Mena; Velhinho, José M
2012-01-01
We study the Fock quantization of scalar fields with a time dependent mass in cosmological scenarios with flat compact spatial sections. This framework describes physically interesting situations like, e.g., cosmological perturbations in flat Friedmann-Robertson-Walker spacetimes, generally including a suitable scaling of them by a background function. We prove that the requirements of vacuum invariance under the spatial isometries and of a unitary quantum dynamics select (a) a unique canonical pair of field variables among all those related by time dependent canonical transformations which scale the field configurations, and (b) a unique Fock representation for the canonical commutation relations of this pair of variables. Though the proof is generalizable to other compact spatial topologies in three or less dimensions, we focus on the case of the three-torus owing to its relevance in cosmology, paying a especial attention to the role played by the spatial isometries in the determination of the representatio...
Schatten-p Class (0 Fock
Institute of Scientific and Technical Information of China (English)
Lian Hua XIAO; Xiao Feng WANG; Jin XIA
2015-01-01
In this paper, we discuss the Schatten-p class (0 < p ≤ ∞ ) of Toeplitz operators on generalized Fock space with the symbol in positive Borel measure. It makes a great diff erence from other papers by using the estimates of the kernel and the weight together instead of separately estimating each other. We also get the equivalent conditions when a Toeplitz operator is in the Schatten-p class.
Mazurek, A. P.; Sadlej-Sosnowska, N.
2000-11-01
A comparison of the ab initio quantum chemical methods: Hartree-Fock (HF) and hybrid density functional theory (DFT)/B3LYP for the treatment of tautomeric equilibria both in the gas phase and in the solution is made. The solvent effects were investigated in terms of the self-consistent reaction field (SCRF). Ionization potentials (IP), calculated by DFT/B3LYP, are also compared with those calculated previously within the HF frame.
Generalization of Cramer's rule and its application to the projection of Hartree-Fock wave function
Hage-Hassan, Mehdi
2009-01-01
We generalize the Cramer's rule of linear algebra. We apply it to calculate the spectra of nucleus by applying Hill-Wheeler projection operator to Hartree-Fock wave function, and to derive L\\"owdin formula and Thouless theorem. We derive by an elementary method the infinitesimal or L\\"owdin projection operators and its integral representation to be useful for the projection of Slater determinant.
On the solution of the Hartree-Fock-Bogoliubov equations by the conjugate gradient method
Energy Technology Data Exchange (ETDEWEB)
Egido, J.L. [Universidad Autonoma de Madrid (Spain). Dept. de Fisica Teorica; Lessing, J. [Universidad Autonoma de Madrid (Spain). Dept. de Fisica Teorica; Martin, V. [Analisis Numerico, Facultad de Informatica, Universidad Politecnica de Madrid, E-28660 Boadilla del Monte, Madrid (Spain); Robledo, L.M. [Universidad Autonoma de Madrid (Spain). Dept. de Fisica Teorica
1995-11-06
The conjugate gradient method is formulated in the Hilbert space for density and non-density dependent Hamiltonians. We apply it to the solution of the Hartree-Fock-Bogoliubov equations with constraints. As a numerical application we show calculations with the finite range density dependent Gogny force. The number of iterations required to reach convergence is reduced by a factor of three to four as compared with the standard gradient method. (orig.).
Can X-ray constrained Hartree-Fock wavefunctions retrieve electron correlation?
Genoni, Alessandro; Dos Santos, Leonardo H R; Meyer, Benjamin; Macchi, Piero
2017-03-01
The X-ray constrained wavefunction (XC-WF) method proposed by Jayatilaka [Jayatilaka & Grimwood (2001) ▸, Acta Cryst. A57, 76-86] has attracted much attention because it represents a possible third way of theoretically studying the electronic structure of atoms and molecules, combining features of the more popular wavefunction- and DFT-based approaches. In its original formulation, the XC-WF technique extracts statistically plausible wavefunctions from experimental X-ray diffraction data of molecular crystals. A weight is used to constrain the pure Hartree-Fock solution to the observed X-ray structure factors. Despite the wavefunction being a single Slater determinant, it is generally assumed that its flexibility could guarantee the capture, better than any other experimental model, of electron correlation effects, absent in the Hartree-Fock Hamiltonian but present in the structure factors measured experimentally. However, although the approach has been known for long time, careful testing of this fundamental hypothesis is still missing. Since a formal demonstration is impossible, the validation can only be done heuristically and, to accomplish this task, X-ray constrained Hartree-Fock calculations have been performed using structure factor amplitudes computed at a very high correlation level (coupled cluster) for selected molecules in isolation, in order to avoid the perturbations due to intermolecular interactions. The results show that a single-determinant XC-WF is able to capture the electron correlation effects only partially. The largest amount of electron correlation is extracted when: (i) a large external weight is used (much larger than what has normally been used in XC-WF calculations using experimental data); and (ii) the high-order reflections, which carry less information on the electron correlation, are down-weighted (or even excluded), otherwise they would bias the fitting towards the unconstrained Hartree-Fock wavefunction.
Can X-ray constrained Hartree–Fock wavefunctions retrieve electron correlation?
Directory of Open Access Journals (Sweden)
Alessandro Genoni
2017-03-01
Full Text Available The X-ray constrained wavefunction (XC-WF method proposed by Jayatilaka [Jayatilaka & Grimwood (2001, Acta Cryst. A57, 76–86] has attracted much attention because it represents a possible third way of theoretically studying the electronic structure of atoms and molecules, combining features of the more popular wavefunction- and DFT-based approaches. In its original formulation, the XC-WF technique extracts statistically plausible wavefunctions from experimental X-ray diffraction data of molecular crystals. A weight is used to constrain the pure Hartree–Fock solution to the observed X-ray structure factors. Despite the wavefunction being a single Slater determinant, it is generally assumed that its flexibility could guarantee the capture, better than any other experimental model, of electron correlation effects, absent in the Hartree–Fock Hamiltonian but present in the structure factors measured experimentally. However, although the approach has been known for long time, careful testing of this fundamental hypothesis is still missing. Since a formal demonstration is impossible, the validation can only be done heuristically and, to accomplish this task, X-ray constrained Hartree–Fock calculations have been performed using structure factor amplitudes computed at a very high correlation level (coupled cluster for selected molecules in isolation, in order to avoid the perturbations due to intermolecular interactions. The results show that a single-determinant XC-WF is able to capture the electron correlation effects only partially. The largest amount of electron correlation is extracted when: (i a large external weight is used (much larger than what has normally been used in XC-WF calculations using experimental data; and (ii the high-order reflections, which carry less information on the electron correlation, are down-weighted (or even excluded, otherwise they would bias the fitting towards the unconstrained Hartree–Fock wavefunction.
Can X-ray constrained Hartree–Fock wavefunctions retrieve electron correlation?
Genoni, Alessandro; Dos Santos, Leonardo H. R.; Meyer, Benjamin; Macchi, Piero
2017-01-01
The X-ray constrained wavefunction (XC-WF) method proposed by Jayatilaka [Jayatilaka & Grimwood (2001) ▸, Acta Cryst. A57, 76–86] has attracted much attention because it represents a possible third way of theoretically studying the electronic structure of atoms and molecules, combining features of the more popular wavefunction- and DFT-based approaches. In its original formulation, the XC-WF technique extracts statistically plausible wavefunctions from experimental X-ray diffraction data of molecular crystals. A weight is used to constrain the pure Hartree–Fock solution to the observed X-ray structure factors. Despite the wavefunction being a single Slater determinant, it is generally assumed that its flexibility could guarantee the capture, better than any other experimental model, of electron correlation effects, absent in the Hartree–Fock Hamiltonian but present in the structure factors measured experimentally. However, although the approach has been known for long time, careful testing of this fundamental hypothesis is still missing. Since a formal demonstration is impossible, the validation can only be done heuristically and, to accomplish this task, X-ray constrained Hartree–Fock calculations have been performed using structure factor amplitudes computed at a very high correlation level (coupled cluster) for selected molecules in isolation, in order to avoid the perturbations due to intermolecular interactions. The results show that a single-determinant XC-WF is able to capture the electron correlation effects only partially. The largest amount of electron correlation is extracted when: (i) a large external weight is used (much larger than what has normally been used in XC-WF calculations using experimental data); and (ii) the high-order reflections, which carry less information on the electron correlation, are down-weighted (or even excluded), otherwise they would bias the fitting towards the unconstrained Hartree–Fock wavefunction. PMID:28250952
Solving Witten's string field theory using the butterfly state
Okawa, Y
2003-01-01
We solve the equation of motion of Witten's cubic open string field theory in a series expansion using the regulated butterfly state. The expansion parameter is given by the regularization parameter of the butterfly state, which can be taken to be arbitrarily small. Unlike the case of level truncation, the equation of motion can be solved for an arbitrary component of the Fock space up to a positive power of the expansion parameter. The energy density of the solution is well-defined and remains finite even in the singular butterfly limit, and it gives approximately 68% of the D25-brane tension for the solution at the leading order. Moreover, it simultaneously solves the equation of motion of vacuum string field theory, providing support for the conjecture at this order. We further improve our ansatz by taking into account next-to-leading terms, and find two numerical solutions which give approximately 88% and 109%, respectively, of the D25-brane tension for the energy density. These values are interestingly c...
Uniqueness of the Fock quantization of scalar fields in spatially flat cosmological spacetimes
Energy Technology Data Exchange (ETDEWEB)
Gomar, Laura Castelló [Facultad de Ciencias Físicas, Universidad Complutense de Madrid, Ciudad Universitaria, 28040 Madrid (Spain); Cortez, Jerónimo [Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico D.F. 04510 (Mexico); Blas, Daniel Martín-de; Marugán, Guillermo A. Mena [Instituto de Estructura de la Materia, CSIC, Serrano 121, 28006 Madrid (Spain); Velhinho, José M., E-mail: laucaste@estumail.ucm.es, E-mail: jacq@ciencias.unam.mx, E-mail: daniel.martin@iem.cfmac.csic.es, E-mail: jvelhi@ubi.pt [Departamento de Física, Faculdade de Ciências, Universidade da Beira Interior, R. Marquês D' Ávila e Bolama, 6201-001 Covilhã (Portugal)
2012-11-01
We study the Fock quantization of scalar fields in (generically) time dependent scenarios, focusing on the case in which the field propagation occurs in –either a background or effective– spacetime with spatial sections of flat compact topology. The discussion finds important applications in cosmology, like e.g. in the description of test Klein-Gordon fields and scalar perturbations in Friedmann-Robertson-Walker spacetime in the observationally favored flat case. Two types of ambiguities in the quantization are analyzed. First, the infinite ambiguity existing in the choice of a Fock representation for the canonical commutation relations, understandable as the freedom in the choice of inequivalent vacua for a given field. Besides, in cosmological situations, it is customary to scale the fields by time dependent functions, which absorb part of the evolution arising from the spacetime, which is treated classically. This leads to an additional ambiguity, this time in the choice of a canonical pair of field variables. We show that both types of ambiguities are removed by the requirements of (a) invariance of the vacuum under the symmetries of the three-torus, and (b) unitary implementation of the dynamics in the quantum theory. In this way, one arrives at a unique class of unitarily equivalent Fock quantizations for the system. This result provides considerable robustness to the quantum predictions and renders meaningful the confrontation with observation.
Dirac fields in flat FLRW cosmology: Uniqueness of the Fock quantization
Energy Technology Data Exchange (ETDEWEB)
Cortez, Jerónimo, E-mail: jacq@ciencias.unam.mx [Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, México D.F. 04510 (Mexico); Elizaga Navascués, Beatriz, E-mail: beatriz.elizaga@iem.cfmac.csic.es [Instituto de Estructura de la Materia, IEM-CSIC, Serrano 121, 28006 Madrid (Spain); Martín-Benito, Mercedes, E-mail: m.martin@hef.ru.nl [Radboud University Nijmegen, Institute for Mathematics, Astrophysics and Particle Physics, Heyendaalseweg 135, NL-6525 AJ Nijmegen (Netherlands); Mena Marugán, Guillermo A., E-mail: mena@iem.cfmac.csic.es [Instituto de Estructura de la Materia, IEM-CSIC, Serrano 121, 28006 Madrid (Spain); Velhinho, José M., E-mail: jvelhi@ubi.pt [Universidade da Beira Interior, Rua Marquês d’Ávila e Bolama, 6201-001, Covilhã (Portugal)
2017-01-15
We address the issue of the infinite ambiguity that affects the construction of a Fock quantization of a Dirac field propagating in a cosmological spacetime with flat compact sections. In particular, we discuss a physical criterion that restricts to a unique possibility (up to unitary equivalence) the infinite set of available vacua. We prove that this desired uniqueness is guaranteed, for any possible choice of spin structure on the spatial sections, if we impose two conditions. The first one is that the symmetries of the classical system must be implemented quantum mechanically, so that the vacuum is invariant under the symmetry transformations. The second and more important condition is that the constructed theory must have a quantum dynamics that is implementable as a (non-trivial) unitary operator in Fock space. Actually, this unitarity of the quantum dynamics leads us to identify as explicitly time dependent some very specific contributions of the Dirac field. In doing that, we essentially characterize the part of the dynamics governed by the Dirac equation that is unitarily implementable. The uniqueness of the Fock vacuum is attained then once a physically motivated convention for the concepts of particles and antiparticles is fixed.
On the NP-completeness of the Hartree-Fock method for translationally invariant systems
Whitfield, James D
2014-01-01
The self-consistent field method utilized for solving the Hartree-Fock (HF) problem and the closely related Kohn-Sham problem, is typically thought of as one of the cheapest methods available to quantum chemists. This intuition has been developed from the numerous applications of the self-consistent field method to a large variety of molecular systems. However, in terms of its worst-case computational complexity, the HF problem is NP-complete. In this work, we investigate how far one can push the boundaries of the NP-completeness by investigating restricted instances of HF. We have constructed two new NP-complete variants of the problem. The first is a set of Hamiltonians whose translationally invariant Hartree-Fock solutions are trivial, but whose broken symmetry solutions are NP-complete. Second, we demonstrate how to embed instances of spin glasses into translationally invariant Hartree-Fock instances and provide a numerical example. These findings are the first steps towards understanding in which cases t...
Lynch, Gillian C.; Steckler, Rozeanne; Varandas, Antonio J. C.; Truhlar, Donald G.; Schwenke, David W.
1991-01-01
New ab initio results and a double many-body expansion formalism have been used to parameterize a new FH2 potential energy surface with improved properties near the saddle point and in the region of long-range attraction. The functional form of the new surface includes dispersion forces by a double many-body expansion. Stationary point properties for the new surface are calculated along with the product-valley barrier maxima of vibrationally adiabatic potential curves for F + H2 - HF(nu-prime = 3) + H, F + HD - HF(nu-prime = 3) + D, and F + D2 - DF(nu-prime = 4) + D. The new surface should prove useful for studying the effect on dynamics of a low, early barrier with a wide, flat bend potential.
Caffarel, Michel; Scemama, Anthony; Ramírez-Solís, Alejandro
2014-01-01
We present a comparative study of the spatial distribution of the spin density (SD) of the ground state of CuCl2 using Density Functional Theory (DFT), quantum Monte Carlo (QMC), and post-Hartree-Fock wavefunction theory (WFT). A number of studies have shown that an accurate description of the electronic structure of the lowest-lying states of this molecule is particularly challenging due to the interplay between the strong dynamical correlation effects in the 3d shell of the copper atom and the delocalization of the 3d hole over the chlorine atoms. It is shown here that qualitatively different results for SD are obtained from these various quantum-chemical approaches. At the DFT level, the spin density distribution is directly related to the amount of Hartree-Fock exchange introduced in hybrid functionals. At the QMC level, Fixed-node Diffusion Monte Carlo (FN-DMC) results for SD are strongly dependent on the nodal structure of the trial wavefunction employed (here, Hartree-Fock or Kohn-Sham with a particula...
Pamplona, Djenane C; Velloso, Raquel Q; Radwanski, Henrique N
2014-01-01
This article discusses skin expansion without considering cellular growth of the skin. An in vivo analysis was carried out that involved expansion at three different sites on one patient, allowing for the observation of the relaxation process. Those measurements were used to characterize the human skin of the thorax during the surgical process of skin expansion. A comparison between the in vivo results and the numerical finite elements model of the expansion was used to identify the material elastic parameters of the skin of the thorax of that patient. Delfino's constitutive equation was chosen to model the in vivo results. The skin is considered to be an isotropic, homogeneous, hyperelastic, and incompressible membrane. When the skin is extended, such as with expanders, the collagen fibers are also extended and cause stiffening in the skin, which results in increasing resistance to expansion or further stretching. We observed this phenomenon as an increase in the parameters as subsequent expansions continued. The number and shape of the skin expanders used in expansions were also studied, both mathematically and experimentally. The choice of the site where the expansion should be performed is discussed to enlighten problems that can lead to frustrated skin expansions. These results are very encouraging and provide insight into our understanding of the behavior of stretched skin by expansion. To our knowledge, this study has provided results that considerably improve our understanding of the behavior of human skin under expansion.
Institute of Scientific and Technical Information of China (English)
汪凯戈; 朱诗尧
2002-01-01
We present a complete description of atomic storage states which may appear in the electromagnetically induced transparency (EIT). The result shows that the spatial coherence has been included in the atomic collective operators and the atomic storage states. In some limits, a set of multimode atomic storage states has been established in correspondence with the multimode Fock states of the electromagnetic field. This gives a better understanding of the fact that, in BIT, the optical coherent information can be preserved and recovered.
Energy Technology Data Exchange (ETDEWEB)
Bouguettoucha, A.
1996-06-14
A possible effects of the C{sub 4}-symmetry in the superdeformed nuclei of the A {approx}150 mass range has been studied microscopically using cranking Strutinsky method with the deformed Woods-Saxon potential and the Hartree-Fock approach with the Skyrme interaction. If the existence of such a symmetry is judged by the moments Q{sub 44}, the results of the calculation indicate a very weak effect of this kind. Four new superdeformed bands in the {sup 148}Gd nucleus have been studied in reaction to the recent experimental observations (Eurogam Phase 2): a backbending has been tentatively observed at very high rotational frequency in the third excited band. One of the other bands exhibits a J{sup (2)} moment very similar to that of the yrast band in {sup 152}Dy, and this is the first example of identical bands which differ by four mass units. Calculations with the methods mentioned above have been used to analyse the band structure in terms of the nucleonic configurations. Calculation have been performed for some nuclear configurations predicted to involve the exotic octupole deformations (Y{sub 30-}`pear shapes`; Y{sub 31-}`banana mode`; Y{sub 32-}`T{sub d}-symmetry` and Y{sub 33-}`C{sub 3}-symmetry`). While the previous calculations based on the Strutinsky method could not treat the coupling between those modes, the Hartree-Fock approach allows to see for the first time in which propositions the various modes couple. (author). 116 refs.
Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.
Khoromskaia, Venera; Khoromskij, Boris N
2015-12-21
We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, first appeared as an accurate tensor calculus for the 3D Hartree potential using 1D complexity operations, and have evolved to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in O(n log n) complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D n × n × n Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D "density fitting" scheme, which yield an almost irreducible number of product basis functions involved in the 3D convolution integrals, depending on a threshold ε > 0. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excitation energies, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is towards the tensor-based Hartree-Fock numerical scheme for finite lattices, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a L × L × L lattice manifests the linear in L computational work, O(L), instead of the usual O(L(3) log L) scaling by the Ewald-type approaches.
Veeraraghavan, Srikant; Mazziotti, David A
2014-03-28
We present a density matrix approach for computing global solutions of restricted open-shell Hartree-Fock theory, based on semidefinite programming (SDP), that gives upper and lower bounds on the Hartree-Fock energy of quantum systems. While wave function approaches to Hartree-Fock theory yield an upper bound to the Hartree-Fock energy, we derive a semidefinite relaxation of Hartree-Fock theory that yields a rigorous lower bound on the Hartree-Fock energy. We also develop an upper-bound algorithm in which Hartree-Fock theory is cast as a SDP with a nonconvex constraint on the rank of the matrix variable. Equality of the upper- and lower-bound energies guarantees that the computed solution is the globally optimal solution of Hartree-Fock theory. The work extends a previously presented method for closed-shell systems [S. Veeraraghavan and D. A. Mazziotti, Phys. Rev. A 89, 010502-R (2014)]. For strongly correlated systems the SDP approach provides an alternative to the locally optimized Hartree-Fock energies and densities with a certificate of global optimality. Applications are made to the potential energy curves of C2, CN, Cr2, and NO2.
Energy Technology Data Exchange (ETDEWEB)
Veeraraghavan, Srikant; Mazziotti, David A., E-mail: damazz@uchicago.edu [Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 (United States)
2014-03-28
We present a density matrix approach for computing global solutions of restricted open-shell Hartree-Fock theory, based on semidefinite programming (SDP), that gives upper and lower bounds on the Hartree-Fock energy of quantum systems. While wave function approaches to Hartree-Fock theory yield an upper bound to the Hartree-Fock energy, we derive a semidefinite relaxation of Hartree-Fock theory that yields a rigorous lower bound on the Hartree-Fock energy. We also develop an upper-bound algorithm in which Hartree-Fock theory is cast as a SDP with a nonconvex constraint on the rank of the matrix variable. Equality of the upper- and lower-bound energies guarantees that the computed solution is the globally optimal solution of Hartree-Fock theory. The work extends a previously presented method for closed-shell systems [S. Veeraraghavan and D. A. Mazziotti, Phys. Rev. A 89, 010502–R (2014)]. For strongly correlated systems the SDP approach provides an alternative to the locally optimized Hartree-Fock energies and densities with a certificate of global optimality. Applications are made to the potential energy curves of C{sub 2}, CN, Cr {sub 2}, and NO {sub 2}.
Time-dependent Hartree-Fock studies of the dynamical fusion threshold
Directory of Open Access Journals (Sweden)
Nakatsukasa Takashi
2012-12-01
Full Text Available A microscopic description of dynamical fusion threshold in heavy ion collisions is performed in the framework of time-dependent Hartree-Fock (TDHF theory using Skyrme energy density functional (EDF. TDHF fusion threshold is in a better agreement with experimental fusion barrier. We find that the onset of extra push lies at the effective fissility 33, which is consistent with the prediction of Swiateckis macroscopic model. The extra push energy in our TDHF simulation is systematically smaller than the prediction in macroscopic model. The important dynamical effects and the way to fit the parameter might be responsible for the different results.
Compactness characterization of operators in the Toeplitz algebra of the Fock space $F_\\alpha ^p$
Bauer, Wolfram
2011-01-01
Let BT be the class of functions $f$ on $\\mathbb{C}^n$ where the Berezin transform $B_\\alpha (|f|)$ associated to the standard weighted Fock space $F_\\alpha ^2$ is bounded, and for $1 < p < \\infty$ let $\\mathcal{T}_p$ be the norm closure of the algebra generated by Toeplitz operators with BT symbols acting on $F_\\alpha ^p$. In this paper, we will show that an operator $A$ is compact on $F_\\alpha ^p$ if and only if $A \\in \\mathcal{T}_p$ and the Berezin transform $B_\\alpha (A)$ of $A$ vanishes at infinity.
Flight test report Focke Wulf Piaggio P149D-TP 2015
CSIR Research Space (South Africa)
Barker, D
2015-09-01
Full Text Available stream_source_info Barker_2015.pdf.txt stream_content_type text/plain stream_size 12410 Content-Encoding UTF-8 stream_name Barker_2015.pdf.txt Content-Type text/plain; charset=UTF-8 Flight Test Report Focke Wulf... Piaggio P149D-TP IASSA 2015 Des Barker Flight Test Society of South Africa Scope • Executive Summary of Flight Test Programme: – Background – Objectives of Test Programme – Scope of Modifications – Flight Test Team – Conditions...
Non-Commutative Fock-Darwin System and Magnetic Field Limits
Institute of Scientific and Technical Information of China (English)
YU Xiao-Min; LI Kang
2008-01-01
A Fock-Darwin system in noncommutative quantum mechanics is studied. By constructing Heisenberg algebra we obtain the levels on noncommutative space and noncommutative phase space, and give the corrections to the results in usual quantum mechanics. Moreover, to search the difference among the three spaces, the degeneracy is analysed by two ways, the value of (ω)/(ω)c and certain algebra realization (SU(2)and SU(1,1)), and some interesting properties in the magnetic field limit are exhibited, such as totally different degeneracy and magic number distribution for the given frequency or mass of a system in strong magnetic field.
Non-commutative Fock-Darwin system and its magnetism properties
Institute of Scientific and Technical Information of China (English)
Yu Xiao-Min; Li Kang
2009-01-01
The Fock-Darwin system is studied in noncommutative quantum mechanics. We not only obtain its energy eigenvalues and eigenstates in noncommutative phase space,but also give an electron orbit description as well as the general expressions of the magnetization and the susceptibility in a noncommutative situation. Further,we discuss two particular cases of temperature and present some interesting results different from those obtained from usual quantum mechanics such as the susceptibility dependent on a magnetic field at high temperatures,the occurrence of the magnetization in a zero magnetic field and zero temperature limit,and so on.
Projected gradient algorithms for Hartree-Fock and density matrix functional theory calculations
Cancès, Eric; Pernal, Katarzyna
2008-04-01
We present projected gradient algorithms designed for optimizing various functionals defined on the set of N-representable one-electron reduced density matrices. We show that projected gradient algorithms are efficient in minimizing the Hartree-Fock or the Müller-Buijse-Baerends functional. On the other hand, they converge very slowly when applied to the recently proposed BBk (k =1,2,3) functionals [O. Gritsenko et al., J. Chem. Phys. 122, 204102 (2005)]. This is due to the fact that the BBk functionals are not proper functionals of the density matrix.
Geometry of Vlasov kinetic moments: A bosonic Fock space for the symmetric Schouten bracket
Energy Technology Data Exchange (ETDEWEB)
Gibbons, John [Department of Mathematics, Imperial College London, London SW7 2AZ (United Kingdom); Holm, Darryl D. [Department of Mathematics, Imperial College London, London SW7 2AZ (United Kingdom); Computer and Computational Science Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Tronci, Cesare [Department of Mathematics, Imperial College London, London SW7 2AZ (United Kingdom); TERA Foundation for Oncological Hadrontherapy, 11 V. Puccini, Novara 28100 (Italy)], E-mail: cesare.tronci@imperial.ac.uk
2008-06-02
The dynamics of Vlasov kinetic moments is shown to be Lie-Poisson on the dual Lie algebra of symmetric contravariant tensor fields. The corresponding Lie bracket is identified with the symmetric Schouten bracket and the moment Lie algebra is related with a bundle of bosonic Fock spaces, where creation and annihilation operators are used to construct the cold plasma closure. Kinetic moments are also shown to define a momentum map, which is infinitesimally equivariant. This momentum map is the dual of a Lie algebra homomorphism, defined through the Schouten bracket. Finally the moment Lie-Poisson bracket is extended to anisotropic interactions.
Superdeformed rotational bands in the mercury region. A cranked Skyrme-Hartree-Fock-Bogoliubov study
Energy Technology Data Exchange (ETDEWEB)
Gall, B. (Centre de Spectrometrie Nucleaire et de Spectrometrie de Masse, 91 Orsay (France)); Bonche, P. (Service de Physique Theorique, DSM, CE Saclay, 91 Gif-sur-Yvette (France)); Dobaczewski, J. (Inst. of Theoretical Physics, Warsaw Univ., Warsaw (Poland)); Flocard, H. (Div. de Physique Theorique, Inst. de Physique Nucleaire, 91 Orsay (France)); Heenen, P.H. (Physique Nucleaire Theorique, Univ. Libre de Bruxelles (Belgium))
1994-05-01
A study of rotational properties of the ground superdeformed bands in [sup 190]Hg, [sup 192]Hg, [sup 194]Hg, and [sup 194]Pb is presented. We use the cranked Hartree-Fock-Bogoliubov method with the SkM* parametrization of the Skyrme force in the particle-hole channel and a seniority interaction in the pairing channel. An approximate particle number projection is performed by means of the Lipkin-Nogami prescription. We analyze the proton and neutron quasiparticle routhians in connection with the present information on about thirty presently observed superdeformed bands in nuclei close neighbours of [sup 192]Hg (orig.)
Superdeformed rotational bands in the mercury region; a cranked Skyrme-Hartree-Fock-Bogoliubov study
Gall, B.; Bonche, P.; Dobaczewski, J.; Flocard, H.; Heenen, P. -H.
1994-01-01
URL: http://www-spht.cea.fr/articles/T94/011 http://fr.arxiv.org/abs/nucl-th/9312011; International audience; A study of rotational properties of the ground superdeformed bands in $ ^{190} {\\rm Hg,} $ $ ^{192} {\\rm Hg,} $ $ ^{194} {\\rm Hg,} $ and $ ^{194} {\\rm Pb} $ is presented. We use the cranked Hartree-Fock-Bogoliubov method with the SkM$ ^\\ast $ parametrization of the Skyrme force in the particle-hole channel and a seniority interaction in the pairing channel. An approximate particle num...
Superdeformed rotational bands in the mercury region. A cranked Skyrme-Hartree-Fock-Bogoliubov study
Gall, B.; Bonche, P.; Dobaczewski, J.; Flocard, H.; Heenen, P.-H.
1994-09-01
A study of rotational properties of the ground superdeformed bands in190Hg,192Hg,194Hg, and194Pb is presented. We use the cranked Hartree-Fock-Bogoliubov method with the SkM* parametrization of the Skyrme force in the particle-hole channel and a seniority interaction in the pairing channel. An approximate particle number projection is performed by means of the Lipkin-Nogami prescription. We analyze the proton and neutron quasiparticle routhians in connection with the present information on about thirty presently observed superdeformed bands in nuclei close neighbours of192Hg.
Superdeformed rotational bands in the Mercury region. A cranked Skyrme-Hartree-Fock-Bogoliubov study
Energy Technology Data Exchange (ETDEWEB)
Gall, B. [Paris-11 Univ., 91 - Orsay (France). Centre de Spectrometrie Nucleaire et de Spectrometrie de Masse; Bonche, P. [CEA Centre d`Etudes de Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique; Dobaczewski, J. [Warsaw Univ. (Poland). Inst. Fizyki Teoretycznej; Heenen, P.H. [Universite Libre de Bruxelles (Belgium). Physique Nucleaire Theorique; Flocard, H.
1993-12-17
A study of rotational properties of the ground superdeformed bands in {sup 190}Hg, {sup 192}Hg, {sup 194}Hg, and {sup 194}Pb is presented. The cranked Hartree-Fock-Bogolyubov method is used with the SkM* parametrization of the Skyrme force in the particle-hole channel and a seniority interaction in the pairing channel. An approximate particle number projection is performed by means of the Lipkin-Nogami prescription. The proton and neutron quasiparticle rhouthians are analyzed in connection with the present information on about thirty presently observed superdeformed bands in nuclei close neighbours of {sup 192}Hg. (authors). 53 refs., 14 figs.
Nuclear relativistic Hartree-Fock calculations including pions interacting with a scalar field
Energy Technology Data Exchange (ETDEWEB)
Marcos, S.; Lopez-Quelle, M.; Niembro, R.; Savushkin, L. N. [Departamento de Fisica Moderna, Universidad de Cantabria, Santander (Spain); Departamento de Fisica Aplicada, Universidad de Cantabria, Santander (Spain); Departamento de Fisica Moderna, Universidad de Cantabria, Santander (Spain); Department of Physics, St. Petersburg University for Telecommunications, St. Petersburg (Russian Federation)
2012-10-20
The effect of pions on the nuclear shell structure is analyzed in a relativistic Hartree-Fock approximation (RHFA). The Lagrangian includes, in particular, a mixture of {pi}N pseudoscalar (PS) and pseudovector (PV) couplings, self-interactions of the scalar field {sigma} and a {sigma} - {pi} interaction that dresses pions with an effective mass (m*{sub {pi}}). It is found that an increase of m*{sub {pi}} strongly reduces the unrealistic effect of pions, keeping roughly unchanged their contribution to the total binding energy.
Fock-Darwin spectrum of a single InAs/GaAs quantum dot
Energy Technology Data Exchange (ETDEWEB)
Babinski, A. [Institute of Experimental Physics, Warsaw University, Hoza 69, 00-681 Warsaw (Poland); Grenoble High Magnetic Field Laboratory, CNRS, BP-166, 38042 Grenoble Cedex 9 (France); Potemski, M. [Grenoble High Magnetic Field Laboratory, CNRS, BP-166, 38042 Grenoble Cedex 9 (France); Raymond, S.; Lapointe, J.; Wasilewski, Z.R. [Institute for Microstructural Sciences, NRC, Ottawa, K1A 0R6 (Canada)
2006-07-01
Magnetospectroscopic study of a highly excited single InAs/GaAs quantum dot is reported. Optical emission from the s- and p-shells is identified and investigated in magnetic fields up to 20T. The zero-field splitting and the Zeeman orbital splitting of the p-shell-related emission lines in magnetic field are observed. The evolution of spectra in magnetic field resembles a classical Fock-Darwin energy diagram, although effects of the electron-electron interaction and asymmetry of localizing potential can be clearly observed. (copyright 2006 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Renormalization and asymptotic expansion of Dirac's polarized vacuum
Gravejat, Philippe; Séré, Eric
2010-01-01
We perform rigorously the charge renormalization of the so-called reduced Bogoliubov-Dirac-Fock (rBDF) model. This nonlinear theory, based on the Dirac operator, describes atoms and molecules while taking into account vacuum polarization effects. We consider the total physical density including both the external density of a nucleus and the self-consistent polarization of the Dirac sea, but no `real' electron. We show that it admits an asymptotic expansion to any order in powers of the physical coupling constant $\\alphaph$, provided that the ultraviolet cut-off behaves as $\\Lambda\\sim e^{3\\pi(1-Z_3)/2\\alphaph}\\gg1$. The renormalization parameter $0
The Brueckner-Hartree-Fock Equation of State for Nuclear Matter and Neutron Skin
Qing-Yang, Bu; Zeng-Hua, Li; Hans-Josef, Schulze
2016-03-01
Not Available Supported by the National Natural Science Foundation of China under Grant Nos 11075037 and 11475045, the Scientific Research Foundation for the Returned Overseas Chinese Scholars of the Ministry of Education of China, the Fundamental Research Funds for the Central Universities of China, the Shanghai Leading Academic Discipline Project under Grant No B107, and the ‘NewCompStar’, COST Action MP1304.
Predicting bond strength from a single Hartree-Fock ground state using the localized pair model.
Hennessey, Dylan C; Sheppard, Brendan J H; Mackenzie, Dalton E C K; Pearson, Jason K
2014-12-14
We present an application of the recently introduced Localized Pair Model (LPM) [Z. A. Zielinksi and J. K. Pearson, Comput. Theor. Chem., 2013, 1003, 7990] to characterize and quantify properties of the chemical bond in a series of substituted benzoic acid molecules. By computing interelectronic distribution functions for doubly-occupied Edmiston-Ruedenberg localized molecular orbitals (LMOs), we show that chemically intuitive electron pairs may be uniquely classified and bond strength may be predicted with remarkable accuracy. Specifically, the HF/u6-311G(d,p) level (where u denotes a complete uncontraction of the basis set) is used to generate the relevant LMOs and their respective interelectronic distribution functions can be linearly correlated to the well-known Hammett σp or σm parameters with near-unity correlation coefficients.
Quantum bits and superposition of displaced Fock states of the cavity field
Energy Technology Data Exchange (ETDEWEB)
Arevalo A, L.M. [Centro de Investigaciones en Optica A.C., Prolongacion de Constitucion No. 607, Apdo. Postal 507, Aguascalientes (Mexico); Moya C, H. [Instituto Nacional de Astrofisica, Optica y Electronica, Apdo. Postal 51 y 216, 72000 Puebla (Mexico)
2002-07-01
We study the effects of counter rotating terms in the interaction of quantized light with a two-level atom, by using the method of small rotations. We give an expression for the wave function of the composed system atom plus field and point out one initial wave function that generates a quantum bit of the electromagnetic field with arbitrary amplitudes. (Author)
34 CFR 361.35 - Innovation and expansion activities.
2010-07-01
... Council, consistent with the plan prepared under 34 CFR 364.21(i). (b) The State plan must— (1) Describe... 34 Education 2 2010-07-01 2010-07-01 false Innovation and expansion activities. 361.35 Section 361... Innovation and expansion activities. (a) The State plan must assure that the State will reserve and use...
Olshanii, Maxim; Pricoupenko, Ludovic
2001-05-01
We introduce a novel one-parametric family of zero-range pseudopotentials hatV^Λ(r) = g_Λ δ(r) [ partialr + Λ ] (r \\cdot ) with g_Λ = fracg_01-Λ a and g0 = 4πhbar^2 a/m , whose scattering length a does not depend on the free parameter Λ. No exact (after the zero-range approximation has been made) many-body observable depends on it, although approximate treatments differ for different Λ (M. Olshanii and L. Pricoupenko, mat/0101275>). We incorporate these pseudopotentials in the Hartree-Fock-Bogoliubov variational formalism, whose conventional (Λ=0) version is known to exhibit UV-divergencies, inconsistencies with both Hugenholtz-Pines theorem and many-body T-matrix calculations, and inability to develop an energy minimum for the atomic condensate leading to a molecular condensate instead. Using Λ as a new variational parameter we resolve all inconsistencies of the Hartree-Fock-Bogoliubov formalism known so far, with no ad hoc modifications of the theory.
Energy Technology Data Exchange (ETDEWEB)
Urbina, Juan Diego; Engl, Thomas; Richter, Klaus [Institute for Theoretical Physics, University of Regensburg (Germany); Arguelles, Arturo [Department of Physics, University of Liege (Belgium); Institute for Theoretical Physics, University of Regensburg (Germany); Dujardin, Julien; Schlagheck, Peter [Department of Physics, University of Liege (Belgium)
2013-07-01
We present a semiclassical theory of quantum interference effects in interacting bosonic fields. We make special emphasis on the difference between genuine quantum interference (due to the superposition principle in the many-body Hilbert space), and classical interference effects due to the wave character of the classical limit. First, we discuss how the usual approaches to this problem are unable to provide the characteristic sum of oscillatory terms, each asociated with a solution of the classical equations of motion, required to semiclassically address interference effects. We show then how to solve this problems by a formal construction of the van Vleck-Gutzwiller propagator for bosonic fields as a sum over paths in the associated Fock space and we identify the classical limit as a Gross-Pitaevskii equation with boundary conditions and multiple solutions. The theory predicts effects akin to weak localization to take place in Fock space, and in particular the enhancement of quantum probability of return due to interference between time-reversed paths there. We support our claims with extensive numerical calculations for a discrete version of an interacting bosonic field.
Hu, Jinniu; Shen, Hong
2016-01-01
We study the properties of nuclear matter with lattice nucleon-nucleon ($NN$) potential in the relativistic Brueckner-Hartree-Fock (RBHF) theory. To use this potential in such a microscopic many-body theory, we firstly have to construct a one-boson-exchange potential (OBEP) based on the latest lattice $NN$ potential. Three mesons, pion, $\\sigma$ meson, and $\\omega$ meson, are considered. Their coupling constants and cut-off momenta are determined by fitting the on-shell behaviors and phase shifts of the lattice force, respectively. Therefore, we obtain two parameter sets of the OBEP potential (named as LOBEP1 and LOBEP2) with these two fitting ways. We calculate the properties of symmetric and pure neutron matter with LOBEP1 and LOBEP2. In non-relativistic Brueckner-Hartree-Fock case, the binding energies of symmetric nuclear matter are around $-3$ and $-5$ MeV at saturation densities, while it becomes $-8$ and $-12$ MeV in relativistic framework with $^1S_0,~^3S_1,$ and $^3D_1$ channels using our two paramet...
A divide and conquer real space finite-element Hartree-Fock method
Alizadegan, R.; Hsia, K. J.; Martinez, T. J.
2010-01-01
Since the seminal contribution of Roothaan, quantum chemistry methods are traditionally expressed using finite basis sets comprised of smooth and continuous functions (atom-centered Gaussians) to describe the electronic degrees of freedom. Although this approach proved quite powerful, it is not well suited for large basis sets because of linear dependence problems and ill conditioning of the required matrices. The finite element method (FEM), on the other hand, is a powerful numerical method whose convergence is also guaranteed by variational principles and can be achieved systematically by increasing the number of degrees of freedom and/or the polynomial order of the shape functions. Here we apply the real-space FEM to Hartree-Fock calculations in three dimensions. The method produces sparse, banded Hermitian matrices while allowing for variable spatial resolution. This local-basis approach to electronic structure theory allows for systematic convergence and promises to provide an accurate and efficient way toward the full ab initio analysis of materials at larger scales. We introduce a new acceleration technique for evaluating the exchange contribution within FEM and explore the accuracy and robustness of the method for some selected test atoms and molecules. Furthermore, we applied a divide-and-conquer (DC) method to the finite-element Hartree-Fock ab initio electronic-structure calculations in three dimensions. This DC approach leads to facile parallelization and should enable reduced scaling for large systems.
Parallel and Low-Order Scaling Implementation of Hartree-Fock Exchange Using Local Density Fitting.
Köppl, Christoph; Werner, Hans-Joachim
2016-07-12
Calculations using modern linear-scaling electron-correlation methods are often much faster than the necessary reference Hartree-Fock (HF) calculations. We report a newly implemented HF program that speeds up the most time-consuming step, namely, the evaluation of the exchange contributions to the Fock matrix. Using localized orbitals and their sparsity, local density fitting (LDF), and atomic orbital domains, we demonstrate that the calculation of the exchange matrix scales asymptotically linearly with molecular size. The remaining parts of the HF calculation scale cubically but become dominant only for very large molecular sizes or with many processing cores. The method is well parallelized, and the speedup scales well with up to about 100 CPU cores on multiple compute nodes. The effect of the local approximations on the accuracy of computed HF and local second-order Møller-Plesset perturbation theory energies is systematically investigated, and default values are established for the parameters that determine the domain sizes. Using these values, calculations for molecules with hundreds of atoms in combination with triple-ζ basis sets can be carried out in less than 1 h, with just a few compute nodes. The method can also be used to speed up density functional theory calculations with hybrid functionals that contain HF exchange.
Applying the Density Matrix Expansion with Coordinate-Space Chiral Interactions
Dyhdalo, A; Furnstahl, R J
2016-01-01
We apply the density matrix expansion (DME) at Hartree-Fock level with long-range chiral effective field theory interactions defined in coordinate space up to next-to-next-to-leading order. We consider chiral potentials both with and without explicit Delta isobars. The challenging algebra associated with applying the DME to three-nucleon forces is tamed using a new organization scheme, which will also facilitate generalizations. We include local regulators on the interactions to mitigate the effects of singular potentials on the DME couplings and simplify the optimization of generalized Skyrme-like functionals.
DEFF Research Database (Denmark)
Kjærgaard, Thomas; Jørgensen, Poul; Thorvaldsen, Andreas;
2009-01-01
-orbital density-matrix based formulation of response theory and use London atomic orbitals to parametrize the magnetic field dependence. It yields a computational procedure which is both gauge-origin independent and suitable for linear-scaling at the level of time-dependent Hartree-Fock and density functional......A Lagrangian approach has been used to derive gauge-origin independent expressions for two properties that rationalize magneto-optical activity, namely the Verdet constant V(ω) of the Faraday effect and the B term of magnetic circular dichroism. The approach is expressed in terms of an atomic...... theory. The formulation includes a modified preconditioned conjugated gradient algorithm, which projects out the excited state component from the solution to the linear response equation. This is required when solving one of the response equations for the determination of the B term and divergence...
Ebata, Shuichiro; Inakura, Tsunenori
2014-01-01
Systematic investigations of the electric dipole (E1) modes of excitation are performed using the canonical-basis time-dependent Hartree-Fock-Bogoliubov (Cb-TDHFB) theory. The Cb-TDHFB is able to describe dynamical pairing correlations in excited states of nuclear systems. We apply the method to the real-time calculation of linear response in even-even nuclei with Skyrme functionals. Effects of shell structure, neutron skin, deformation, and neutron chemical potential (separation energy) are studied in a systematic way. This reveals a number of characteristic features of the low-energy E1 modes. We also find a universal behavior in the low-energy E1 modes for heavy neutron-rich isotopes, which suggests the emergence of decoupled E1 peaks beyond N = 82.
Neese, Frank
2007-10-28
The zero-field splitting (ZFS) (expressed in terms of the D tensor) is the leading spin-Hamiltonian parameter for systems with a ground state spin S>12. To first order in perturbation theory, the ZFS arises from the direct spin-spin dipole-dipole interaction. To second order, contributions arise from spin-orbit coupling (SOC). The latter contributions are difficult to treat since the SOC mixes states of different multiplicities. This is an aspect of dominant importance for the correct prediction of the D tensor. In this work, the theory of the D tensor is discussed from the point of view of analytic derivative theory. Starting from a general earlier perturbation treatment [F. Neese and E. I. Soloman, Inorg. Chem. 37, 6568 (1998)], straightforward response equations are derived that are readily transferred to the self-consistent field (SCF) Hartree-Fock (HF) or density functional theory (DFT) framework. The main additional effort in such calculations arises from the solution of nine sets of nonstandard coupled-perturbed SCF equations. These equations have been implemented together with the spin-orbit mean-field representation of the SOC operator and a mean-field treatment of the direct spin-spin interaction into the ORCA electronic structure program. A series of test calculations on diatomic molecules with accurately known zero-field splittings shows that the new approach corrects most of the shortcomings of previous DFT based methods and, on average, leads to predictions within 10% of the experimental values. The slope of the correlation line is essentially unity for the B3LYP and BLYP functionals compared to approximately 0.5 in previous treatments.
Goriely, S.; Chamel, N.; Pearson, J. M.
2016-03-01
Extending our earlier work, a new family of three Hartree-Fock-Bogoliubov (HFB) mass models, labeled HFB-30, HFB-31, and HFB-32, is presented, along with their underlying interactions, BSk30, BSk31, and BSk32, respectively. The principle new feature is a purely phenomenological pairing term that depends on the density gradient. This enables us to have a bulk pairing term that is fitted to realistic nuclear-matter calculations in which for the first time the self-energy corrections are included, while the behavior of the nucleon effective masses in asymmetric homogeneous nuclear matter is significantly improved. Furthermore, in the particle-hole channel all the highly realistic constraints of our earlier work are retained. In particular, the unconventional Skyrme forces containing t4 and t5 terms are still constrained to fit realistic equations of state of neutron matter stiff enough to support the massive neutron stars PSR J1614-2230 and PSR J0348+0432. All unphysical long-wavelength spin and spin-isospin instabilities of nuclear matter, including the unphysical transition to a polarized state in neutron-star matter, are eliminated. Our three interactions are characterized by values of the symmetry coefficient J of 30, 31, and 32 MeV, respectively. The best fit to the database of 2353 nuclear masses is found for model HFB-31 (J =31 MeV ) with a model error of 0.561 MeV. This model also fits the charge-radius data with an root-mean-square error of 0.027 fm.
Symbolic computation of the Hartree-Fock energy from a chiral EFT three-nucleon interaction at N 2LO
Gebremariam, B.; Bogner, S. K.; Duguet, T.
2010-06-01
We present the first of a two-part Mathematica notebook collection that implements a symbolic approach for the application of the density matrix expansion (DME) to the Hartree-Fock (HF) energy from a chiral effective field theory (EFT) three-nucleon interaction at N 2LO. The final output from the notebooks is a Skyrme-like energy density functional that provides a quasi-local approximation to the non-local HF energy. In this paper, we discuss the derivation of the HF energy and its simplification in terms of the scalar/vector-isoscalar/isovector parts of the one-body density matrix. Furthermore, a set of steps is described and illustrated on how to extend the approach to other three-nucleon interactions. Program summaryProgram title: SymbHFNNN Catalogue identifier: AEGC_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGC_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 96 666 No. of bytes in distributed program, including test data, etc.: 378 083 Distribution format: tar.gz Programming language: Mathematica 7.1 Computer: Any computer running Mathematica 6.0 and later versions Operating system: Windows Xp, Linux/Unix RAM: 256 Mb Classification: 5, 17.16, 17.22 Nature of problem: The calculation of the HF energy from the chiral EFT three-nucleon interaction at N 2LO involves tremendous spin-isospin algebra. The problem is compounded by the need to eventually obtain a quasi-local approximation to the HF energy, which requires the HF energy to be expressed in terms of scalar/vector-isoscalar/isovector parts of the one-body density matrix. The Mathematica notebooks discussed in this paper solve the latter issue. Solution method: The HF energy from the chiral EFT three-nucleon interaction at N 2LO is cast into a form suitable for an automatic simplification of
Energy Technology Data Exchange (ETDEWEB)
Barrera, G D [Departamento de QuImica, Universidad Nacional de la Patagonia SJB, Ciudad Universitaria, 9000 Comodoro Rivadavia (Argentina); Bruno, J A O [Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de QuImica Inorganica, AnalItica y QuImica FIsica, Pabellon 2, Ciudad Universitaria, 1428 Buenos Aires (Argentina); Barron, T H K [School of Chemistry, University of Bristol, Cantock' s Close, Bristol BS8 1TS (United Kingdom); Allan, N L [School of Chemistry, University of Bristol, Cantock' s Close, Bristol BS8 1TS (United Kingdom)
2005-02-02
There has been substantial renewed interest in negative thermal expansion following the discovery that cubic ZrW{sub 2}O{sub 8} contracts over a temperature range in excess of 1000 K. Substances of many different kinds show negative thermal expansion, especially at low temperatures. In this article we review the underlying thermodynamics, emphasizing the roles of thermal stress and elasticity. We also discuss vibrational and non-vibrational mechanisms operating on the atomic scale that are responsible for negative expansion, both isotropic and anisotropic, in a wide range of materials. (topical review)
Shepherd, James J; Booth, George H; Kresse, Georg; Alavi, Ali
2012-01-01
Using the finite simulation-cell homogeneous electron gas (HEG) as a model, we investigate the convergence of the correlation energy to the complete basis set (CBS) limit in methods utilising plane-wave wavefunction expansions. Simple analytic and numerical results from second-order M{\\o}ller-Plesset theory (MP2) suggest a 1/M decay of the basis-set incompleteness error where M is the number of plane waves used in the calculation, allowing for straightforward extrapolation to the CBS limit. As we shall show, the choice of basis set truncation when constructing many-electron wavefunctions is far from obvious, and here we propose several alternatives based on the momentum transfer vector, which greatly improve the rate of convergence. This is demonstrated for a variety of wavefunction methods, from MP2 to coupled-cluster doubles theory (CCD) and the random-phase approximation plus second-order screened exchange (RPA+SOSEX). Finite basis-set energies are presented for these methods and compared with exact benchm...
Fuel Thermal Expansion (FTHEXP). [BWR; PWR
Energy Technology Data Exchange (ETDEWEB)
Reymann, G. A.
1978-07-01
A model is presented which deals with dimensional changes in LWR fuel pellets caused by changes in temperature. It is capable of dealing with any combination of UO/sub 2/ and PuO/sub 2/ in solid, liquid or mixed phase states, and includes expansion due to the solid-liquid phase change. The function FTHEXP models fuel thermal expansion as a function of temperature, fraction of PuO/sub 2/, and the fraction of fuel which is molten.
Bučinský, Lukáš
2015-05-11
"Kramers pairs symmetry breaking" is evaluated at the 2-component (2c) Kramers unrestricted and/or general complex Hartree-Fock (GCHF) level of theory, and its analogy with "spin contamination" at the 1-component (1c) unrestricted Hartree-Fock (UHF) level of theory is emphasized. The GCHF "Kramers pairs symmetry breaking" evaluation is using the square of overlaps between the set of occupied spinorbitals with the projected set of Kramers pairs. In the same fashion, overlaps between α and β orbitals are used in the evaluation of "spin contamination" at the UHF level of theory. In this manner, UHF Š2 expectation value is made formally extended to the GCHF case. The directly evaluated GCHF expectation value of the Š2 operator is considered for completeness. It is found that the 2c GCHF Kramers pairs symmetry breaking has a very similar extent in comparison to the 1c UHF spin contamination. Thus higher excited states contributions to the 1c and 2c unrestricted wave functions of open shell systems have almost the same extent and physical consequences. Moreover, it is formally shown that a single determinant wave function in the restricted open shell Kramers case has the expectation value of K2 operator equal to the negative number of open shell electrons, while the eigenvalue of K2 for the series of simple systems (H, He, He*-triplet, Li and Li*-quartet) are found to be equal to minus the square of the number of open shell electrons. The concept of unpaired electron density is extended to the GCHF regime and compared to UHF and restricted open shell Hartree-Fock spin density. The "collinear" and "noncollinear" analogs of spin density at the GCHF level of theory are considered as well. Spin contamination and/or Kramers pairs symmetry breaking, spin populations and spin densities are considered for H2O+, Cl, HCl+, phenoxyl radical (C6H5O) as well as for Cu, Cu2+, Fe and the [OsCl5(1H-pyrazole)]- anion. The 1c and 2c unpaired electron density representation is found
Pernpointner, M.
2004-11-01
In this paper we present the third-order extension of the four-component one-particle propagator method in the non-Dyson version of the algebraic diagrammatic construction (ADC) for the calculation of valence ionization energies. Relativistic and electron correlation effects are incorporated consistently by starting from the Dirac-Hamiltonian. The ADC equations derived from the Feynman diagrams can hereby be used in their spin-orbital form and need not be transformed to the spin-free version as required for a nonrelativistic treatment. For the calculation of the constant self-energy contribution the Dyson expansion method was implemented being superior to a perturbational treatment of Σ(∞). The Dirac-Hartree-Fock- (DHF-) ADC(3) was applied to the calculation of valence photoionization spectra of the noble gas atoms, carbon monoxide and ICN now also reproducing spin-orbit features in the spectrum. Comparison with DHF-ADC(2), nonrelativistic ADC(3), and experimental data was made in order to demonstrate the characteristics and performance of the method.
Rynkun, P.; Jönsson, P.; Gaigalas, G.; Froese Fischer, C.
2014-03-01
Based on relativistic wavefunctions from multiconfiguration Dirac-Hartree-Fock and configuration interaction calculations, E1, M1, E2, and M2 transition rates, weighted oscillator strengths, and lifetimes are evaluated for the states of the (1s2)2s22p3,2s2p4, and 2p5 configurations in all nitrogen-like ions between F III and Kr XXX. The wavefunction expansions include valence, core-valence, and core-core correlation effects through single-double multireference expansions to increasing sets of active orbitals. The computed energies agree very well with experimental values, with differences of only 300-600 cm-1 for the majority of the levels and ions in the sequence. Computed transitions rates are in close agreement with available data from MCHF-BP calculations by Tachiev and Froese Fischer [G.I. Tachiev, C. Froese Fischer, A&A 385 (2002) 716].
Fakhruddin, Hasan
1993-01-01
Describes a paradox in the equation for thermal expansion. If the calculations for heating a rod and subsequently cooling a rod are determined, the new length of the cool rod is shorter than expected. (PR)
Schunck, N.; Dobaczewski, J.; McDonnell, J.; Satuła, W.; Sheikh, J. A.; Staszczak, A.; Stoitsov, M.; Toivanen, P.
2012-01-01
-consistent Hartree-Fock equations, even for heavy nuclei, and for various nucleonic ( n-particle- n-hole) configurations, deformations, excitation energies, or angular momenta. Similarly, Local Density Approximation in the particle-particle channel, which is equivalent to using a zero-range interaction, allows for a simple implementation of pairing effects within the Hartree-Fock-Bogolyubov method. Solution method: The program uses the Cartesian harmonic oscillator basis to expand single-particle or single-quasiparticle wave functions of neutrons and protons interacting by means of the Skyrme effective interaction and zero-range pairing interaction. The expansion coefficients are determined by the iterative diagonalization of the mean-field Hamiltonians or Routhians which depend non-linearly on the local neutron and proton densities. Suitable constraints are used to obtain states corresponding to a given configuration, deformation or angular momentum. The method of solution has been presented in: [J. Dobaczewski, J. Dudek, Comput. Phys. Commun. 102 (1997) 166]. Reasons for new version: Version 2.49s of HFODD provides a number of new options such as the isospin mixing and projection of the Skyrme functional, the finite-temperature HF and HFB formalism and optimized methods to perform multi-constrained calculations. It is also the first version of HFODD to contain threading and parallel capabilities. Summary of revisions: Isospin mixing and projection of the HF states has been implemented. The finite-temperature formalism for the HFB equations has been implemented. The Lipkin translational energy correction method has been implemented. Calculation of the shell correction has been implemented. The two-basis method for the solution to the HFB equations has been implemented. The Augmented Lagrangian Method (ALM) for calculations with multiple constraints has been implemented. The linear constraint method based on the cranking approximation of the RPA matrix has been implemented. An
Dirac-Fock-Breit-Gaunt calculations for tungsten hexacarbonyl W(CO)6.
Malli, Gulzari L
2016-05-21
The first all-electron fully relativistic Dirac-Fock-Breit-Gaunt (DFBG), Dirac-Fock (DF), and nonrelativistic (NR) Hartree-Fock (HF) calculations are reported for octahedral (Oh) tungsten hexacarbonyl W(CO)6. Our DF and NR HF calculations predict atomization energy of 73.76 and 70.33 eV, respectively. The relativistic contribution of ∼3.4 eV to the atomization energy of W(CO)6 is fairly significant. The DF and NR energy for the reaction W + 6CO → W(CO)6 is calculated as -7.90 and -8.86 eV, respectively. The mean bond energy predicted by our NR and DF calculations is 142.5 kJ/mol and 177.5 kJ/mol, respectively, and our predicted DF mean bond energy is in excellent agreement with the experimental value of 179 kJ/mol quoted in the literature. The relativistic effects contribute ∼35 kJ/mol to the mean bond energy and the calculated BSSE is 1.6 kcal/mol, which indicates that the triple zeta basis set used here is fairly good. The mean bond energy and the atomization energy calculated in our DFBG SCF calculations, which include variationally both the relativistic and magnetic Breit effects, is 157.4 kJ/mol and 68.84 eV, respectively. The magnetic Breit effects lead to a decrease of ∼20 kJ/mol and ∼4.9 eV for the mean bond energy and atomization energy, respectively, for W(CO)6. Our calculated magnetic Breit interaction energy of -9.79 eV for the energy of reaction (ΔE) for W + 6CO → W(CO)6 is lower by ∼1.90 eV as compared to the corresponding DF value (ΔE) and contributes significantly to the ΔE. A detailed discussion is presented of electronic structure, bonding, and molecular energy levels at various levels of theory for W(CO)6.
Multiple scattering expansion with distortion
Tandy, P. C.; Thaler, R. M.
1980-12-01
A multiple scattering description of elastic scattering is formulated in terms of impulsive scatterings from single target nucleons and pairs of target nucleons. In this description, distortion effects on the projectile from the residual medium are also described by multiple scattering in terms of the same single and pair amplitudes. At the level of single scattering, this procedure yields the first order optical potential result of Kerman, McManus, and Thaler. When scattering from both single nucleons and pairs of nucleons is included, the method leads to a one-body integral equation which requires the physical projectile-nucleon and projectile-pair transition amplitudes as input. This input is similar, but not exactly equivalent to that required by the spectator expansion for the optical potential truncated at second order. A principal advantage of the present formulation is that there need be no explicit dependence upon the projection operator Q which projects off the target ground state. This feature introduces a scaling which appears to be a direct extension of the first order Kerman, McManus, and Thaler type of scaling. We follow up suggestions arising in the foregoing to show that the exact optical potential to second order in the spectator expansion can also be cast into a form having no explicit dependence upon Q, and requiring physical projectile-nucleon and projectile-pair transition amplitudes as input. NUCLEAR REACTIONS Multiple scattering from single nucleons, pairs of nucleons in nucleus. Distortion from residual medium. Optical potential. spectator expansion.
Urban underground network expansion planning
Energy Technology Data Exchange (ETDEWEB)
Bozic, Z. [Sinclair Knight Merz Pty Ltd., Perth (Australia); Hobson, E. [HI Consulting Services Pty Ltd., Adelaide (Australia)
1997-03-01
The authors describe a three step approach to expansion planning of high voltage (HV) urban underground distribution networks. Although the techniques are specifically oriented to underground systems, they are equally applicable to overhead system design. The fundamental engineering problem is how to connect individual high voltage to low voltage substations (HV/LV SS) and zone HV SS into a future urban underground network. The problem is to rearrange the HV network to minimise the cost of expansion subject to provision of an alternative supply, specified load transfer among the neighbouring zone SS, and other general planning constraints such as feeder capacity, voltage regulation, operational requirements and losses. A review of the current state of the art of distribution expansion planning is provided. The normal manual approach is discussed together with more recent research into computer methods. Three lines of computer research are identified and classified as radially constrained, security constrained and utilisation of travelling salesman/vehicle routing problem algorithms (TSP/VRP). The TSP/VRP line of research has been extended here to produce practical techniques for the assistance of network planners. (Author)
Institute of Scientific and Technical Information of China (English)
曾仲毅; 徐帮树; 胡世权; 陈诚
2014-01-01
针对小河沟膨胀土隧道降雨增湿塌方现象，以围岩含水率分布变化引起膨胀应力场为主要研究内容，展开增湿对隧道支护结构的影响研究。首先，利用热传导热能量平衡方程与孔隙渗流连续方程数学描述相似性，推导出热传导膨胀模拟增湿膨胀的替代方程。然后，结合室内试验和文献资料，率定膨胀土膨胀力及渗流参数。最后，在正确考虑地质构造影响的基础上运用有限差分软件 FLAC3D热-力耦合模块进行建模计算，分别对不同膨胀力模型的增湿过程进行仿真模拟，得出支护结构受力变形随含水率分布及膨胀力大小的变化规律。分析得到了对隧道支护结构造成不良影响的关键含水率和膨胀力值。研究成果可以有效指导膨胀性黄土隧道支护设计和变形控制。%In light of the collapse of an expansive soil tunnel owing to rainfall infiltration, swelling stress field caused by the change in the moisture content distribution of surrounding soil was taken into consideration to solve the problem. At first, due to the similarity of continuum heat conduction energy-balance equation and seepage continuity equation, an alternative expansive equation is derived based on the theory of heat conduction expansive to simulate water-increased expansion of expansive soil, and then determine the swelling force and seepage parameters by laboratory test and engineering simulation. Finally, considering the proper geologic factors, a numerical model of tunnel is established by means of thermal-mechanical coupling of FLAC3D. And by the simulations of tunnel with different swelling forces under water-increased state, relation curves are acquired between liner deformation and moisture content, swelling force. According to the above analysis, turning points of moisture content and swelling force to prevent liner from failure are proposed, which can effectively guide the design and
Amour, Laurent; Nourrigat, Jean
2011-01-01
We study the Wick symbol of a solution of the time dependent Hartree Fock equation, under weaker hypotheses than those needed for the Weyl symbol in the first paper with thesame title. With similar, we prove some kind of Ehrenfest theorem for observables that are not pseudo-differential operators.
Twist-averaged boundary conditions for nuclear pasta Hartree-Fock calculations
Schuetrumpf, B
2015-01-01
Background: Nuclear pasta phases, present in the inner crust of neutron stars, are associated with nucleonic matter at sub-saturation densities arranged in regular shapes. Those complex phases, residing in a layer which is approximately 100 m thick, impact many features of neutron stars. Theoretical quantum-mechanical simulations of nuclear pasta are usually carried out in finite 3D boxes assuming periodic boundary conditions (PBC). The resulting solutions are affected by spurious finite-size effects. Purpose: In order to remove spurious finite-size effects, it is convenient to employ twist-averaged boundary conditions (TABC) used in condensed matter, nuclear matter, and lattice QCD applications. In this work, we study the effectiveness of TABC in the context of pasta phases simulations within nuclear density functional theory. Methods: We perform Skyrme-Hartree-Fock calculations in three dimensions by implementing Bloch boundary conditions. The TABC averages are obtained by means of Gauss-Legendre integratio...
The exact calculation of the edge components of the angular Fock coefficients
Liverts, Evgeny Z
2016-01-01
The present paper constitutes the development of our previous work devoted to calculations of the angular Fock coefficients, $\\psi_{k,p}(\\alpha,\\theta)$. The explicit analytic representations for the edge components $\\psi_{k,0}^{(0)}$ and $\\psi_{k,0}^{(k)}$ with $k\\leq8$ are derived. The methods developed enable such a calculation for arbitrary $k$. The single-series representation for subcomponent $\\psi_{3,0}^{(2e)}$ missed in the previous paper is developed. It is shown how to express some of the complicated subcomponents through the hypergeometric and the elementary functions, as well. Using the specific operator of the Wolfram Mathematica, the simple explicit representations for some complex mathematical objects under consideration are obtained.
A New Decomposition Approach of Dirac Brueckner Hartree-Fock G Matrix for Asymmetric Nuclear Matter
Institute of Scientific and Technical Information of China (English)
刘玲; 马中玉
2002-01-01
Asymmetric nuclear matter is investigated by the Dirac Brueckner Hartree-Fock (DBHF) approach with a new decomposition of the Dirac structure of nucleon self-energy from the G matrix. It is found that the isospin dependence of the scalar and vector potentials is relatively weak, although both potentials for neutron (proton)become deep (shallow) in the neutron-rich nuclear matter. The results in asymmetric nuclear matter are rather different from those obtained by a simple method, where the nucleon self-energy is deduced from the single-particle energy. The nuclear binding energy as a function of the asymmetry parameter fulfils the empirical parabolic law up to very extreme isospin asymmetric nuclear matter in the DBHF approach. The behaviour of the density dependence of the asymmetry energy is different from that obtained by non-relativistic approaches, although both give similar asymmetry energy at the nuclear saturation density.
Pion tensor force and nuclear binding energy in the relativistic Hartree-Fock formalism
Marcos, S.; López-Quelle, M.; Niembro, R.; Savushkin, L. N.
2014-03-01
The binding energies of several isotopic families are studied within the relativistic Hartree-Fock approximation with the pseudovector coupling for the πN vertex, to find out a suitable strength for the effective pion tensor force (EPTF). An approximation for determining separately the contributions of the central and tensor forces generated by pion is considered. The results for heavy nuclei indicate that a realistic strength for the EPTF is smaller than a half of that appearing in the OPEP. This conclusion also applies to the results for the single-particle energies. Besides, it has been found that there is a genuine relativistic contribution of the EPTF in nuclear matter which is small but significant.
Hartree-Fock mean-field theory for trapped dirty bosons
Khellil, Tama; Pelster, Axel
2016-06-01
Here we work out in detail a non-perturbative approach to the dirty boson problem, which relies on the Hartree-Fock theory and the replica method. For a weakly interacting Bose gas within a trapped confinement and a delta-correlated disorder potential at finite temperature, we determine the underlying free energy. From it we determine via extremization self-consistency equations for the three components of the particle density, namely the condensate density, the thermal density, and the density of fragmented local Bose-Einstein condensates within the respective minima of the random potential landscape. Solving these self-consistency equations in one and three dimensions in two other publications has revealed how these three densities change for increasing disorder strength.
Fock-Lorentz transformations and time-varying speed of light
Manida, S N
1999-01-01
The theory of relativity was built up on linear Lorentz transformation. However, in his fundamental work "Theory of Space, Time and Gravitation" V.A.Fock shows that the general form of the transformation between the coordinates in the two inertial frames could be taken to be linear fractional. The implicit form of this transformation contains two constants of different space-time dimensions. They can be reduced to the constant "c" with the dimension of speed ("speed of light"), and to the constant "R" with the dimension of length (an invariant radius of the visible part of the Universe). The geometry of the "light cones" shows that "R" is a fundamental constant, but "c" depends on the time of transformation.
Criteria for the determination of time dependent scalings in the Fock quantization of scalar fields
Cortez, Jerónimo; Olmedo, Javier; Velhinho, José M
2012-01-01
The quantization of scalar fields in nonstationary spacetimes is plagued with ambiguities that undermine the significance of physical predictions. A context in which this kind of ambiguities arises and prevents the derivation of robust results is, e.g., in the quantum analysis of cosmological perturbations. In these situations, typically, a suitable scaling of the field by a time dependent function leads to a description in an auxiliary static background, though the nonstationarity still shows up in a time dependent mass. For such a field description, and assuming the compactness of the spatial sections, we recently proved in three or less spatial dimensions that the criteria of a natural implementation of the spatial isometries and of a unitary time evolution are able to select a unique class of unitarily equivalent vacua, and hence of Fock representations. In this work, we extend our uniqueness result to the consideration of all possible field descriptions that can be reached by a time dependent canonical t...
Pseudospin symmetry in finite nuclei within the relativistic Hartree-Fock framework
Energy Technology Data Exchange (ETDEWEB)
Lopez-Quelle, M [Departamento de Fisica Aplicada, Universidad de Cantabria, E-39005 Santander (Spain); Savushkin, L N [Department of Physics, St Petersburg University for Telecommunications, 191186 St Petersburg (Russian Federation); Marcos, S [Departamento de Fisica Moderna, Universidad de Cantabria, E-39005 Santander (Spain); Niembro, R [Departamento de Fisica Moderna, Universidad de Cantabria, E-39005 Santander (Spain)
2005-10-01
In the present work, we analyse the behaviour of the pseudospin symmetry (PSS) in heavy nuclei ({sup 208}Pb) in the framework of the relativistic Hartree-Fock approximation (RHFA). The quasidegeneracy of the pseudospin partners and the similarity of the small F components of their respective Dirac spinors have a somewhat lower degree of accuracy than in the relativistic mean field approximation (RMFA). Both properties improve when the number of nodes of the small component increases, as happens in the RMFA. The behaviour of the single-particle potentials appearing in the Dirac equation of the pseudospin partners is analysed. There is no dominance of the pseudocentrifugal barrier (PCB) compared to the pseudospin-orbit potential (PSOP). In the RHFA, the PSS is an approximately satisfied symmetry in nuclei and its dynamical character is reinforced with respect to the RMFA.
Phase structure of the massive chiral Gross-Neveu model from Hartree-Fock
Boehmer, Christian; Kraus, Sebastian; Thies, Michael
2008-01-01
The phase diagram of the massive chiral Gross-Neveu model (the massive Nambu-Jona-Lasinio model in 1+1 dimensions) is constructed. In the large N limit, the Hartree-Fock approach can be used. We find numerically a chiral crystal phase separated from a massive Fermi gas phase by a 1st order transition. Using perturbation theory, we also construct the critical sheet where the homogeneous phase becomes unstable in a 2nd order transition. A tricritical curve is located. The phase diagram is mapped out as a function of fermion mass, chemical potential and temperature and compared with the one of the discrete chiral Gross-Neveu model. As a by-product, we illustrate the crystal structure of matter at zero temperature for various densities and fermion masses.
Comparative study of metal cluster fission in Hartree-Fock and LDA
Lyalin, A; Greiner, W; Lyalin, Andrey; Solov'yov, Andrey; Greiner, Walter
2001-01-01
Fission of doubly charged metal clusters is studied using the open-shell two-center deformed jellium Hartree-Fock model and Local Density Approximation. Results of calculations of the electronic structure and fission barriers for the symmetric and asymmetric channels associated with the following processes Na_{10}^{2+} --> Na_{7}^{+} + Na_{3}^{+}, Na_{18}^{2+} --> Na_{15}^{+} + Na_{3}^{+} and Na_{18}^{2+} --> 2 Na_{9}^{+} are presented. The role of the exact exchange and many-body correlation effects in metal clusters fission is analysed. It is demonstrated that the influence of many-electron correlation effects on the height of the fission barrier is more profound if the barrier arises nearby or beyond the scission point. The importance of cluster deformation effects in the fission process is elucidated with the use of the overlapping-spheroids shape parametrization allowing one an independent variation of deformations in the parent and daughter clusters.
Ab-initio Hartree-Fock study of tritium desorption from Li{sub 2}O
Energy Technology Data Exchange (ETDEWEB)
Taniguchi, Masaki; Tanaka, Satoru [Tokyo Univ. (Japan). Faculty of Engineering
1998-03-01
Dissociative adsorption of hydrogen on Li{sub 2}O (110) surface has been investigated with ab-initio Hartree-Fock quantum chemical calculation technique. Heat of adsorption and potential energy surface for H{sub 2} dissociative adsorption was evaluated by calculating the total energy of the system. Calculation results on adsorption heat indicated that H{sub 2} adsorption is endothermic. However, when oxygen vacancy exists adjacent to the adsorption sites, heat of adsorption energy became less endothermic and the activation energy required to dissociate the H-H bonding was smaller than that for the terrace site. This is considered to be caused by the excess charge localized near the defect. (author)
Monge Distance between Quantum States
Zyczkowski, K; Zyczkowski, Karol; Slomczynski, Wojciech
1998-01-01
We define a metric in the space of quantum states taking the Monge distance between corresponding Husimi distributions (Q--functions). This quantity fulfills the axioms of a metric and satisfies the following semiclassical property: the distance between two coherent states is equal to the Euclidean distance between corresponding points in the classical phase space. We compute analytically distances between certain states (coherent, squeezed, Fock and thermal) and discuss a scheme for numerical computation of Monge distance for two arbitrary quantum states.
Composite asymptotic expansions
Fruchard, Augustin
2013-01-01
The purpose of these lecture notes is to develop a theory of asymptotic expansions for functions involving two variables, while at the same time using functions involving one variable and functions of the quotient of these two variables. Such composite asymptotic expansions (CAsEs) are particularly well-suited to describing solutions of singularly perturbed ordinary differential equations near turning points. CAsEs imply inner and outer expansions near turning points. Thus our approach is closely related to the method of matched asymptotic expansions. CAsEs offer two unique advantages, however. First, they provide uniform expansions near a turning point and away from it. Second, a Gevrey version of CAsEs is available and detailed in the lecture notes. Three problems are presented in which CAsEs are useful. The first application concerns canard solutions near a multiple turning point. The second application concerns so-called non-smooth or angular canard solutions. Finally an Ackerberg-O’Malley resonance pro...
Novel Foraminal Expansion Technique
Senturk, Salim; Ciplak, Mert; Oktenoglu, Tunc; Sasani, Mehdi; Egemen, Emrah; Yaman, Onur; Suzer, Tuncer
2016-01-01
The technique we describe was developed for cervical foraminal stenosis for cases in which a keyhole foraminotomy would not be effective. Many cervical stenosis cases are so severe that keyhole foraminotomy is not successful. However, the technique outlined in this study provides adequate enlargement of an entire cervical foraminal diameter. This study reports on a novel foraminal expansion technique. Linear drilling was performed in the middle of the facet joint. A small bone graft was placed between the divided lateral masses after distraction. A lateral mass stabilization was performed with screws and rods following the expansion procedure. A cervical foramen was linearly drilled medially to laterally, then expanded with small bone grafts, and a lateral mass instrumentation was added with surgery. The patient was well after the surgery. The novel foraminal expansion is an effective surgical method for severe foraminal stenosis. PMID:27559460
Steppe expansion in Patagonia?
Veblen, Thomas T.; Markgraf, Vera
1988-11-01
Westward expansion of the Patagonian steppe and retrocession of Andean forests due to increasing aridity over the past one or two millennia has been a persistent theme in the ecological and paleoecological literature for at least half a century. New evidence from pollen profiles, tree-ring analysis, vegetation structure, and photographic and documentary historical sources does not show the expansion of the steppe. Instead, over the past century trees have invaded the steppe as a consequence mainly of human-induced changes in the fire regime, and trees have regenerated in forest areas that were heavily burnt at the onset of European colonization.
Directory of Open Access Journals (Sweden)
Massimo Giovannini
2015-06-01
Full Text Available Cosmological singularities are often discussed by means of a gradient expansion that can also describe, during a quasi-de Sitter phase, the progressive suppression of curvature inhomogeneities. While the inflationary event horizon is being formed the two mentioned regimes coexist and a uniform expansion can be conceived and applied to the evolution of spatial gradients across the protoinflationary boundary. It is argued that conventional arguments addressing the preinflationary initial conditions are necessary but generally not sufficient to guarantee a homogeneous onset of the conventional inflationary stage.
Energy Technology Data Exchange (ETDEWEB)
Giovannini, Massimo, E-mail: massimo.giovannini@cern.ch [Department of Physics, Theory Division, CERN, 1211 Geneva 23 (Switzerland); INFN, Section of Milan-Bicocca, 20126 Milan (Italy)
2015-06-30
Cosmological singularities are often discussed by means of a gradient expansion that can also describe, during a quasi-de Sitter phase, the progressive suppression of curvature inhomogeneities. While the inflationary event horizon is being formed the two mentioned regimes coexist and a uniform expansion can be conceived and applied to the evolution of spatial gradients across the protoinflationary boundary. It is argued that conventional arguments addressing the preinflationary initial conditions are necessary but generally not sufficient to guarantee a homogeneous onset of the conventional inflationary stage.
Energy Technology Data Exchange (ETDEWEB)
Alves, Josias Manoel [Universidade Federal de Goias (UFG), Goiania, GO (Brazil); Instituto Federal de Educacao, Ciencia e Tecnologia de Goias (CEFET/GO), Goiania, GO (Brazil)
2004-07-01
The electric energy is an important tool to rural communities, promoting quality of life through its use at home or as part of the productive process. The Rural Electrical Project of the State of Goias began with the collaboration between The Overseas Economic Cooperation Fund (OECF) and the Electric Company of the State of Goias. The subject of this paper is to characterize the electric energy use in three farms attended by OECF project, in Rio Verde, Jatai and Mineiro. It was done the checking, analysis and description of situations related to the electric installation, motors starting, conservation and use of alternative energy source. It was evident that all farms use electric motors to several purposes (irrigation, manufacture of ration, triturates, mechanic milking, etc). Two farms used electric fences, while only one used hybrid system. It was verified at the visited farms presented an expressive use of the electric energy in its domestic usage as much as an input to the productive process. (author)
Gustafsson, S.; Jönsson, P.; Froese Fischer, C.; Grant, I. P.
2017-01-01
Multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations and relativistic configuration interaction (RCI) calculations were performed for states of the 3l3l', 3l4l' and 3s5l configurations in the Mg-like ions Ca IX - As XXII and Kr XXV. Valence and core-valence electron correlation effects are accounted for through large configuration state function expansions. Calculated excitation energies are in very good agreement with observations for the lowest levels. For higher lying levels observations are often missing and present energies aid line identification in spectra. Lifetimes and transition data are given for all ions. There is an excellent agreement for both lifetimes and transition data with recent multiconfiguration Hartree-Fock Breit Pauli calculations. Tables for energy levels, lifetimes, and transition data and full Tables 2, 4, and 6 are available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/597/A76
For the Long Island, New Jersey, and southern New England region, one facet of marsh drowning as a result of accelerated sea level rise is the expansion of salt marsh ponds and pannes. Over the past century, marsh ponds and pannes have formed and expanded in areas of poor drainag...
Kowalski, Emmanuel
2010-01-01
This is a survey report for the Bourbaki Seminar (Exp. no. 1028, November 2010) concerning sieve and expanders, in particular the recent works of Bourgain, Gamburd and Sarnak introducing "sieve in orbits", and the related developments concerning expansion properties of Cayley graphs of finite linear groups.
Physics suggests that the interplay of momentum, continuity, and geometry in outward radial flow must produce density and concomitant pressure reductions. In other words, this flow is intrinsically auto-expansive. It has been proposed that this process is the key to understanding...
On storm weakening during substorm expansion phase
Directory of Open Access Journals (Sweden)
G. L. Siscoe
Full Text Available Iyemori and Rao recently presented evidence that the strength of a magnetic storm, as measured by -Dst, weakens, or its rate of growth slows, during the substorm expansion phase. Yet the expansion phase is known to inject energetic particles into the ring current, which should strengthen the storm. We propose to reconcile these apparently contradictory results by combining the virial theorem and a principle of energy partitioning between energy storage elements in a system with dissipation. As applied to the unloading description of the substorm expansion phase, the virial theorem states that -Dst is proportional to the sum of the total magnetic energy and twice the total kinetic energy in the magnetosphere including the tail. Thus if expansion phase involves converting magnetic energy stored in the tail into kinetic energy stored in the ring current, a drop in -Dst during expansion phase requires that less than half the drop in magnetic energy goes into the ring current, the rest going into the ionosphere. Indeed Weiss et al., have estimated that the energy dissipated in the ionosphere during expansion phase is twice that injected into the ring current. This conclusion is also consistent with the mentioned energy partitioning principle, which requires that more energy be dissipated than transferred between storage elements. While Iyemori and Rao's observations seem to contradict the hypothesis that storms consist at least in part of a sum of substorms, this mode of description might nonetheless be preserved by including the substorm's growth-phase contribution. Then the change in storm strength measured from before the growth phase to after the expansion phase is positive, even though the expansion phase alone makes a negative contribution.
Schimeczek, C.; Engel, D.; Wunner, G.
2014-05-01
Our previously published code for calculating energies and bound-bound transitions of medium-Z elements at neutron star magnetic field strengths [D. Engel, M. Klews, G. Wunner, Comp. Phys. Comm. 180, 3-2-311 (2009)] was based on the adiabatic approximation. It assumes a complete decoupling of the (fast) gyration of the electrons under the action of the magnetic field and the (slow) bound motion along the field under the action of the Coulomb forces. For the single-particle orbitals this implied that each is a product of a Landau state and an (unknown) longitudinal wave function whose B-spline coefficients were determined self-consistently by solving the Hartree-Fock equations for the many-electron problem on a finite-element grid. In the present code we go beyond the adiabatic approximation, by allowing the transverse part of each orbital to be a superposition of Landau states, while assuming that the longitudinal part can be approximated by the same wave function in each Landau level. Inserting this ansatz into the energy variational principle leads to a system of coupled equations in which the B-spline coefficients depend on the weights of the individual Landau states, and vice versa, and which therefore has to be solved in a doubly self-consistent manner. The extended ansatz takes into account the back-reaction of the Coulomb motion of the electrons along the field direction on their motion in the plane perpendicular to the field, an effect which cannot be captured by the adiabatic approximation. The new code allows for the inclusion of up to 8 Landau levels. This reduces the relative error of energy values as compared to the adiabatic approximation results by typically a factor of three (1/3 of the original error) and yields accurate results also in regions of lower neutron star magnetic field strengths where the adiabatic approximation fails. Further improvements in the code are a more sophisticated choice of the initial wave functions, which takes into
Bigravity from gradient expansion
Energy Technology Data Exchange (ETDEWEB)
Yamashita, Yasuho [Yukawa Institute for Theoretical Physics, Kyoto University,606-8502, Kyoto (Japan); Tanaka, Takahiro [Yukawa Institute for Theoretical Physics, Kyoto University,606-8502, Kyoto (Japan); Department of Physics, Kyoto University,606-8502, Kyoto (Japan)
2016-05-04
We discuss how the ghost-free bigravity coupled with a single scalar field can be derived from a braneworld setup. We consider DGP two-brane model without radion stabilization. The bulk configuration is solved for given boundary metrics, and it is substituted back into the action to obtain the effective four-dimensional action. In order to obtain the ghost-free bigravity, we consider the gradient expansion in which the brane separation is supposed to be sufficiently small so that two boundary metrics are almost identical. The obtained effective theory is shown to be ghost free as expected, however, the interaction between two gravitons takes the Fierz-Pauli form at the leading order of the gradient expansion, even though we do not use the approximation of linear perturbation. We also find that the radion remains as a scalar field in the four-dimensional effective theory, but its coupling to the metrics is non-trivial.
Operator product expansion algebra
Energy Technology Data Exchange (ETDEWEB)
Holland, Jan [CPHT, Ecole Polytechnique, Paris-Palaiseau (France)
2014-07-01
The Operator Product Expansion (OPE) is a theoretical tool for studying the short distance behaviour of products of local quantum fields. Over the past 40 years, the OPE has not only found widespread computational application in high-energy physics, but, on a more conceptual level, it also encodes fundamental information on algebraic structures underlying quantum field theories. I review new insights into the status and properties of the OPE within Euclidean perturbation theory, addressing in particular the topics of convergence and ''factorisation'' of the expansion. Further, I present a formula for the ''deformation'' of the OPE algebra caused by a quartic interaction. This formula can be used to set up a novel iterative scheme for the perturbative computation of OPE coefficients, based solely on the zeroth order coefficients (and renormalisation conditions) as initial input.
Generalized Schr\\"odinger cat states and their classical emulation
Perez-Leija, Armando; Szameit, Alexander; Christodoulides, Demetrios N; Moya-Cessa, Hector
2015-01-01
We demonstrate that superpositions of coherent and displaced Fock states, also referred to as generalized Schr\\"odinger cats cats, can be created by application of a nonlinear displacement operator which is a deformed version of the Glauber displacement operator. Consequently, such generalized cat states can be formally considered as nonlinear coherent states. We then show that Glauber-Fock photonic lattices endowed with alternating positive and negative coupling coefficients give rise to classical analogs of such cat states. In addition, it is pointed out that the analytic propagator of these deformed Glauber-Fock arrays explicitly contains the Wigner operator opening the possibility to observe Wigner functions of the quantum harmonic oscillator in the classical domain.
Systematic study of even-even nuclei with Hartree-Fock+BCS method using Skyrme SIII force
Energy Technology Data Exchange (ETDEWEB)
Tajima, Naoki; Takahara, Satoshi; Onishi, Naoki [Tokyo Univ. (Japan). Coll. of Arts and Sciences
1997-03-01
We have applied the Hartree-Fock+BCS method with Skyrme SIII force formulated in a three-dimensional Cartesian-mesh representation to even-even nuclei with 2 {<=} Z {<=} 114. We discuss the results concerning the atomic masses, the quadrupole (m=0, 2) and hexadecapole (m=0, 2, 4) deformations, the skin thicknesses, and the halo radii. We also discuss the energy difference between oblate and prolate solutions and the shape difference between protons and neutrons. (author)
Energy Technology Data Exchange (ETDEWEB)
Fischer, C F
1977-11-01
This technical report contains a listing of a general program for multi-configuration Hartree--Fock (MCHF) calculations, including its documentation. Several examples are given showing how the program may be used. Typical output for several cases is also presented. This program has been tested over an extended period of time for a large variety of cases. This program is written for the IBM 360 or 370 in double-precision arithmetic.
General technique for analytical derivatives of post-projected Hartree-Fock
Tsuchimochi, Takashi; Ten-no, Seiichiro
2017-02-01
In electronic structure theory, the availability of an analytical derivative is one of the desired features for a method to be useful in practical applications, as it allows for geometry optimization as well as computation of molecular properties. With the recent advances in the development of symmetry-projected Hartree-Fock (PHF) methods, we here aim at further extensions by devising the analytic gradients of post-PHF approaches with a special focus on spin-extended (spin-projected) configuration interaction with single and double substitutions (ECISD). Just like standard single-reference methods, the mean-field PHF part does not require the corresponding coupled-perturbed equation to be solved, while the correlation energy term needs the orbital relaxation effect to be accounted for, unless the underlying molecular orbitals are variationally optimized in the presence of the correlation energy. We present a general strategy for post-PHF analytical gradients, which closely parallels that for single-reference methods, yet addressing the major difference between them. The similarity between ECISD and multi-reference CI not only in the energy but also in the optimized geometry is clearly demonstrated by the numerical examples of ozone and cyclobutadiene.
Fock space, symbolic algebra, and analytical solutions for small stochastic systems.
Santos, Fernando A N; Gadêlha, Hermes; Gaffney, Eamonn A
2015-12-01
Randomness is ubiquitous in nature. From single-molecule biochemical reactions to macroscale biological systems, stochasticity permeates individual interactions and often regulates emergent properties of the system. While such systems are regularly studied from a modeling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low-copy-number stochasticity. Nevertheless, classical studies remained limited to the abstract level, demonstrating a more general applicability and equivalence between systems in physics and biology rather than exploiting the physics tools to study biological systems. Here the Fock space representation, used in quantum mechanics, is combined with the symbolic algebra of creation and annihilation operators to consider explicit solutions for the chemical master equations describing small, well-mixed, biochemical, or biological systems. This is illustrated with an exact solution for a Michaelis-Menten single enzyme interacting with limited substrate, including a consideration of very short time scales, which emphasizes when stiffness is present even for small copy numbers. Furthermore, we present a general matrix representation for Michaelis-Menten kinetics with an arbitrary number of enzymes and substrates that, following diagonalization, leads to the solution of this ubiquitous, nonlinear enzyme kinetics problem. For this, a flexible symbolic maple code is provided, demonstrating the prospective advantages of this framework compared to stochastic simulation algorithms. This further highlights the possibilities for analytically based studies of stochastic systems in biology and chemistry using tools from theoretical quantum physics.
Exploration of (super-)heavy elements using the Skyrme-Hartree-Fock model
Energy Technology Data Exchange (ETDEWEB)
Erler, Jochen
2011-01-31
Motivated by the steadily increasing number of known nuclei and nuclear properties, theories of nuclear structure are presently a field of intense research. This work concentrates on the self-consistent description of nuclei in terms of the Skyrme-Hartree-Fock (SHF) approach. The extrapolation of nuclear shell structure to the region of super-heavy elements (SHE) using the SHF model, the dependence on different parameterization and the influence of collective correlation will be studied. The general scope of this work are large scale calculation for a global survey of properties of SHE like binding energies, separation energies and decay characteristics and lifetimes. These calculations were done in a collaboration with the theory group of the GSI in Darmstadt and have the aim to develop a database of lifetimes and reaction rates for {alpha}, {beta}-decay and spontaneous fission in a very wide range with proton numbers 86 {<=} Z {<=} 120 and neutron numbers up to N {approx} 260 relevant for the astrophysical r-process. The results of this study for example predictions of a possible islands of very stable nuclei and information of favored decay mode for each nuclei are also applicable in the recent experimental synthesis of exotic SHE. For these calculation a framework to calculate {beta}-decay half-lives within the SHF model has been developed and the existing axial SHF code has been extended to compute {beta}-transition matrix elements and so to provide an estimation of half-lives. (orig.)
The Hartree-Fock exchange effect on the CO adsorption by the boron nitride nanocage
Vessally, E.; Soleimani-Amiri, S.; Hosseinian, A.; Edjlali, L.; Bekhradnia, A.
2017-03-01
We studied the effect of Hartree-Fock (HF) exchange percentage of a density functional on the adsorption properties and electronic sensitivity of the B12N12 nanocluster to CO molecule. It was found that by an increase in the %HF, the LUMO level is nearly constant while the HOMO level is strongly stabilized, expanding the HOMO-LUMO gap (Eg). Also, the volume of the all structures decreased and the sensitivity of the B12N12 is slightly increased to CO molecule. For the pristine B12N12 cluster, the B66 and B64 bonds are about 1.43 and 1.49 Å at 10% HF, and 1.23 and 1.26 Å at 100% HF, respectively. The HF exchange between 10-20% may predict an accurate Eg for the B12N12 system. We concluded that functionals with a large %HF such as M06-HF, and M06-2X may significantly overestimate the Eg, and bond strength. We obtained a parabolic relationship between the %HF and the adsorption energy of CO molecule on the B12N12 cluster. Also, an increase in the %HF predicts a larger charge transfer from the CO molecule to the cage.
Exact exchange potential evaluated solely from occupied Kohn-Sham and Hartree-Fock solutions
Cinal, M
2011-01-01
The reported new algorithm determines the exact exchange potential v_x in a iterative way using energy and orbital shifts (ES, OS) obtained - with finite-difference formulas - from the solutions (occupied orbitals and their energies) of the Hartree-Fock-like equation and the Kohn-Sham-like equation, the former used for the initial approximation to v_x and the latter - for increments of ES and OS due to subsequent changes of v_x. Thus, solution of the differential equations for OS, used by Kummel and Perdew (KP) [Phys. Rev. Lett. 90, 043004 (2003)], is avoided. The iterated exchange potential, expressed in terms of ES and OS, is improved by modifying ES at odd iteration steps and OS at even steps. The modification formulas are related to the OEP equation (satisfied at convergence) written as the condition of vanishing density shift (DS) - they are obtained, respectively, by enforcing its satisfaction through corrections to approximate OS and by determining optimal ES that minimize the DS norm. The proposed met...
Aryal, M. M.; Maharjan, N. B.; Paudyal, D. D.; Mishra, D. R.; Byahut, S. R.; Scheicher, R. H.; Badu, S. R.; Jeong, J.; Chow, Lee; Das, T. P.
2008-03-01
Using the first-principles Hartree-Fock Cluster Procedure, we have studied the electronic structures of pure chain like Selenium and Tellurium, pure ring structured Selenium, Tellurium impurity in chain and ring-structured Selenium and Selenium impurity in chain-structured Tellurium chain. For our investigations in all the systems we have carried out convergence studies with respect to variational basis set sizes,sizes of clusters and electron correlation effects using many-body perturbation theory. Using our calculated electronic field-gradient parameters q in the pure chain systems and employing the experimental quadrupole coupling constants (e^2qQ), the values Q(^77Se)=(0.50±0.04) 10-28 m^2 and Q(^125Te)=-(0.2±0.02) 10-28m^2. Results will also be presented for the asymmetry parameters η for the pure chain systems and the e^2qQ and η for ^77Se in selenium ring. Our calculated values for e^2qQ and η for the impurity systems will also be presented and compared with available experimental data and earlier theoretical results.
Coordinate-Space Hartree-Fock-Bogoliubov Solvers for Superfluid Fermi Systems in Large Boxes
Energy Technology Data Exchange (ETDEWEB)
Pei, J. C. [University of Tennessee (UTK) and Oak Ridge National Laboratory (ORNL); Fann, George I [ORNL; Harrison, Robert J [ORNL; Nazarewicz, W. [University of Tennessee (UTK) and Oak Ridge National Laboratory (ORNL); Hill, Judith C [ORNL; Galindo, Diego A [ORNL; Jia, Jun [ORNL
2012-01-01
The self-consistent Hartree-Fock-Bogoliubov problem in large boxes can be solved accurately in the coordinate space with the recently developed solvers HFB-AX (2D) and MADNESS-HFB (3D). This is essential for the description of superfluid Fermi systems with complicated topologies and significant spatial extend, such as fissioning nuclei, weakly-bound nuclei, nuclear matter in the neutron star rust, and ultracold Fermi atoms in elongated traps. The HFB-AX solver based on B-spline techniques uses a hybrid MPI and OpenMP programming model for parallel computation for distributed parallel computation, within a node multi-threaded LAPACK and BLAS libraries are used to further enable parallel calculations of large eigensystems. The MADNESS-HFB solver uses a novel multi-resolution analysis based adaptive pseudo-spectral techniques to enable fully parallel 3D calculations of very large systems. In this work we present benchmark results for HFB-AX and MADNESS-HFB on ultracold trapped fermions.
Self-consistent theory of finite Fermi systems and Skyrme–Hartree–Fock method
Energy Technology Data Exchange (ETDEWEB)
Saperstein, E. E., E-mail: saper@mbslab.kiae.ru; Tolokonnikov, S. V. [National Research Center Kurchatov Institute (Russian Federation)
2016-11-15
Recent results obtained on the basis of the self-consistent theory of finite Fermi systems by employing the energy density functional proposed by Fayans and his coauthors are surveyed. These results are compared with the predictions of Skyrme–Hartree–Fock theory involving several popular versions of the Skyrme energy density functional. Spherical nuclei are predominantly considered. The charge radii of even and odd nuclei and features of low-lying 2{sup +} excitations in semimagic nuclei are discussed briefly. The single-particle energies ofmagic nuclei are examined inmore detail with allowance for corrections to mean-field theory that are induced by particle coupling to low-lying collective surface excitations (phonons). The importance of taking into account, in this problem, nonpole (tadpole) diagrams, which are usually disregarded, is emphasized. The spectroscopic factors of magic and semimagic nuclei are also considered. In this problem, only the surface term stemming from the energy dependence induced in the mass operator by the exchange of surface phonons is usually taken into account. The volume contribution associated with the energy dependence initially present in the mass operator within the self-consistent theory of finite Fermi systems because of the exchange of high-lying particle–hole excitations is also included in the spectroscopic factor. The results of the first studies that employed the Fayans energy density functional for deformed nuclei are also presented.
Madsen, Lars Bojer; Jensen, Frank; Dnestryan, Andrey I.; Tolstikhin, Oleg I.
2017-07-01
In the leading-order approximation of the weak-field asymptotic theory (WFAT), the dependence of the tunneling ionization rate of a molecule in an electric field on its orientation with respect to the field is determined by the structure factor of the ionizing molecular orbital. The WFAT yields an expression for the structure factor in terms of a local property of the orbital in the asymptotic region. However, in general quantum chemistry approaches molecular orbitals are expanded in a Gaussian basis which does not reproduce their asymptotic behavior correctly. This hinders the application of the WFAT to polyatomic molecules, which are attracting increasing interest in strong-field physics. Recently, an integral-equation approach to the WFAT for tunneling ionization of one electron from an arbitrary potential has been developed. The structure factor is expressed in an integral form as a matrix element involving the ionizing orbital. The integral is not sensitive to the asymptotic behavior of the orbital, which resolves the difficulty mentioned above. Here, we extend the integral representation for the structure factor to many-electron systems treated within the Hartree-Fock method and show how it can be implemented on the basis of standard quantum chemistry software packages. We validate the methodology by considering noble-gas atoms and the CO molecule, for which accurate structure factors exist in the literature. We also present benchmark results for CO2 and for NH3 in the pyramidal and planar geometries.
Hassaneen, Khaled; Mansour, Hesham
2017-02-01
The single-particle potentials and other properties at absolute zero temperature in isospin asymmetric nuclear matter are investigated in the frame of an extended Brueckner theory. Also thermal quantities are calculated in asymmetric nuclear matter using CD-Bonn potential and the Urbana three-body forces (3BF). Also, the effects of the hole-hole contributions are investigated within the self-consistent Greens function approach. The inclusion of 3BF or the hole-hole contributions improves the predicted saturation property of symmetric nuclear matter within the Brueckner-Hartree-Fock approach and it leads to a significant stiffening of the density dependence of symmetry energy at high densities but the exact saturation point is not reproduced. This is of great importance in astrophysical calculation. A phenomenological term simulating the three-body interaction is introduced to assure the empirical saturation property. The hot properties of asymmetric nuclear matter such as the internal energy and the pressure are analyzed using T2-approximation method at low temperatures.
A simple and efficient dispersion correction to the Hartree-Fock theory.
Yoshida, Tatsusada; Mashima, Akira; Sasahara, Katsunori; Chuman, Hiroshi
2014-02-15
One of the most challenging problems in computational chemistry and in drug discovery is the accurate prediction of the binding energy between a ligand and a protein receptor. It is well known that the binding energy calculated with the Hartree-Fock molecular orbital theory (HF) lacks the dispersion interaction energy that significantly affects the accuracy of the total binding energy of a large molecular system. We propose a simple and efficient dispersion energy correction to the HF theory (HF-Dtq). The performance of HF-Dtq was compared with those of several recently proposed dispersion corrected density functional theory methods (DFT-Ds) as to the binding energies of 68 small non-covalent complexes. The overall performance of HF-Dtq was found to be nearly equivalent to that of more sophisticated B3LYP-D3. HF-Dtq will thus be a useful and powerful method for accurately predicting the binding energy between a ligand and a protein, albeit it is a simple correction procedure based on HF.
Energy Technology Data Exchange (ETDEWEB)
Cho, Daeheum; Ko, Kyoung Chul; Lee, Jin Yong, E-mail: jinylee@skku.edu [Department of Chemistry, Sungkyunkwan University, Suwon 440-746 (Korea, Republic of); Ikabata, Yasuhiro; Wakayama, Kazufumi; Yoshikawa, Takeshi [Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555 (Japan); Nakai, Hiromi, E-mail: nakai@waseda.jp [Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555 (Japan); Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555 (Japan); CREST, Japan Science and Technology Agency, Tokyo 102-0075 (Japan); Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Katsura, Kyoto 615-8520 (Japan)
2015-01-14
The intramolecular magnetic coupling constant (J) of diradical systems linked with five- or six-membered aromatic rings was calculated to obtain the scaling factor (experimental J/calculated J ratio) for various density functional theory (DFT) functionals. Scaling factors of group A (PBE, TPSSh, B3LYP, B97-1, X3LYP, PBE0, and BH and HLYP) and B (M06-L, M06, M06-2X, and M06-HF) were shown to decrease as the amount of Hartree-Fock exact exchange (HFx) increases, in other words, overestimation of calculated J becomes more severe as the HFx increases. We further investigated the effect of HFx fraction of DFT functional on J value, spin contamination, and spin density distributions by comparing the B3LYP analogues containing different amount of HFx. It was revealed that spin contamination and spin densities at each atom increases as the HFx increases. Above all, newly developed BLYP-5 functional, which has 5% of HFx, was found to have the scaling factor of 1.029, indicating that calculated J values are very close to that of experimental values without scaling. BLYP-5 has potential to be utilized for accurate evaluation of intramolecular magnetic coupling constant (J) of diradicals linked by five- or six-membered aromatic ring couplers.
Uniqueness of the Fock quantization of the Gowdy $T^3$ model
Cortez, J; Velhinho, J M; Cortez, Jeronimo; Marugan, Guillermo A. Mena; Velhinho, Jose M.
2007-01-01
After its reduction by a gauge-fixing procedure, the family of linearly polarized Gowdy $T^3$ cosmologies admit a scalar field description whose evolution is governed by a Klein-Gordon type equation in a flat background in 1+1 dimensions with the spatial topology of $S^1$, though in the presence of a time-dependent potential. The model is still subject to a homogeneous constraint, which generates $S^1$-translations. Recently, a Fock quantization of this scalar field was introduced and shown to be unique under the requirements of unitarity of the dynamics and invariance under the gauge group of $S^1$-translations. In this work, we extend and complete this uniqueness result by considering other possible scalar field descriptions, resulting from reasonable field reparameterizations of the induced metric of the reduced model. In the reduced phase space, these alternate descriptions can be obtained by means of a time-dependent scaling of the field, the inverse scaling of its canonical momentum, and the possible ad...
Teleportation of Cavity Field States via Cavity QED
Guerra, E S
2004-01-01
In this article we discuss two schemes of teleportation of cavity field states. In the first scheme we consider cavities prepared in a coherent state and in the second scheme we consider cavities prepared in a superposition of zero and one Fock states.
Rayka, Milad; Shahbazian, Shant
2016-01-01
In this communication, an effective set of the Hartree-Fock equations are derived only for electrons of the muonic systems, i.e., molecules containing a positively charged muon, conceiving the muon as a quantum oscillator. In these equations, a non-Coulombic potential is added to the orthodox coulomb and exchange potential energy terms, which describes the interaction of the muon and electrons effectively. The explicit form of the effective potential depends on the nature of muon vibrations and is derived for a combination of Cartesian Gaussian functions that are used to expand the muonic spatial orbital. The resulting effective Hartree-Fock equations are implemented computationally and used successfully, as a proof of concept, in the case of MuCN molecule, which results from replacing the proton of HCN molecule with a muon. The developed effective Hartree-Fock theory is quite general and in principle can be used for any muonic system while it is the starting point for a general effective electronic structure...
Ising Expansion for the Hubbard Model
Shi, Zhu-Pei; Singh, Rajiv R. P.
1995-01-01
We develop series expansions for the ground state properties of the Hubbard model, by introducing an Ising anisotropy into the Hamiltonian. For the two-dimensional (2D) square lattice half-filled Hubbard model, the ground state energy, local moment, sublattice magnetization, uniform magnetic susceptibility and spin stiffness are calculated as a function of $U/t$, where $U$ is the Coulomb constant and $t$ is the hopping parameter. Magnetic susceptibility data indicate a crossover around $U\\app...
Strategic Expansion Models in Academic Radiology.
Natesan, Rajni; Yang, Wei T; Tannir, Habib; Parikh, Jay
2016-03-01
In response to economic pressures, academic institutions in the United States and their radiology practices, are expanding into the community to build a larger network, thereby driving growth and achieving economies of scale. These economies of scale are being achieved variously via brick-and-mortar construction, community practice acquisition, and partnership-based network expansion. We describe and compare these three expansion models within a 4-part framework of: (1) upfront investment; (2) profitability impact; (3) brand impact; and (4) risk of execution.
Thermal expansion of glassy polymers.
Davy, K W; Braden, M
1992-01-01
The thermal expansion of a number of glassy polymers of interest in dentistry has been studied using a quartz dilatometer. In some cases, the expansion was linear and therefore the coefficient of thermal expansion readily determined. Other polymers exhibited non-linear behaviour and values appropriate to different temperature ranges are quoted. The linear coefficient of thermal expansion was, to a first approximation, a function of both the molar volume and van der Waal's volume of the repeating unit.
Kondayya, Gundra; Shukla, Alok
2012-03-01
present because of the tremendous interest in the physics of conjugated polymers and graphene nanoribbons. The computer program described in this paper provides an efficient way of solving the Hartree-Fock equations for such systems within the P-P-P model. In addition to the Bloch orbitals, band structure, and the density of states, the program can also compute quantities such as the linear absorption spectrum, and the electro-absorption spectrum of these systems. Solution method: For a one-dimensional periodic π-conjugated system lying in the xy-plane, the single-particle Bloch orbitals are expressed as linear combinations of p-orbitals of individual atoms. Then using various parameters defining the P-P-P Hamiltonian, the Hartree-Fock equations are set up as a matrix eigenvalue problem in the k-space. Thereby, its solutions are obtained in a self-consistent manner, using the iterative diagonalizing technique at several k points. The band structure and the corresponding Bloch orbitals thus obtained are used to perform a variety of calculations such as the density of states, linear optical absorption spectrum, electro-absorption spectrum, etc. Running time: Most of the examples provided take only a few seconds to run. For a large system, however, depending on the system size, the run time may be a few minutes to a few hours.
Stefańska, Patrycja
2011-01-01
The Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30 (1997) 825; erratum 30 (1997) 2747] is exploited to derive closed-form expressions for electric ($\\sigma_{\\mathrm{E}}$) and magnetic ($\\sigma_{\\mathrm{M}}$) dipole shielding constants for the ground state of the relativistic hydrogen-like atom with a point-like and spinless nucleus of charge $Ze$. It is found that $\\sigma_{\\mathrm{E}}=Z^{-1}$ (as it should be) and $$\\sigma_{\\mathrm{M}}=-(2Z\\alpha^{2}/27)(4\\gamma_{1}^{3}+6\\gamma_{1}^{2}-7\\gamma_{1}-12) /[\\gamma_{1}(\\gamma_{1}+1)(2\\gamma_{1}-1)],$$ where $\\gamma_{1}=\\sqrt{1-(Z\\alpha)^{2}}$ ($\\alpha$ is the fine-structure constant). This expression for $\\sigma_{\\mathrm{M}}$ agrees with earlier findings of several other authors, obtained with the use of other analytical techniques, and is elementary compared to an alternative one presented recently by Cheng \\emph{et al.} [J. Chem. Phys. 130 (2009) 144102], which involves an infinite series of ratios of the Euler'...
A meaningful expansion around detailed balance
Colangeli, Matteo; Wynants, Bram
2011-01-01
We consider Markovian dynamics modeling open mesoscopic systems which are driven away from detailed balance by a nonconservative force. A systematic expansion is obtained of the stationary distribution around an equilibrium reference, in orders of the nonequilibrium forcing. The first order around equilibrium has been known since the work of McLennan (1959), and involves the transient irreversible entropy flux. The expansion generalizes the McLennan formula to higher orders, complementing the entropy flux with the dynamical activity. The latter is more kinetic than thermodynamic and is a possible realization of Landauer's insight (1975) that, for nonequilibrium, the relative occupation of states also depends on the noise along possible escape routes. In that way nonlinear response around equilibrium can be meaningfully discussed in terms of two main quantities only, the entropy flux and the dynamical activity. The expansion makes mathematical sense as shown in the simplest cases from exponential ergodicity.
Cosmological Constant, Quintessence and Expansive Nondecelerative Universe
Sima, J; Sima, Jozef; Sukenik, Miroslav
2001-01-01
Recent observations of the Universe have led to a conclusion suppressing an up-to-now supposed deceleration of the Universe caused by attractive gravitational forces. Contrary, there is a renaissance of the cosmological member lambda and introduction of enigmatic repulsive dark energy in attempts to rationalize a would-be acceleration of the Universe expansion. It is documented that the model of Expansive Nondecelerative Universe is capable to offer acceptable answers to the questions on the Universe expansion, state equations of the Universe, the parameter omega, the cosmological member lambda without any necessity to introduce new strange kinds of matter or energy being in accord with the fundamental conservation laws and generally accepted parameters of the Universe.
Operator product expansion algebra
Energy Technology Data Exchange (ETDEWEB)
Holland, Jan [School of Mathematics, Cardiff University, Senghennydd Rd, Cardiff CF24 4AG (United Kingdom); Hollands, Stefan [School of Mathematics, Cardiff University, Senghennydd Rd, Cardiff CF24 4AG (United Kingdom); Institut für Theoretische Physik, Universität Leipzig, Brüderstr. 16, Leipzig, D-04103 (Germany)
2013-07-15
We establish conceptually important properties of the operator product expansion (OPE) in the context of perturbative, Euclidean φ{sup 4}-quantum field theory. First, we demonstrate, generalizing earlier results and techniques of hep-th/1105.3375, that the 3-point OPE,
Eriksen, Janus J.; Matthews, Devin A.; Jørgensen, Poul; Gauss, Jürgen
2016-05-01
We extend our assessment of the potential of perturbative coupled cluster (CC) expansions for a test set of open-shell atoms and organic radicals to the description of quadruple excitations. Namely, the second- through sixth-order models of the recently proposed CCSDT(Q-n) quadruples series [J. J. Eriksen et al., J. Chem. Phys. 140, 064108 (2014)] are compared to the prominent CCSDT(Q) and ΛCCSDT(Q) models. From a comparison of the models in terms of their recovery of total CC singles, doubles, triples, and quadruples (CCSDTQ) energies, we find that the performance of the CCSDT(Q-n) models is independent of the reference used (unrestricted or restricted (open-shell) Hartree-Fock), in contrast to the CCSDT(Q) and ΛCCSDT(Q) models, for which the accuracy is strongly dependent on the spin of the molecular ground state. By further comparing the ability of the models to recover relative CCSDTQ total atomization energies, the discrepancy between them is found to be even more pronounced, stressing how a balanced description of both closed- and open-shell species—as found in the CCSDT(Q-n) models—is indeed of paramount importance if any perturbative CC model is to be of chemical relevance for high-accuracy applications. In particular, the third-order CCSDT(Q-3) model is found to offer an encouraging alternative to the existing choices of quadruples models used in modern computational thermochemistry, since the model is still only of moderate cost, albeit markedly more costly than, e.g., the CCSDT(Q) and ΛCCSDT(Q) models.
Eriksen, Janus J; Matthews, Devin A; Jørgensen, Poul; Gauss, Jürgen
2016-05-21
We extend our assessment of the potential of perturbative coupled cluster (CC) expansions for a test set of open-shell atoms and organic radicals to the description of quadruple excitations. Namely, the second- through sixth-order models of the recently proposed CCSDT(Q-n) quadruples series [J. J. Eriksen et al., J. Chem. Phys. 140, 064108 (2014)] are compared to the prominent CCSDT(Q) and ΛCCSDT(Q) models. From a comparison of the models in terms of their recovery of total CC singles, doubles, triples, and quadruples (CCSDTQ) energies, we find that the performance of the CCSDT(Q-n) models is independent of the reference used (unrestricted or restricted (open-shell) Hartree-Fock), in contrast to the CCSDT(Q) and ΛCCSDT(Q) models, for which the accuracy is strongly dependent on the spin of the molecular ground state. By further comparing the ability of the models to recover relative CCSDTQ total atomization energies, the discrepancy between them is found to be even more pronounced, stressing how a balanced description of both closed- and open-shell species-as found in the CCSDT(Q-n) models-is indeed of paramount importance if any perturbative CC model is to be of chemical relevance for high-accuracy applications. In particular, the third-order CCSDT(Q-3) model is found to offer an encouraging alternative to the existing choices of quadruples models used in modern computational thermochemistry, since the model is still only of moderate cost, albeit markedly more costly than, e.g., the CCSDT(Q) and ΛCCSDT(Q) models.
Engineering Properties of Expansive Soil
Institute of Scientific and Technical Information of China (English)
DAI Shaobin; SONG Minghai; HUANG Jun
2005-01-01
The components of expansive soil were analyzed with EDAX, and it is shown that the main contents of expansive soil in the northern Hubei have some significant effects on engineering properties of expansive soil. Furthermore, the soil modified by lime has an obvious increase of Ca2+ and an improvement of connections between granules so as to reduce the expansibility and contractility of soil. And it also has a better effect on the modified expansive soil than the one modified by pulverized fuel ash.
The Effect of the Affordable Care Act Medicaid Expansion on Migration.
Goodman, Lucas
2017-01-01
The expansion of Medicaid to low-income nondisabled adults is a key component of the Affordable Care Act's strategy to increase health insurance coverage, but many states have chosen not to take up the expansion. As a result, for many low-income adults, there has been stark variation across states in access to Medicaid since the expansions took effect in 2014. This study investigates whether individuals migrate in order to gain access to these benefits. Using an empirical model in the spirit of a difference-in-differences, this study finds that migration from non-expansion states to expansion states did not increase in 2014 relative to migration in the reverse direction. The estimates are sufficiently precise to rule out a migration effect that would meaningfully affect the number of enrollees in expansion states, which suggests that Medicaid expansion decisions do not impose a meaningful fiscal externality on other states.
Generalized Schrödinger cat states and their classical emulation
Perez-Leija, Armando; Szameit, Alexander; Ramos-Prieto, Irán; Moya-Cessa, Hector; Christodoulides, Demetrios N.
2016-05-01
We demonstrate that superpositions of coherent states and displaced Fock states, also referred to as generalized Schrödinger cat states, can be generated by application of a deformed Glauber displacement operator on number states, coherent states, and displaced Fock states. Based on such a deformed displacement operator we introduce a deformed version of the so-called Glauber photonic lattices. These novel lattices are endowed with alternating positive and negative coupling coefficients and give rise to classical analogs of Schrödinger cat states. Finally, we show that the analytic propagator of these new Glauber-Fock arrays explicitly contains the Wigner operator opening the possibility to emulate Wigner functions of the quantum harmonic oscillator in the classical domain.
The Monge distance between quantum states
Energy Technology Data Exchange (ETDEWEB)
Zyczkowski, Karol [Institute for Plasma Research, University of Maryland, College Park, MD (United States); Slomczynski, Wojciech [Instytut Matematyki, Uniwersytet Jagiellonski, Cracow (Poland)
1998-11-13
We define a metric in the space of quantum states taking the Monge distance between corresponding Husimi distributions (Q-functions). This quantity fulfils the axioms of a metric and satisfies the following semiclassical property: the distance between two coherent states is equal to the Euclidean distance between corresponding points in the classical phase space. We compute analytically distances between certain states (coherent, squeezed, Fock and thermal) and discuss a scheme for numerical computation of Monge distance for two arbitrary quantum states. (author)
Probing the physical determinants of thermal expansion of folded proteins.
Dellarole, Mariano; Kobayashi, Kei; Rouget, Jean-Baptiste; Caro, José Alfredo; Roche, Julien; Islam, Mohammad M; Garcia-Moreno E, Bertrand; Kuroda, Yutaka; Royer, Catherine A
2013-10-24
The magnitude and sign of the volume change upon protein unfolding are strongly dependent on temperature. This temperature dependence reflects differences in the thermal expansivity of the folded and unfolded states. The factors that determine protein molar expansivities and the large differences in thermal expansivity for proteins of similar molar volume are not well understood. Model compound studies have suggested that a major contribution is made by differences in the molar volume of water molecules as they transfer from the protein surface to the bulk upon heating. The expansion of internal solvent-excluded voids upon heating is another possible contributing factor. Here, the contribution from hydration density to the molar thermal expansivity of a protein was examined by comparing bovine pancreatic trypsin inhibitor and variants with alanine substitutions at or near the protein-water interface. Variants of two of these proteins with an additional mutation that unfolded them under native conditions were also examined. A modest decrease in thermal expansivity was observed in both the folded and unfolded states for the alanine variants compared with the parent protein, revealing that large changes can be made to the external polarity of a protein without causing large ensuing changes in thermal expansivity. This modest effect is not surprising, given the small molar volume of the alanine residue. Contributions of the expansion of the internal void volume were probed by measuring the thermal expansion for cavity-containing variants of a highly stable form of staphylococcal nuclease. Significantly larger (2-3-fold) molar expansivities were found for these cavity-containing proteins relative to the reference protein. Taken together, these results suggest that a key determinant of the thermal expansivities of folded proteins lies in the expansion of internal solvent-excluded voids.
Mechanism of actuation in conducting polymers: Osmotic expansion
DEFF Research Database (Denmark)
Bay, Lasse; Jacobsen, Torben; West, Keld;
2001-01-01
Conducting polymers expand or contract when their redox state is changed. This expansion/contraction effect can be separated in an intrinsic part because of changes of the polymer backbone on reduction/oxidation and a part depending on the surrounding electrolyte phase, because of osmotic expansi...... and designing actuator experiments and when comparing experimental results from different sources.......Conducting polymers expand or contract when their redox state is changed. This expansion/contraction effect can be separated in an intrinsic part because of changes of the polymer backbone on reduction/oxidation and a part depending on the surrounding electrolyte phase, because of osmotic expansion...... is compared with measurements on PPy(DBS) films. The experiments show that the expansion decreases as the electrolyte concentration is increased. This means that a considerable part of the total expansion is due to the osmotic effect. The osmotic effect should be taken into account when interpreting...
Directory of Open Access Journals (Sweden)
Rajat K. Chaudhuri
2003-12-01
Full Text Available Abstract: The coupled cluster based linear response theory which is applicable to the direct calculation of atomic and molecular properties are presented and applied to compute the ionization potentials and excitation energies of light and moderately heavy atoms. The eÃ‚Â®ect of electron correlation on the ground and excited states is studied using Hartree-Fock, Dirac-Fock and approximate two-component relativistic spinors.
Medicaid Managed Care Penetration Rates and Expansion Enr...
U.S. Department of Health & Human Services — The Medicaid managed care penetration rates and expansion enrollment by state charts are composed annually by the Data and System Group (DSG) of the Centers for...
Denis-Petit, David; Gosselin, Gilbert; Hannachi, Fazia; Tarisien, Medhi; Bonnet, Thomas; Comet, Maxime; Gobet, Franck; Versteegen, Maud; Morel, Pascal; Méot, Vincent; Matea, Iolanda
2017-08-01
One promising candidate for the first detection of nuclear excitation in plasma is the 463-keV, 20.26-min-lifetime isomeric state in 84Rb, which can be excited via a 3.5-keV transition to a higher lying state. According to our preliminary calculations, under specific plasma conditions, nuclear excitation by electron transition (NEET) may be its strongest excitation process. Evaluating a reliable NEET rate requires, in particular, a thorough examination of all atomic transitions contributing to the rate under plasma conditions. We report the results of a detailed evaluation of the NEET rate based on multiconfiguration Dirac Fock (MCDF) atomic calculations, in a rubidium plasma at local thermodynamic equilibrium with a temperature of 400 eV and a density of 10-2g /cm3 and based on a more precise energy measurement of the nuclear transition involved in the excitation.
Directory of Open Access Journals (Sweden)
Alejandro Cabo Montes de Oca
2010-03-01
Full Text Available This work expands the results and derivations presented in a recent letter. It is argued that symmetry breaking Hartree-Fock (HF solutions of a simple model of the Cu-O planes in La2CuO4, are able to describe the insulator and antiferromagnetic characters of this material. Then, this classical primer of a Mott insulator is alternatively obtained here as an exact Slater insulator within the simplest of the first principles schemes. Moreover, pseudogap HF states are also predicted. The maximal energy gap of 100 meV over the Fermi surface of this wavefunction, reasonably well matches the ARPES upper pseudogap measurements for La2CuO4 in the zero doping limit. These surprising results followed after eliminating spin and crystal symmetry constraints usually imposed on the HF orbitals. The discussion helps to clarify the role of the antiferromagnetism and pseudogaps in the physics of the HTSC materials and indicates a promising way to start conciliating the Mott and Slater pictures for the description of the transition metal oxides.
de Lara-Castells, María Pilar; Mitrushchenkov, Alexander O.; Stoll, Hermann
2015-09-01
A combined density functional (DFT) and incremental post-Hartree-Fock (post-HF) approach, proven earlier to calculate He-surface potential energy surfaces [de Lara-Castells et al., J. Chem. Phys. 141, 151102 (2014)], is applied to describe the van der Waals dominated Ag2/graphene interaction. It extends the dispersionless density functional theory developed by Pernal et al. [Phys. Rev. Lett. 103, 263201 (2009)] by including periodic boundary conditions while the dispersion is parametrized via the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)]. Starting with the elementary cluster unit of the target surface (benzene), continuing through the realistic cluster model (coronene), and ending with the periodic model of the extended system, modern ab initio methodologies for intermolecular interactions as well as state-of-the-art van der Waals-corrected density functional-based approaches are put together both to assess the accuracy of the composite scheme and to better characterize the Ag2/graphene interaction. The present work illustrates how the combination of DFT and post-HF perspectives may be efficient to design simple and reliable ab initio-based schemes in extended systems for surface science applications.
Seel, M.; Ladik, J.
1985-10-01
Hartree-Fock Green's-function studies of end effects on the core-level structure of metallic and insulating quasi-one-dimensional model polymers reveal additional core peaks outside the bulk bands. In the metallic case, shifts to both lower (~-150 meV) and higher (~+50 meV) binding energies are observed, whereas in the insulating case, split-off peaks occur only at the lower-binding-energy side (~-150 meV). It is shown that a positive or negative net valence population alone does not determine the direction of the shift. The binding-energy changes are determined by a detailed balance between the energy loss due to a decrease in the electron-nuclear attraction and the energy gain due to a decrease in the electron-electron repulsion experienced by the core electrons of the end atoms. This can probably also explain why for some metal surfaces, shifts towards lower, and for others, shifts towards higher, binding energies are found. In the valence region of the investigated lithium chains, the ends do not produce localized end states.
Nemykin, Victor N; Hadt, Ryan G
2006-10-01
Influence of molecular geometry, type of exchange-correlation functional, and contraction scheme of basis set applied at the iron nuclei have been tested in the calculation of 57Fe Mössbauer isomer shifts and quadrupole splittings for a wide range of ligand types, as well as oxidation and spin states, in inorganic and organometallic systems. It has been found that uncontraction of the s-part of Wachter's full-electron basis set at the iron nuclei does not appreciably improve the calculated isomer shifts. The observed correlations for all tested sets of geometries are close to each other and predominantly depend on the employed exchange-correlation functional with B3LYP functional being slightly better as compared to BPW91. Both hybrid (B3LYP) and pure (BPW91) exchange-correlation functionals are suitable for the calculation of isomer shifts in organometallic compounds. Surprisingly, it has been found that the hybrid B3LYP exchange-correlation functional completely fails in accurate prediction of quadrupole splittings in ferrocenes, while performance of the pure BPW91 functional for the same systems was excellent. This observation has been explained on the basis of relationship between the amount of Hartree-Fock exchange involved in the applied exchange-correlation functional and the calculated HOMO-LUMO energy gap in ferrocenes. On the basis of this explanation, use of only pure exchange-correlation functionals has been suggested for accurate prediction of Mössbauer spectra parameters in ferrocenes.
Energy Technology Data Exchange (ETDEWEB)
Lara-Castells, María Pilar de, E-mail: Pilar.deLara.Castells@csic.es [Instituto de Física Fundamental (C.S.I.C.), Serrano 123, E-28006 Madrid (Spain); Mitrushchenkov, Alexander O. [Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallée (France); Stoll, Hermann [Institut für Theoretische Chemie, Universität Stuttgart, D-70550 Stuttgart (Germany)
2015-09-14
A combined density functional (DFT) and incremental post-Hartree-Fock (post-HF) approach, proven earlier to calculate He-surface potential energy surfaces [de Lara-Castells et al., J. Chem. Phys. 141, 151102 (2014)], is applied to describe the van der Waals dominated Ag{sub 2}/graphene interaction. It extends the dispersionless density functional theory developed by Pernal et al. [Phys. Rev. Lett. 103, 263201 (2009)] by including periodic boundary conditions while the dispersion is parametrized via the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)]. Starting with the elementary cluster unit of the target surface (benzene), continuing through the realistic cluster model (coronene), and ending with the periodic model of the extended system, modern ab initio methodologies for intermolecular interactions as well as state-of-the-art van der Waals-corrected density functional-based approaches are put together both to assess the accuracy of the composite scheme and to better characterize the Ag{sub 2}/graphene interaction. The present work illustrates how the combination of DFT and post-HF perspectives may be efficient to design simple and reliable ab initio-based schemes in extended systems for surface science applications.
Conformal expansions and renormalons
Gardi, E; Gardi, Einan; Grunberg, Georges
2001-01-01
The large-order behaviour of QCD is dominated by renormalons. On the other hand renormalons do not occur in conformal theories, such as the one describing the infrared fixed-point of QCD at small beta_0 (the Banks--Zaks limit). Since the fixed-point has a perturbative realization, all-order perturbative relations exist between the conformal coefficients, which are renormalon-free, and the standard perturbative coefficients, which contain renormalons. Therefore, an explicit cancellation of renormalons should occur in these relations. The absence of renormalons in the conformal limit can thus be seen as a constraint on the structure of the QCD perturbative expansion. We show that the conformal constraint is non-trivial: a generic model for the large-order behaviour violates it. We also analyse a specific example, based on a renormalon-type integral over the two-loop running-coupling, where the required cancellation does occur.
Optical imaging. Expansion microscopy.
Chen, Fei; Tillberg, Paul W; Boyden, Edward S
2015-01-30
In optical microscopy, fine structural details are resolved by using refraction to magnify images of a specimen. We discovered that by synthesizing a swellable polymer network within a specimen, it can be physically expanded, resulting in physical magnification. By covalently anchoring specific labels located within the specimen directly to the polymer network, labels spaced closer than the optical diffraction limit can be isotropically separated and optically resolved, a process we call expansion microscopy (ExM). Thus, this process can be used to perform scalable superresolution microscopy with diffraction-limited microscopes. We demonstrate ExM with apparent ~70-nanometer lateral resolution in both cultured cells and brain tissue, performing three-color superresolution imaging of ~10(7) cubic micrometers of the mouse hippocampus with a conventional confocal microscope.
Medicaid enrollment after liver transplantation: Effects of medicaid expansion.
Tumin, Dmitry; Hayes, Don; Washburn, W Kenneth; Tobias, Joseph D; Black, Sylvester M
2016-08-01
Liver transplantation (LT) recipients in the United States have low rates of paid employment, making some eligible for Medicaid public health insurance after transplant. We test whether recent expansions of Medicaid eligibility increased Medicaid enrollment and insurance coverage in this population. Patients of ages 18-59 years receiving first-time LTs in 2009-2013 were identified in the United Network for Organ Sharing registry and stratified according to insurance at transplantation (private versus Medicaid/Medicare). Posttransplant insurance status was assessed through June 2015. Difference-in-difference multivariate competing-risks models stratified on state of residence estimated effects of Medicaid expansion on Medicaid enrollment or use of uninsured care after LT. Of 12,837 patients meeting inclusion criteria, 6554 (51%) lived in a state that expanded Medicaid eligibility. Medicaid participation after LT was more common in Medicaid-expansion states (25%) compared to nonexpansion states (19%; P expansion (January 1, 2014), the hazard of posttransplant Medicaid enrollment increased in states participating in Medicaid expansion (hazard ratio [HR] = 1.5; 95% confidence interval [CI] = 1.1-2.0; P = 0.01), but not in states opting out of Medicaid expansion (HR = 0.8; 95% CI = 0.5-1.3; P = 0.37), controlling for individual characteristics and time-invariant state-level factors. No effects of Medicaid expansion on the use of posttransplant uninsured care were found, regardless of private or government insurance status at transplantation. Medicaid expansion increased posttransplant Medicaid enrollment among patients who had private insurance at transplantation, but it did not improve overall access to health insurance among LT recipients. Liver Transplantation 22 1075-1084 2016 AASLD.
A quantum Monte Carlo study of the ground state chromium dimer
Hongo, Kenta
2011-01-01
We report variational and diffusion quantum Monte Carlo (VMC and DMC) studies of the binding curve of the ground-state chromium dimer. We employed various single determinant (SD) or multi-determinant (MD) wavefunctions multiplied by a Jastrow fuctor as a trial/guiding wavefunction. The molecular orbitals (MOs) in the SD were calculated using restricted or unrestricted Hartree-Fock or density functional theory (DFT) calculations where five commonly-used local (SVWN5), semi-local (PW91PW91 and BLYP), and hybrid (B1LYP and B3LYP) functionals were examined. The MD expansions were obtained from the complete-active space SCF, generalized valence bond, and unrestricted configuration interaction methods. We also adopted the UB3LYP-MOs to construct the MD expansion (UB3LYP-MD) and optimized their coefficients at the VMC level. In addition to the wavefunction dependence, we investigated the time-step bias in the DMC calculation and the effects of pseudopotentials and backflow transformation for the UB3LYP-SD case. Some...
Burial Ground Expansion Hydrogeologic Characterization
Energy Technology Data Exchange (ETDEWEB)
Gaughan , T.F.
1999-02-26
Sirrine Environmental Consultants provided technical oversight of the installation of eighteen groundwater monitoring wells and six exploratory borings around the location of the Burial Ground Expansion.
Perez-Leija, Armando; Szameit, Alexander; Abouraddy, Ayman; Moya-Cessa, Hector; Christodoulides, Demetrios N
2011-01-01
We demonstrate that single-photon as well as biphoton revivals are possible in a new class of dynamic optical systems-the so-called Glauber-Fock oscillator lattices. In these arrays, both Bloch-like oscillations and dynamic delocalization can occur which can be described in closed form. The bunching and anti-bunching response of path-entangled photons can be pre-engineered in such coupled optical arrangements and the possibility of emulating Fermionic behavior in this family of lattices is also considered. We elucidate these effects via pertinent examples and we discuss the prospect of experimentally observing these quantum interactions.
Energy Technology Data Exchange (ETDEWEB)
Miyasita, Mitiyasu, E-mail: miyasita.mitiyasu@gmail.com [Graduate School of Science and Engineering, Shinshu University, Ueda 386-8567 (Japan); Higuchi, Katsuhiko [Graduate School of Advanced Science of Matter, Hiroshima University, Higashi-Hiroshima 739-8527 (Japan); Higuchi, Masahiko [Department of Physics, Faculty of Science, Shinshu University, Matsumoto 390-8621 (Japan)
2012-07-15
We present an alternative scheme for calculating the unrestricted Hartree-Fock (HF) equation. The scheme is based on the variational method utilizing the sophisticated basis functions that include no adjustable parameters. The validity of the present scheme is confirmed by actual calculations of the boron and neon atoms. The total energy of the present scheme is lower than that of the conventional restrictive HF equation, but higher than that of the CI method. Also, the resultant wave function satisfies the electron-nucleus cusp condition.
Motional Quantum State Engineering Via a Single Laser-ion Interaction
Institute of Scientific and Technical Information of China (English)
ZHENG Shibiao
2001-01-01
We propose a scheme to prepare superpositions of several Fock states for the one-dimensional motion of a trapped ion. In the scheme the ion is simultaneously excited by N+1 laser beams, with the nth laser tuned to the nth upper vibrational sideband. After a short interaction time, a measurement of the internal state may project the vibrational motion onto a superposition of the first N+1 Fock states. The scheme can be easily generalized to synthesize entangled states for the two-dimensional ion motion.
Thermal expansion anomaly regulated by entropy.
Liu, Zi-Kui; Wang, Yi; Shang, ShunLi
2014-11-13
Thermal expansion, defined as the temperature dependence of volume under constant pressure, is a common phenomenon in nature and originates from anharmonic lattice dynamics. However, it has been poorly understood how thermal expansion can show anomalies such as colossal positive, zero, or negative thermal expansion (CPTE, ZTE, or NTE), especially in quantitative terms. Here we show that changes in configurational entropy due to metastable micro(scopic)states can lead to quantitative prediction of these anomalies. We integrate the Maxwell relation, statistic mechanics, and first-principles calculations to demonstrate that when the entropy is increased by pressure, NTE occurs such as in Invar alloy (Fe3Pt, for example), silicon, ice, and water, and when the entropy is decreased dramatically by pressure, CPTE is expected such as in anti-Invar cerium, ice and water. Our findings provide a theoretic framework to understand and predict a broad range of anomalies in nature in addition to thermal expansion, which may include gigantic electrocaloric and electromechanical responses, anomalously reduced thermal conductivity, and spin distributions.
Ackerman, Margareta; Lopez-Ortiz, Alejandro
2011-01-01
Over the last fifteen years, web searching has seen tremendous improvements. Starting from a nearly random collection of matching pages in 1995, today, search engines tend to satisfy the user's informational need on well-formulated queries. One of the main remaining challenges is to satisfy the users' needs when they provide a poorly formulated query. When the pages matching the user's original keywords are judged to be unsatisfactory, query expansion techniques are used to alter the result set. These techniques find keywords that are similar to the keywords given by the user, which are then appended to the original query leading to a perturbation of the result set. However, when the original query is sufficiently ill-posed, the user's informational need is best met using entirely different keywords, and a small perturbation of the original result set is bound to fail. We propose a novel approach that is not based on the keywords of the original query. We intentionally seek out orthogonal queries, which are r...
Lattice harmonics expansion revisited
Kontrym-Sznajd, G.; Holas, A.
2017-04-01
The main subject of the work is to provide the most effective way of determining the expansion of some quantities into orthogonal polynomials, when these quantities are known only along some limited number of sampling directions. By comparing the commonly used Houston method with the method based on the orthogonality relation, some relationships, which define the applicability and correctness of these methods, are demonstrated. They are verified for various sets of sampling directions applicable for expanding quantities having the full symmetry of the Brillouin zone of cubic and non-cubic lattices. All results clearly show that the Houston method is always better than the orthogonality-relation one. For the cubic symmetry we present a few sets of special directions (SDs) showing how their construction and, next, a proper application depend on the choice of various sets of lattice harmonics. SDs are important mainly for experimentalists who want to reconstruct anisotropic quantities from their measurements, performed at a limited number of sampling directions.
... Facts Home State Health Facts Search State Health Facts: Choose Category - or - Choose Location Demographics and the ... Expansion Enrollment Featured State Data Resources Medicaid State Fact Sheets What percentage of people are covered by ...
Isotropic Negative Thermal Expansion Metamaterials.
Wu, Lingling; Li, Bo; Zhou, Ji
2016-07-13
Negative thermal expansion materials are important and desirable in science and engineering applications. However, natural materials with isotropic negative thermal expansion are rare and usually unsatisfied in performance. Here, we propose a novel method to achieve two- and three-dimensional negative thermal expansion metamaterials via antichiral structures. The two-dimensional metamaterial is constructed with unit cells that combine bimaterial strips and antichiral structures, while the three-dimensional metamaterial is fabricated by a multimaterial 3D printing process. Both experimental and simulation results display isotropic negative thermal expansion property of the samples. The effective coefficient of negative thermal expansion of the proposed models is demonstrated to be dependent on the difference between the thermal expansion coefficient of the component materials, as well as on the circular node radius and the ligament length in the antichiral structures. The measured value of the linear negative thermal expansion coefficient of the three-dimensional sample is among the largest achieved in experiments to date. Our findings provide an easy and practical approach to obtaining materials with tunable negative thermal expansion on any scale.
Thermal expansion accompanying the glass-liquid transition and crystallization
Directory of Open Access Journals (Sweden)
M. Q. Jiang
2015-12-01
Full Text Available We report the linear thermal expansion behaviors of a Zr-based (Vitreloy 1 bulk metallic glass in its as-cast, annealed and crystallized states. Accompanying the glass-liquid transition, the as-cast Vitreloy 1 shows a continuous decrease in the thermal expansivity, whereas the annealed glass shows a sudden increase. The crystallized Vitreloy 1 exhibits an almost unchanged thermal expansivity prior to its melting. Furthermore, it is demonstrated that the nucleation of crystalline phases can induce a significant thermal shrinkage of the supercooled liquid, but with the growth of these nuclei, the thermal expansion again dominates. These results are explained in the framework of the potential energy landscape, advocating that the configurational and vibrational contributions to the thermal expansion of the glass depend on both, structure and temperature.
On genus expansion of superpolynomials
Mironov, A; Sleptsov, A; Smirnov, A
2013-01-01
Recently it was shown that the (Ooguri-Vafa) generating function of HOMFLY polynomials is the Hurwitz partition function, i.e. that the dependence of the HOMFLY polynomials on representation is naturally captured by symmetric group characters (cut-and-join eigenvalues). The genus expansion and expansion through Vassiliev invariants explicitly demonstrate this phenomenon. In the present letter we claim that the superpolynomials are not functions of such a type: symmetric group characters do not provide an adequate linear basis for their expansions. Deformation to superpolynomials is, however, straightforward in the multiplicative basis:the Casimir operators are beta-deformed to Hamiltonians of the Calogero-Moser-Sutherland system. Applying this trick to the genus and Vassiliev expansions, we observe that the deformation is rather straightforward only for the thin knots. Beyond this family additional algebraically independent terms appear in the Vassiliev and genus expansions. This can suggest that the superpol...
Small, David W; Sundstrom, Eric J; Head-Gordon, Martin
2015-01-14
Restricted Hartree Fock using complex-valued orbitals (cRHF) is studied. We introduce an orbital pairing theorem, with which we obtain a concise connection between cRHF and real-valued RHF, and use it to uncover the close relationship between cRHF, unrestricted Hartree Fock, and generalized valence bond perfect pairing. This enables an intuition for cRHF, contrasting with the generally unintuitive nature of complex orbitals. We also describe an efficient computer implementation of cRHF and its corresponding stability analysis. By applying cRHF to the Be + H2 insertion reaction, a Woodward-Hoffmann violating reaction, and a symmetry-driven conical intersection, we demonstrate in genuine molecular systems that cRHF is capable of removing certain potential energy surface singularities that plague real-valued RHF and related methods. This complements earlier work that showed this capability in a model system. We also describe how cRHF is the preferred RHF method for certain radicaloid systems like singlet oxygen and antiaromatic molecules. For singlet O2, we show that standard methods fail even at the equilibrium geometry. An implication of this work is that, regardless of their individual efficacies, cRHF solutions to the HF equations are fairly commonplace.
Energy Technology Data Exchange (ETDEWEB)
Weimer, Martin; Hieringer, Wolfgang; Sala, Fabio Della; Goerling, Andreas
2005-02-21
The electronic and optical properties of extended functionalized carbyne chains, polyynes and cumulenes, are investigated with the localized Hartree-Fock method, with conventional Kohn-Sham methods, and with the Hartree-Fock method. It is found that even for very long polyynes the carbon-carbon bond lengths within a polyyne alternate while for long cumulenes no carbon-carbon bond length alternation occurs. Polyynes exhibit a finite HOMO-LUMO gap even if they become very long while cumulenes are found to become metallic in the limit of long chain lengths. The geometry and the electro-optical properties of polyynes cannot be influenced significantly by simple sp-{sigma}-bonded end groups. The optically active {sup 1}{sigma}{sub u}{sup +} <- X{sup 1}{sigma}{sub g}{sup +} electronic transition in polyynes is investigated by time-dependent density-functional theory (TDDFT). The known systematic underestimation of excitation energies in large chain-like systems by TDDFT methods is also found for the systems considered here. Deficiencies in the commonly used exchange-correlation kernels are identified as the main source of this shortcoming of TDDFT methods. Unphysical Coulomb self-interactions present in conventional Kohn-Sham potentials seem to not contribute significantly to the problem.
Energy Technology Data Exchange (ETDEWEB)
Bernardos, P. [Universidad de Cantabria, Departamento de Matematica Aplicada y Ciencias de la Computacion, 39005, Santander (Spain); Fomenko, V.N. [St Petersburg University for Railway Engineering, Department of Mathematics, 190031, St Petersburg (Russian Federation); Marcos, S.; Niembro, R. [Universidad de Cantabria, Departamento de Fisica Moderna, 39005, Santander (Spain); Lopez-Quelle, M. [Universidad de Cantabria, Departamento de Fisica Aplicada, 39005, Santander (Spain); Savushkin, L.N. [St Petersburg University for Telecommunications, Department of Physics, 191186, St Petersburg (Russian Federation)
2001-02-01
An effective nuclear model describing {omega}-, {rho}- and axial-mesons as gauge fields is applied to nuclear matter in the relativistic Hartree-Fock approximation. The isoscalar two-pion exchange is simulated by a scalar field s similar to that used in the conventional relativistic mean-field approach. Two more scalar fields are essential ingredients of the present treatment: the {sigma}-field, the chiral partner of the pion, and the {sigma}-field, the Higgs field for the {omega}-meson. Two versions of the model are used depending on whether the {sigma}-field is considered as a dynamical variable or 'frozen', by taking its mass as infinite. The model contains four free parameters in the first case and three in the second one which are fitted to the nuclear matter saturation conditions. The nucleon and meson effective masses, compressibility modulus and symmetry energy are calculated. The results prove the reliability of the Dirac-Hartree-Fock approach within the linear realization of the chiral symmetry. (author)
Energy Technology Data Exchange (ETDEWEB)
Small, David W.; Sundstrom, Eric J.; Head-Gordon, Martin [Department of Chemistry, University of California, Berkeley, California 94720, USA and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)
2015-01-14
Restricted Hartree Fock using complex-valued orbitals (cRHF) is studied. We introduce an orbital pairing theorem, with which we obtain a concise connection between cRHF and real-valued RHF, and use it to uncover the close relationship between cRHF, unrestricted Hartree Fock, and generalized valence bond perfect pairing. This enables an intuition for cRHF, contrasting with the generally unintuitive nature of complex orbitals. We also describe an efficient computer implementation of cRHF and its corresponding stability analysis. By applying cRHF to the Be + H{sub 2} insertion reaction, a Woodward-Hoffmann violating reaction, and a symmetry-driven conical intersection, we demonstrate in genuine molecular systems that cRHF is capable of removing certain potential energy surface singularities that plague real-valued RHF and related methods. This complements earlier work that showed this capability in a model system. We also describe how cRHF is the preferred RHF method for certain radicaloid systems like singlet oxygen and antiaromatic molecules. For singlet O{sub 2}, we show that standard methods fail even at the equilibrium geometry. An implication of this work is that, regardless of their individual efficacies, cRHF solutions to the HF equations are fairly commonplace.
Barreto, L.; Schoorl, J.M.; Kok, K.; Veldkamp, A.; Hass, A.
2013-01-01
In Brazil, agriculture expansion is taking place primarily in the Cerrado ecosystems. With the aim of supporting policy development and protecting the natural environment at relevant hotspots, a scenario study was conducted that concerned not only land-use change, but also the resulting effects on e