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

Time-dependent mean-field theory and quantized bound states

Shimon Levit, John W. Negele, Zvi Paltiel

Published Apr 1, 1980• 80 citations
Publisher

Abstract

A theory is presented in which approximations to quantum observables are obtained by applying the stationary-phase approximation to an exact functional integral representation of the many-body evolution operator. The requirement that the leading correction to the stationary-phase approximation vanish leads to a time-dependent Hartree-Fock mean field. Application of the theory to the Fourier transform of the trace of the evolution operator and the study of its poles yields quantized bound states with large amplitude. The theory is shown to reproduce the familiar static Hartree-Fock and random-phase approximations in the appropriate limits and yields an excellent approximation to the entire spectrum of the exactly solvable Lipkin model.NUCLEAR STRUCTURE Derivation of time-dependent mean-field theory from functional integral representation. Quantum theory of large amplitude collective motion. Application to Lipkin model.

DOI
10.1103/physrevc.21.1603

Related papers

Time-dependent mean-field approximation for nuclear dynamical problems

Shimon Levit

A general method for a microscopic description of nuclear dynamical problems is discussed. The method is based on a functional integral representation for the many-body time evolution operator $U({t}_{f},{t}_{i})$. In the stationary phase limit, a time-dependent mean-field approximation for the matrix elements of $U$ is obtained. Using standard procedures this allows for extraction of quantum mechanical information about bound states, tunneling, or scattering phenomena in a many-nucleon system. The approximation represents a natural generalization of the time-dependent Hartree-Fock method.NUCLEAR STRUCTURE, NUCLEAR REACTIONS derived mean-field approximation for matrix elements of $\mathrm{exp}(\ensuremath{-}iHt)$ from exact functional integral; discussed relation to static HF, TDHF, and scattering calculations.

Physical Review C•Apr 1, 1980•64 citations

Mean-field approximation for inclusive observables

Y. Alhassid, Berndt Müller, S. E. Koonin

The excitation of a many-body system by a one-body perturbation is considered. The stationary phase approximation to a functional-integral representation of the many-body evolution operator shows that the optimal mean field for describing the final expectation values of one- and two-body operators is that given by the time-dependent Hartree-Fock method. The forced Lipkin model is considered as a test of the mean-field approximation.NUCLEAR REACTIONS Mean-field approximation, inclusive observables. Time-dependent Hartree-Fock.

Physical Review C•Jan 1, 1981•11 citations

Mean-field approximation to the many-body S matrix

Y. Alhassid, S. E. Koonin

A nonperturbative method is developed for calculating the excitation of a many-body system by a time-dependent Hamiltonian. The stationary-phase approximation to a functional-integral representation of the interaction-picture many-body evolution operator results in a mean-field approximation to the $S$ matrix which is asymptotically time independent. A one-body temporally nonlocal evolution equation defines the stationary mean-field configurations. The general method and character of the stationary solutions are illustrated by application to the forced harmonic oscillator and forced Lipkin model. Potential applications to realistic nuclear and atomic scattering situations are discussed.NUCLEAR REACTIONS Mean-field approximation, many-body $S$ matrix, time-dependent Hartree Fock.

Physical Review C•Apr 1, 1981•36 citations

Time-dependent mean-field approximations for many-body observables

T. Troudet, S. E. Koonin

The excitation of a many-body system by a time-dependent perturbation is considered within the framework of functional integration. The stationary phase approximation to a functional-integral representation of the final expectation values of many-body observables in the interaction picture leads to a new time-dependent mean-field theory. The resulting equations of motion depend upon the observable itself and consequently are nonlocal in time. The method is illustrated by an analytically soluble application to the forced harmonic oscillator.NUCLEAR REACTIONS Functional integral representation of expectation values of many-body observables. Stationary phase approximation. Time-dependent mean fields.

Physical Review C•Oct 1, 1983•4 citations

Time-dependent coupled-cluster approximation to nuclear dynamics. I. Application to a solvable model

Pervez Amirali Hoodbhoy, John W. Negele

A general hierarchy of approximations to the many-body Schr\"odinger equation is presented which reduces to the time-dependent mean-field approximation in lowest order and provides systematic corrections in subsequent orders. The theory is applied to two interacting systems described by the Lipkin model Hamiltonian. Comparison of the results of the lowest two orders of approximation with the exact solution demonstrates the practicality of the method and its potential for generalizing nuclear dynamics beyond the mean field theory.NUCLEAR STRUCTURE Time-dependent approximation to nuclear dynamics. Corrections to time-dependent mean-field theory. Solution of Lipkin model for two interacting systems.

Physical Review C•Nov 1, 1978•65 citations

Quantum mean estimation for lattice field theory

Erik Gustafson, Henry Lamm, Judah Unmuth-Yockey

exact expression for an observable of interest is written using a functional integral representation for the evolution operator, and tractable time-dependent mean field equations are obtained by application of the stationary-phase approximation (SPA) to the functional integral. Corrections to the lowest-order theory may be systematically enumerated. 6 figures. (RWR)

•May 30, 2023•0 citations
A theory is presented in which approximations to quantum observables are obtained by applying the stationary-phase approximation to an exact functional integral representation of the many-body evolution operator. The requirement that the leading correction to the stationary-phase approximation vanish leads to a time-dependent Hartree-Fock mean field. Application of the theory to the Fourier transform of the trace of the evolution operator and the study of its poles yields quantized bound states with large amplitude. The theory is shown to reproduce the familiar static Hartree-Fock and random-phase approximations in the appropriate limits and yields an excellent approximation to the entire spectrum of the exactly solvable Lipkin model.NUCLEAR STRUCTURE Derivation of time-dependent mean-field theory from functional integral representation. Quantum theory of large amplitude collective motion. Application to Lipkin model.
A general method for a microscopic description of nuclear dynamical problems is discussed. The method is based on a functional integral representation for the many-body time evolution operator U(tf,ti)U({t}_{f},{t}_{i})U(tf​,ti​). In the stationary phase limit, a time-dependent mean-field approximation for the matrix elements of UUU is obtained. Using standard procedures this allows for extraction of quantum mechanical information about bound states, tunneling, or scattering phenomena in a many-nucleon system. The approximation represents a natural generalization of the time-dependent Hartree-Fock method.NUCLEAR STRUCTURE, NUCLEAR REACTIONS derived mean-field approximation for matrix elements of $\mathrm{exp}(\ensuremath{-}iHt)$ from exact functional integral; discussed relation to static HF, TDHF, and scattering calculations.
The excitation of a many-body system by a one-body perturbation is considered. The stationary phase approximation to a functional-integral representation of the many-body evolution operator shows that the optimal mean field for describing the final expectation values of one- and two-body operators is that given by the time-dependent Hartree-Fock method. The forced Lipkin model is considered as a test of the mean-field approximation.NUCLEAR REACTIONS Mean-field approximation, inclusive observables. Time-dependent Hartree-Fock.
A nonperturbative method is developed for calculating the excitation of a many-body system by a time-dependent Hamiltonian. The stationary-phase approximation to a functional-integral representation of the interaction-picture many-body evolution operator results in a mean-field approximation to the SSS matrix which is asymptotically time independent. A one-body temporally nonlocal evolution equation defines the stationary mean-field configurations. The general method and character of the stationary solutions are illustrated by application to the forced harmonic oscillator and forced Lipkin model. Potential applications to realistic nuclear and atomic scattering situations are discussed.NUCLEAR REACTIONS Mean-field approximation, many-body SSS matrix, time-dependent Hartree Fock.
The excitation of a many-body system by a time-dependent perturbation is considered within the framework of functional integration. The stationary phase approximation to a functional-integral representation of the final expectation values of many-body observables in the interaction picture leads to a new time-dependent mean-field theory. The resulting equations of motion depend upon the observable itself and consequently are nonlocal in time. The method is illustrated by an analytically soluble application to the forced harmonic oscillator.NUCLEAR REACTIONS Functional integral representation of expectation values of many-body observables. Stationary phase approximation. Time-dependent mean fields.
A general hierarchy of approximations to the many-body Schr\"odinger equation is presented which reduces to the time-dependent mean-field approximation in lowest order and provides systematic corrections in subsequent orders. The theory is applied to two interacting systems described by the Lipkin model Hamiltonian. Comparison of the results of the lowest two orders of approximation with the exact solution demonstrates the practicality of the method and its potential for generalizing nuclear dynamics beyond the mean field theory.NUCLEAR STRUCTURE Time-dependent approximation to nuclear dynamics. Corrections to time-dependent mean-field theory. Solution of Lipkin model for two interacting systems.