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

Physical Review C

Dynamic realization of statistical state in finite systems

Xi-Zhen Wu, Fumihiko Sakata, Yizhong Zhuo, Zhuxia Li, Nguyen Dinh Dang

Published Mar 1, 1996• 6 citations
Publisher

Abstract

Evolution of the large-amplitude dissipative collective motion in a simple soluble model is studied within the time-dependent Hartree-Fock theory, by using a general microscopic transport theory, which optimally divides the total system into the collective and intrinsic subsystems. Even though the total system reaches some statistical stationary state, it is shown that the subsystem cannot alone remain stationary by being separated from the other subsystem, when they are strongly correlated with each other. Dynamic response functions are used in exploring an instantaneous structure of each subsystem. When the total system reaches a statistical stationary state, it is shown by using the dynamical response function that the influence of the intrinsic subsystem on the collective one can be effectively taken into account by replacing the intrinsic system by the heat bath. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevc.53.1233

Related papers

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

Collective, Dissipative and Stochastic Motions in the TDHF Theory

K. Muramatsu, Fumihiko Sakata, Y. Yamamoto +1 more

By applying the microscopic theory of dynamical collective submanifold, which has been formulated by the present authors, to a system with a simple model Hamiltonian, characteristic features of large-amplitude motion described by the time-dependent Hartree-Fock (TDHF) theory are visualized. Our theory dynamically defines an “optimum” submanifold out of the TDHF symplectic manifold (phase space) in such a way that the Hamiltonian on the submanifold is stationary with respect to variations perpendicular to it. The theory also classifies the submanifold into three different regions in terms of stablility and separability conditions. It is displayed that these three regions characterize collective, dissipative and stochastic motions in the TDHF theory.

Progress of Theoretical Physics•Feb 1, 1987•4 citations

Equations of Collective Submanifold for Large Amplitude Collective Motion and Its Coupling with Intrinsic Degrees of Freedom. I

M. Yamamura, A. Kuriyama

A theory based on the time•dependent Hartree•Fock theory is proposed with the aim of describing large amplitude collective motion and its coupling with intrinsic degrees of freedom.With the use of time•dependent canonical transformation, the whole system is separated into two types of degrees of freedom.Under the condition of unique separation, two kinds of equations of collective submanifold are obtained.One js for the collective motion and of the same form as that previously given by the present authors.The other is for the intrinsic degrees of freedom and consists of a set of linear partial differential equations.It is reduced to the old one, the form of which is non-linear.

Progress of Theoretical Physics•Feb 1, 1986•9 citations

Large amplitude collective dynamic beyond the independent particle/quasiparticle picture

Denis Lacroix A

In the present note, a summary of selected aspects of timedependent mean-field theory is first recalled. This approach is optimized to describe one-body degrees of freedom. A special focus is made on how this microscopic theory can be reduced to a macroscopic dynamic for a selected set of collective variables. Important physical phenomena like adiabaticity/diabaticity, one-body dissipation or memory effect are discussed. Special aspects related to the use of a time-dependent density functional instead of a time-dependent Hartree-Fock theory based on a bare hamiltonian are underlined. The absence of proper description of complex internal correlations however strongly impacts the predictive power of mean-field. A brief overview of theories going beyond the independent particles/quasi-particles theory is given. Then, a special attention is paid for finite fermionic systems at low internal excitation. In that case, quantum fluctuations in collective space that are poorly treated at the meanfield level, are important. Several approaches going beyond mean-field, that are anticipated to improve the description of quantum fluctuations, are discussed: the Balian-V´en´eroni variational principle, the Time-Dependent Random Phase Approximation and the recently proposed Stochastic Mean-Field theory. Relations between these theories are underlined as well as their advantages and shortcomings.

arXiv:1504.01499•Frontiers in nuclear and particle physics•Jun 27, 2019•5 citations

Collective motion in a quantum diffusive environment

V. M. Kolomietz, Sven Åberg, S. V. Radionov

The general problem of dissipation in macroscopic large-amplitude collective motion and its relation to energy diffusion of intrinsic degrees of freedom of a nucleus is studied. By applying the cranking approach to the nuclear many-body system, a set of coupled dynamical equations for the collective classical variable and the quantum mechanical occupancies of the intrinsic nuclear states is derived in the limit of weak coupling of the collective and intrinsic subsystems. Different dynamical regimes of the intrinsic nuclear motion and its consequences on time properties of collective dissipation are discussed.

arXiv:0706.2406•Physical Review C•Jan 9, 2008•6 citations

Random matrix approach to quantum dissipation

Aurel Bulgac, G. Do Dang, Dimitri Kusnezov

The microscopic origin of dissipation in collective motion of a quantum many-body system is addressed in the framework of a parametric random matrix approach to the intrinsic dynamics. There are noticeable violations of the fluctuation-dissipation theorem and the energy diffusion has a markedly non-Gaussian character. Such features do not support the usual Fokker-Planck approach to dissipation in large amplitude motion of many fermion systems. \textcopyright{} 1996 The American Physical Society.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Oct 1, 1996•43 citations
Evolution of the large-amplitude dissipative collective motion in a simple soluble model is studied within the time-dependent Hartree-Fock theory, by using a general microscopic transport theory, which optimally divides the total system into the collective and intrinsic subsystems. Even though the total system reaches some statistical stationary state, it is shown that the subsystem cannot alone remain stationary by being separated from the other subsystem, when they are strongly correlated with each other. Dynamic response functions are used in exploring an instantaneous structure of each subsystem. When the total system reaches a statistical stationary state, it is shown by using the dynamical response function that the influence of the intrinsic subsystem on the collective one can be effectively taken into account by replacing the intrinsic system by the heat bath. \textcopyright{} 1996 The American Physical Society.
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.
By applying the microscopic theory of dynamical collective submanifold, which has been formulated by the present authors, to a system with a simple model Hamiltonian, characteristic features of large-amplitude motion described by the time-dependent Hartree-Fock (TDHF) theory are visualized. Our theory dynamically defines an “optimum” submanifold out of the TDHF symplectic manifold (phase space) in such a way that the Hamiltonian on the submanifold is stationary with respect to variations perpendicular to it. The theory also classifies the submanifold into three different regions in terms of stablility and separability conditions. It is displayed that these three regions characterize collective, dissipative and stochastic motions in the TDHF theory.
A theory based on the time•dependent Hartree•Fock theory is proposed with the aim of describing large amplitude collective motion and its coupling with intrinsic degrees of freedom.With the use of time•dependent canonical transformation, the whole system is separated into two types of degrees of freedom.Under the condition of unique separation, two kinds of equations of collective submanifold are obtained.One js for the collective motion and of the same form as that previously given by the present authors.The other is for the intrinsic degrees of freedom and consists of a set of linear partial differential equations.It is reduced to the old one, the form of which is non-linear.
In the present note, a summary of selected aspects of timedependent mean-field theory is first recalled. This approach is optimized to describe one-body degrees of freedom. A special focus is made on how this microscopic theory can be reduced to a macroscopic dynamic for a selected set of collective variables. Important physical phenomena like adiabaticity/diabaticity, one-body dissipation or memory effect are discussed. Special aspects related to the use of a time-dependent density functional instead of a time-dependent Hartree-Fock theory based on a bare hamiltonian are underlined. The absence of proper description of complex internal correlations however strongly impacts the predictive power of mean-field. A brief overview of theories going beyond the independent particles/quasi-particles theory is given. Then, a special attention is paid for finite fermionic systems at low internal excitation. In that case, quantum fluctuations in collective space that are poorly treated at the meanfield level, are important. Several approaches going beyond mean-field, that are anticipated to improve the description of quantum fluctuations, are discussed: the Balian-V´en´eroni variational principle, the Time-Dependent Random Phase Approximation and the recently proposed Stochastic Mean-Field theory. Relations between these theories are underlined as well as their advantages and shortcomings.
The general problem of dissipation in macroscopic large-amplitude collective motion and its relation to energy diffusion of intrinsic degrees of freedom of a nucleus is studied. By applying the cranking approach to the nuclear many-body system, a set of coupled dynamical equations for the collective classical variable and the quantum mechanical occupancies of the intrinsic nuclear states is derived in the limit of weak coupling of the collective and intrinsic subsystems. Different dynamical regimes of the intrinsic nuclear motion and its consequences on time properties of collective dissipation are discussed.