Time-Dependent Hartree-Fock Method and Its Extension

Yamamura, Masatoshi; Kuriyama, Atsushi

doi:10.1143/ptps.93.1

Cited by 67 publications

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“…Their work is, however, still tied to the SCCM of Marumori, Sakata, et al and to the anharmonic limit; no algorithm applicable to large amplitude collective motion is given. In subsequent work [185][186][187], they have carried through a deeper mathematical study of the same set of ideas. All this work plus other uses of TDHF are reviewed in Ref.…”

Section: A Survey Of Literaturementioning

confidence: 99%

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Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

2000

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The goal of the present account is to review our efforts to obtain and apply a "collective" Hamiltonian for a few, approximately decoupled, adiabatic degrees of freedom, starting from a Hamiltonian system with more or many more degrees of freedom. The approach is based on an analysis of the classical limit of quantum-mechanical problems. Initially, we study the classical problem within the framework of Hamiltonian dynamics and derive a fully self-consistent theory of large amplitude collective motion with small velocities. We derive a measure for the quality of decoupling of the collective degree of freedom. We show for several simple examples, where the classical limit is obvious, that when decoupling is good, a quantization of the collective Hamiltonian leads to accurate descriptions of the low energy properties of the systems studied. In nuclear physics problems we construct the classical Hamiltonian by means of time-dependent mean-field theory, and we transcribe our formalism to this case. We report studies of a model for monopole vibrations, of 28 Si with a realistic interaction, several qualitative models of heavier nuclei, and preliminary results for a more realistic approach to heavy nuclei. Other * Email: Giu.Dodang@th.u-psud.fr † Email: aklein@walet.physics.upenn.edu ‡ Email: Niels.Walet@umist.ac.uk 1 topics included are a nuclear Born-Oppenheimer approximation for an ab initio quantum theory and a theory of the transfer of energy between collective and non-collective degrees of freedom when the decoupling is not exact. The explicit account is based on the work of the authors, but a thorough survey of other work is included. PACS number(s): 21.60.-n, 21.60.Jz, 21.60.Ev

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Section: A Survey Of Literaturementioning

confidence: 99%

“…All this work plus other uses of TDHF are reviewed in Ref. [187], where one also finds a few applications. Following this work, the authors, in collaboration with J. da Providencia, undertook to investigate, using the methods of thermo field dynamics [121], the application of TDHF to systems at finite excitation energy.…”

Section: A Survey Of Literaturementioning

confidence: 99%

Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

2000

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“…The set of the expressions (3·17) is nothing but the c-number replacement of the Holstein-Primakoff type representation of tpe su(2)-algebra. 1 ), 3) The relations (3·17) can be rewritten as…”

Section: [13s B;]=5/s-tims/2s [Ms 13;]=2b; [5 B;]=[s Ms]=o (2·18)mentioning

confidence: 99%

“…1) In the shell model language, it consists of two singleparticle levels, the degeneracies of which are the same as that of each other. In this frame, we can contact with three one-body fermion operators, which obey the su(2)-algebra.…”

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confidence: 99%

On the Coherent and the Squeezed State in the su(2)-Boson Model

Yamamura

Kuriyama

Tsue

1992

Progress of Theoretical Physics

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719With the use of the coherent and the squeezed state combined with canonicity condition in the time· dependent Hartree-Fock theory, quantal fluctuation appearing in the su(2)·boson model, which is well known as Schwinger boson representation, is investigated. Especially, the attention is focussed on the least quantal effect: 1) the minimal uncertainty and 2) the quantal fluctuation energy. The Lipkin model, an example obeying the su(2)-algebra, is adopted for demonstrating the basic idea. § 1. IntroductionIt is well known that the time-dependent Hartree-Fock (TDHF) theory has been recognized as a quite powerful method for investigating dynamics of many-fermion system. This method contains two characteristic aspects. First is related with obtaining a classical counterpart of many-fermion system. With the aid of Slater determinant parametrized by classical canonical variables, we can get a classical counterpart of the original quantal system. Then, under an appropriate requantization procedure, the counterpart comes back to the original system in a disguised form. Second is closely related with a problem discussed in this paper. The TDHF theory gives us a method for approximate description of time evolution of many-fermion system. This method starts from a chosen Slater determinant lsi> as a trial wave packet for the time-dependent variational procedure. In the canonical form, the wave packet contains certain parameters which obey canonicity condition and, in this sense, we can regard them as canonical variables. Under the variational procedure, we can prove that their time-dependence is determined by solving the Hamilton equation of motion for these variables. )This statement is quite interesting, because the time evolution of the quantal system is reduced to that in the classical mechanics. The Hamiltonian (H)SI, which prescribes the time evolution, can be given as the expectation value of the original Hamiltonian Ii for the wave packet, lsi>, i.e., (H)SI =. In the TDHF theory, anyone-body fermion operator Oi corresponds to the expectation value of Oi for the wave packet, (Oi)81( =,

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“…In the conventional BCS plus RPA approach, 7) the degrees of freedom given by quasi-particles describe the non-collective, single-particle-like mode. Our present approach automatically classifies the degrees of freedom into two types: One describes non-collective modes and the other collective modes.…”

Section: §1 Introductionmentioning

confidence: 99%

Pairing Model and Mixed State Representation. I: Thermal Equilibrium State

Kuriyama

Providência

Tsue

et al. 2001

Progress of Theoretical Physics

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We apply the mixed state representation to the description of the thermal properties of the pairing model. We derive an extended form of the boson realization of the quasi-spin operators in a classical image. We introduce a density operator and entropy combined with the mixed state representation. Then we define a thermal equilibrium state with use of the variation principle. In this representation, the seniority number is specified by a distribution of the Fermi type as a function of temperature. We study the pairing collective modes that induce no change in the entropy. §1. IntroductionIn a series of papers, 1), 2) we have developed a mixed state representation as a canonical formulation of thermal field theory. We have applied this formulation to the description of the thermal properties of the Lipkin model, 3) and shown that it constitutes a mean field approximation for the grand partition function. 4) Under this mean field approximation, it has been shown that the thermal equilibrium state is stable in the non-condensed phase of particle-hole pairs with coupled angular momentum 0, but it becomes unstable in the condensed phase of particle-hole pairs. 5)The Lipkin model is a typical example of a system with an interaction of the particle-hole type. Another typical example is the pairing model with an interaction of the pairing type, that is, the interaction among the nucleon pairs with coupled angular momentum 0. Hence it is important to study the thermal stability of the pairing model, especially in its condensed phase. This is one reason why we investigate the thermal properties of the pairing model in this paper.We also successfully applied the mixed state representation to the description of an imperfect boson system, in particular of its condensation. 6) We adopted the same type of interaction among bosons as among fermions in the pairing model, except that the former interaction is repulsive, while the latter attractive. The condensation property of bosons is impeded by the repulsive interaction. On the other hand, the exclusiveness property of fermions is counteracted by the attractive interaction. Hence we would like to describe the condensation both in a boson system and in a fermion system in a similar formulation. This is the second motivation.In the pairing model, the collective mode of the pairing vibration exists as the lowest excited state of the condensed phase. In the conventional BCS plus RPA ap-

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Time-Dependent Hartree-Fock Method and Its Extension

Cited by 67 publications

References 0 publications

Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

On the Coherent and the Squeezed State in the su(2)-Boson Model

Pairing Model and Mixed State Representation. I: Thermal Equilibrium State

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