Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Communications in Theoretical Physics

Extended Time-Dependent Hartree-Fock Approximation and Dissipative Diabatic Dynamic

Shun-Jin Wang

Published Nov 1, 1985• 0 citations
Publisher

Abstract

The extended time-dependent Hartree-Fock approximation (ETDHF) is derived in a new approach in which the equations of motion for many-body correlation matrices are given up to the second order. The eigen representation of the ETDHF is established and compared with other representations. A possible parametrization of the ETDHF is presented in the limit of low collective velocity and the diabatic shell model single particle bases are discussed from the viewpoint of the parametrized ETDHF. The dissipative diabatic dynamics(DDD) is derived from the ETDHF and it 1s proved to be a realization of the ETDHF in the time-dependent shell model representation. The formal solutions of the occupation number are given in reasonable approximations and they are proved to bear the basic features of the DDD. Finally the decaying diabatic potential proposed phenomenologically in DDD is derived microscopically.

DOI
10.1088/0253-6102/4/6/827

Related papers

Gaussian phase-space representation of fermion dynamics: Beyond the time-dependent Hartree-Fock approximation

Saar Rahav, Shaul Mukamel

A Gaussian operator representation for the many-body density matrix of fermionic systems, developed by Corney and Drummond [Phys. Rev. Lett. 93, 260401 (2004)], is used to derive approximate decoupling schemes for their dynamics. In this approach the reduced single electron density-matrix elements serve as stochastic variables which satisfy an exact Fokker-Planck equation. The number of variables scales as $\ensuremath{\sim}{N}^{2}$ rather than $\ensuremath{\sim}\text{exp}(N)$ with the basis set size, and the time-dependent Hartree-Fock approximation (TDHF) is recovered in the ``classical'' limit. An approximate closed set of equations of motion for the one- and two-particle reduced density matrices provides a direct generalization of the TDHF.

arXiv:0902.3227•Physical Review B•Apr 10, 2009•10 citations

Extended Time-Dependent Hartree-Fock Approximation with Particle Collisions

Cheuk-Yin Wong, Henry H. K. Tang

We formulate an extended time-dependent Hartree-Fock approximation which includes particle collisions. As the configuration-space analog of the quantum Boltzmann equation, it can be utilized to study the dynamics of nuclear or other fermion systems when irreversible dissipation is present.

Physical Review Letters•Apr 17, 1978•149 citations

Dynamics of nuclear fluid. V. Extended time-dependent Hartree-Fock approximation illuminates the approach to thermal equilibrium

Cheuk-Yin Wong, Henry H. K. Tang

In the time-dependent Hartree-Fock approximation, the fermions are assumed to interact only through the mean field and the collisions between particles are neglected. We formulate an extended time-dependent Hartree-Fock approximation which incorporates particle collisions due to the residual interaction, with the usual time-dependent Hartree-Fock approximation as the collisionless limit. It is obtained by a truncation of the Martin-Schwinger hierarchy at the second level and by using a simple representation of the one-body Green's function in terms of time-dependent occupation numbers. The final set of coupled equations consists of a modified time-dependent Hartree-Fock equation and a master equation for the occupation numbers. These results are physically transparent and describe properly the physics of the collision process. They may also be simple enough to be of practical use to study heavy-ion collisions or the dynamics of other fermion systems. Furthermore, as the configuration-space analog of the quantum Boltzmann equation, many important results concerning statistical dynamics are obtained. Concepts such as entropy, temperature, and local and thermal equilibrium can be quantitatively introduced. The well-known $H$ theorem that entropy never decreases can be readily recovered. With the collision term explicitly exhibited, the macroscopic equations (equations of continuity, momentum flux, and energy) and their associated conservation theorems can also be derived. Analytic solutions for the master equation for simple cases lead to new "level crossing" formulas having characteristics distinctly different from the Landau-Zener level-crossing formula and illuminate the salient features as to how a nonequilibrium fermion system approaches thermal equilibrium.NUCLEAR REACTIONS Extension of time-dependent Hartree-Fock approximation. Collisions between particles. Master equation for occupation probabilities. Entropy, temperature, and thermal equilibrium. $H$ theorem. Analytic solution of the master equation. New types of level crossing formula.

Physical Review C•Oct 1, 1979•62 citations

A Microscopic Derivation of the Time-Dependent Hartree-Fock Equation with Coulomb Two-Body Interaction

Froehlich, Juerg, Antti Knowles

We study the dynamics of a Fermi gas with a Coulomb interaction potential, and show that, in a mean-field limiting regime, the dynamics is described by the Hartree-Fock equation. This extends previous work of Bardos et al. to the case of unbounded interaction potentials. We also express the mean-field limit as a "superhamiltonian" system, and state our main result in terms of a Heisenberg-picture dynamics of observables. This is a Egorov-type theorem.

arXiv:0810.4282•Oct 23, 2008•2 citations

Dissipation in time-dependent Hartree-Fock calculations

Kit-Keung Kan, Taro Tamura

Dissipation is studied in a one-dimensional time-dependent Hartree-Fock system which simulates the capture of a slow neutron by a nucleus. It is shown that this time-dependent Hartree-Fock system is unable to approach thermodynamic equilibrium and that the time of damping of a collective vibration, induced by the capture, is much longer than the relaxation time of realistic nuclear collective motion. The dissipation in this time-dependent Hartree-Fock system is further compared with predictions of various one-body dissipation theories.NUCLEAR REACTIONS time-dependent Hartree-Fock calculation, slow neutron capture, one-body dissipation.

Physical Review C•Apr 1, 1979•0 citations

Dynamic response function and large-amplitude dissipative collective motion

Xi-Zhen Wu, Fumihiko Sakata, Yizhong Zhuo +1 more

Aiming at exploring microscopic dynamics responsible for the dissipative large-amplitude collective motion, the dynamic response and correlation functions are introduced within the general theory of nuclear coupled-master equations. The theory is based on the microscopic theory of nuclear collective dynamics which has been developed within the time-dependent Hartree-Fock (TDHF) theory for disclosing the complex structure of the TDHF manifold. A systematic numerical method for calculating the dynamic response and correlation functions is proposed. By performing numerical calculation for a simple model Hamiltonian, it is pointed out that the dynamic response function gives important information in understanding the large-amplitude dissipative collective motion which is described by an ensemble of trajectories within the TDHF manifold.

Physical Review C•Sep 1, 1993•7 citations
The extended time-dependent Hartree-Fock approximation (ETDHF) is derived in a new approach in which the equations of motion for many-body correlation matrices are given up to the second order. The eigen representation of the ETDHF is established and compared with other representations. A possible parametrization of the ETDHF is presented in the limit of low collective velocity and the diabatic shell model single particle bases are discussed from the viewpoint of the parametrized ETDHF. The dissipative diabatic dynamics(DDD) is derived from the ETDHF and it 1s proved to be a realization of the ETDHF in the time-dependent shell model representation. The formal solutions of the occupation number are given in reasonable approximations and they are proved to bear the basic features of the DDD. Finally the decaying diabatic potential proposed phenomenologically in DDD is derived microscopically.
A Gaussian operator representation for the many-body density matrix of fermionic systems, developed by Corney and Drummond [Phys. Rev. Lett. 93, 260401 (2004)], is used to derive approximate decoupling schemes for their dynamics. In this approach the reduced single electron density-matrix elements serve as stochastic variables which satisfy an exact Fokker-Planck equation. The number of variables scales as $\ensuremath{\sim}{N}^{2}$ rather than $\ensuremath{\sim}\text{exp}(N)$ with the basis set size, and the time-dependent Hartree-Fock approximation (TDHF) is recovered in the ``classical'' limit. An approximate closed set of equations of motion for the one- and two-particle reduced density matrices provides a direct generalization of the TDHF.
In the time-dependent Hartree-Fock approximation, the fermions are assumed to interact only through the mean field and the collisions between particles are neglected. We formulate an extended time-dependent Hartree-Fock approximation which incorporates particle collisions due to the residual interaction, with the usual time-dependent Hartree-Fock approximation as the collisionless limit. It is obtained by a truncation of the Martin-Schwinger hierarchy at the second level and by using a simple representation of the one-body Green's function in terms of time-dependent occupation numbers. The final set of coupled equations consists of a modified time-dependent Hartree-Fock equation and a master equation for the occupation numbers. These results are physically transparent and describe properly the physics of the collision process. They may also be simple enough to be of practical use to study heavy-ion collisions or the dynamics of other fermion systems. Furthermore, as the configuration-space analog of the quantum Boltzmann equation, many important results concerning statistical dynamics are obtained. Concepts such as entropy, temperature, and local and thermal equilibrium can be quantitatively introduced. The well-known HHH theorem that entropy never decreases can be readily recovered. With the collision term explicitly exhibited, the macroscopic equations (equations of continuity, momentum flux, and energy) and their associated conservation theorems can also be derived. Analytic solutions for the master equation for simple cases lead to new "level crossing" formulas having characteristics distinctly different from the Landau-Zener level-crossing formula and illuminate the salient features as to how a nonequilibrium fermion system approaches thermal equilibrium.NUCLEAR REACTIONS Extension of time-dependent Hartree-Fock approximation. Collisions between particles. Master equation for occupation probabilities. Entropy, temperature, and thermal equilibrium. HHH theorem. Analytic solution of the master equation. New types of level crossing formula.
Dissipation is studied in a one-dimensional time-dependent Hartree-Fock system which simulates the capture of a slow neutron by a nucleus. It is shown that this time-dependent Hartree-Fock system is unable to approach thermodynamic equilibrium and that the time of damping of a collective vibration, induced by the capture, is much longer than the relaxation time of realistic nuclear collective motion. The dissipation in this time-dependent Hartree-Fock system is further compared with predictions of various one-body dissipation theories.NUCLEAR REACTIONS time-dependent Hartree-Fock calculation, slow neutron capture, one-body dissipation.
Aiming at exploring microscopic dynamics responsible for the dissipative large-amplitude collective motion, the dynamic response and correlation functions are introduced within the general theory of nuclear coupled-master equations. The theory is based on the microscopic theory of nuclear collective dynamics which has been developed within the time-dependent Hartree-Fock (TDHF) theory for disclosing the complex structure of the TDHF manifold. A systematic numerical method for calculating the dynamic response and correlation functions is proposed. By performing numerical calculation for a simple model Hamiltonian, it is pointed out that the dynamic response function gives important information in understanding the large-amplitude dissipative collective motion which is described by an ensemble of trajectories within the TDHF manifold.