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

Progress of Theoretical Physics Supplement

Time-Dependent Hartree-Fock Method and Its Extension

Masatoshi Yamamura, A. Kuriyama

Published Jan 1, 1987• 45 citations
Publisher

Abstract

The study of large-amplitude collective motion has been stimulated in Japan, by Professor T. Marumori through his paper published in 1977. Under this situation, a series of annual research projects were organized by the Research Institute for Fundamental Physics, Kyoto University, entitled “Large Amplitude Collective Motion and Microscopic Theory”, “Time-Dependent Self-Consistent Field Method and Quantization”, “Microscopic Theories of Large Amplitude Collective Motions”, and so forth from 1980 to 1985. The present volume of Progress of Theoretical Physics Supplement is edited to give a comprehensive review on the theoretical study reported mainly by the authors engaged in those research projects.

DOI
10.1143/ptps.93.1

Related papers

Path-integral approach to time-dependent self-consistent field theories

Hugo Reinhardt

With the aim of obtaining a field theory of large amplitude collective motion the author formulates the time-dependent Hartree approximation within a path-integral approach.

Journal of Physics G Nuclear Physics•Jun 1, 1979•15 citations

Number-Constrained Canonical Equation for Large Amplitude Pairing Motion and Time-Dependent Hartree-Fock Method

A. Kuriyama

Atsushi Kuriyama; Number-Constrained Canonical Equation for Large Amplitude Pairing Motion and Time-Dependent Hartree-Fock Method, Progress of Theoretical Physi

Progress of Theoretical Physics•Aug 1, 1977•0 citations

Quantum Theory of Collective Motion: Quantized Self-Consistent Collective-Coordinate Method for the Large-Amplitude Nuclear Collective Motion

Toshio Marumori, Fumihiko Sakata, Tsutomu Une +2 more

This is the third in a series of papers which intends to develop a new microscopic theory capable by itself to determine the “maximaldecoupled” collective subspace in the many-particle Hilbert space as well as the collective Hamiltonian specifying the subspace. The fundamental principle to formulate the theory is called the invariance principle of the Schrödinger equation. The main purpose of this paper is to show that, when we positively utilize the invariance principle, we can directly obtain a quantum theory of collective motion going beyond the random phase approximation.

Progress of Theoretical Physics•Nov 1, 1981•6 citations

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

M. Yamamura, A. Kuriyama

From the viewpoint defferent from that of Part I, the time-dependent Harteree-Fock theory is formulated for describing large amplitude collective motion and its coupling with intrinsic degrees of freedom. The basic idea consists of the introduction of an additional degree of freedom for the collective motion and the use of Dirac’s canonical theory with constraints. The formalism is essentially equivalent to the ordinary time-dependent Hartree-Fock theory presented in Part I. The result given in Part I is completely reproduced.

Progress of Theoretical Physics•Jan 1, 1987•5 citations

A Few Methods for the Theory of Collective Motions and Collisions

BERTRAND G. GIRAUD

The title originally planned for this series of lectures was “Time-dependent Hartree Fock Theory of Nuclear Motions and Collisions”. In fact, in what follows, the TDHF method will be considered for collective motion only. This is because a new, more practical theory of collisions has recently emerged. These lectures thus contain two main and distinct chapters, the first dedicated to this new theory of collisions and the second to collective motion. As a distraction to the reader, a last and small chapter recalls elementary ideas about some conjectured mechanisms for the dynamics of a very special system with collective motions, namely a living organ in the nervous system. This Summer School being dedicated to the subject of order and chaos, it is hoped that the considerations which follow never go too far from that fascinating subject indeed. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Birkhäuser Boston eBooks•Jan 1, 1985•0 citations

Determination of the collective Hamiltonian in a self-consistent theory of large amplitude adiabatic motion

G. Do Dang, Aurel Bulgac, Abraham Klein

The starting point for most studies of large amplitude collective motion in nuclear physics, the time-dependent Hartree-Fock equations, can be mapped to a problem in classical Hamiltonian mechanics, which is the form of the problem studied in this work. For a system with N degrees of freedom, collective motion is identified with motion completely confined to a surface in K<N dimensions. Conditions for the existence of such decoupled surfaces are worked out and a procedure for constructing them is formulated. For most practical problems, where such surfaces do not strictly exist, a concept of approximate decoupling is developed and a test of its accuracy is described. Our results generalize the method of maximum global decoupling found in the earlier literature.

Physical Review C•Dec 1, 1987•11 citations
The study of large-amplitude collective motion has been stimulated in Japan, by Professor T. Marumori through his paper published in 1977. Under this situation, a series of annual research projects were organized by the Research Institute for Fundamental Physics, Kyoto University, entitled “Large Amplitude Collective Motion and Microscopic Theory”, “Time-Dependent Self-Consistent Field Method and Quantization”, “Microscopic Theories of Large Amplitude Collective Motions”, and so forth from 1980 to 1985. The present volume of Progress of Theoretical Physics Supplement is edited to give a comprehensive review on the theoretical study reported mainly by the authors engaged in those research projects.
This is the third in a series of papers which intends to develop a new microscopic theory capable by itself to determine the “maximaldecoupled” collective subspace in the many-particle Hilbert space as well as the collective Hamiltonian specifying the subspace. The fundamental principle to formulate the theory is called the invariance principle of the Schrödinger equation. The main purpose of this paper is to show that, when we positively utilize the invariance principle, we can directly obtain a quantum theory of collective motion going beyond the random phase approximation.
From the viewpoint defferent from that of Part I, the time-dependent Harteree-Fock theory is formulated for describing large amplitude collective motion and its coupling with intrinsic degrees of freedom. The basic idea consists of the introduction of an additional degree of freedom for the collective motion and the use of Dirac’s canonical theory with constraints. The formalism is essentially equivalent to the ordinary time-dependent Hartree-Fock theory presented in Part I. The result given in Part I is completely reproduced.
The title originally planned for this series of lectures was “Time-dependent Hartree Fock Theory of Nuclear Motions and Collisions”. In fact, in what follows, the TDHF method will be considered for collective motion only. This is because a new, more practical theory of collisions has recently emerged. These lectures thus contain two main and distinct chapters, the first dedicated to this new theory of collisions and the second to collective motion. As a distraction to the reader, a last and small chapter recalls elementary ideas about some conjectured mechanisms for the dynamics of a very special system with collective motions, namely a living organ in the nervous system. This Summer School being dedicated to the subject of order and chaos, it is hoped that the considerations which follow never go too far from that fascinating subject indeed. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The starting point for most studies of large amplitude collective motion in nuclear physics, the time-dependent Hartree-Fock equations, can be mapped to a problem in classical Hamiltonian mechanics, which is the form of the problem studied in this work. For a system with N degrees of freedom, collective motion is identified with motion completely confined to a surface in K<N dimensions. Conditions for the existence of such decoupled surfaces are worked out and a procedure for constructing them is formulated. For most practical problems, where such surfaces do not strictly exist, a concept of approximate decoupling is developed and a test of its accuracy is described. Our results generalize the method of maximum global decoupling found in the earlier literature.