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Title: Exact and approximate many-body dynamics with stochastic one-body density matrix evolution

Abstract

We show that the dynamics of interacting fermions can be exactly replaced by a quantum jump theory in the many-body density matrix space. In this theory, jumps occur between densities formed of pairs of Slater determinants, D{sub ab}= vertical bar {phi}{sub a}><{phi}{sub b} vertical bar, where each state evolves according to the stochastic Schroedinger equation given by O. Juillet and Ph. Chomaz [Phys. Rev. Lett. 88, 142503 (2002)]. A stochastic Liouville-von Neumann equation is derived as well as the associated. Bogolyubov-Born-Green-Kirwood-Yvon hierarchy. Due to the specific form of the many-body density along the path, the presented theory is equivalent to a stochastic theory in one-body density matrix space, in which each density matrix evolves according to its own mean-field augmented by a one-body noise. Guided by the exact reformulation, a stochastic mean-field dynamics valid in the weak coupling approximation is proposed. This theory leads to an approximate treatment of two-body effects similar to the extended time-dependent Hartree-Fock scheme. In this stochastic mean-field dynamics, statistical mixing can be directly considered and jumps occur on a coarse-grained time scale. Accordingly, numerical effort is expected to be significantly reduced for applications.

Authors:
 [1]
  1. Laboratoire de Physique Corpusculaire, ENSICAEN and Universite de Caen, IN2P3-CNRS, Blvd. du Marechal Juin, F-14050 Caen (France)
Publication Date:
OSTI Identifier:
20698750
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 71; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevC.71.064322; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; BOLTZMANN-VLASOV EQUATION; COUPLING; DENSITY MATRIX; FERMIONS; HARTREE-FOCK METHOD; MEAN-FIELD THEORY; QUANTUM FIELD THEORY; SCHROEDINGER EQUATION; SLATER METHOD; STATISTICAL MODELS; STOCHASTIC PROCESSES; TIME DEPENDENCE; TWO-BODY PROBLEM

Citation Formats

Lacroix, Denis. Exact and approximate many-body dynamics with stochastic one-body density matrix evolution. United States: N. p., 2005. Web. doi:10.1103/PhysRevC.71.064322.
Lacroix, Denis. Exact and approximate many-body dynamics with stochastic one-body density matrix evolution. United States. doi:10.1103/PhysRevC.71.064322.
Lacroix, Denis. 2005. "Exact and approximate many-body dynamics with stochastic one-body density matrix evolution". United States. doi:10.1103/PhysRevC.71.064322.
@article{osti_20698750,
title = {Exact and approximate many-body dynamics with stochastic one-body density matrix evolution},
author = {Lacroix, Denis},
abstractNote = {We show that the dynamics of interacting fermions can be exactly replaced by a quantum jump theory in the many-body density matrix space. In this theory, jumps occur between densities formed of pairs of Slater determinants, D{sub ab}= vertical bar {phi}{sub a}><{phi}{sub b} vertical bar, where each state evolves according to the stochastic Schroedinger equation given by O. Juillet and Ph. Chomaz [Phys. Rev. Lett. 88, 142503 (2002)]. A stochastic Liouville-von Neumann equation is derived as well as the associated. Bogolyubov-Born-Green-Kirwood-Yvon hierarchy. Due to the specific form of the many-body density along the path, the presented theory is equivalent to a stochastic theory in one-body density matrix space, in which each density matrix evolves according to its own mean-field augmented by a one-body noise. Guided by the exact reformulation, a stochastic mean-field dynamics valid in the weak coupling approximation is proposed. This theory leads to an approximate treatment of two-body effects similar to the extended time-dependent Hartree-Fock scheme. In this stochastic mean-field dynamics, statistical mixing can be directly considered and jumps occur on a coarse-grained time scale. Accordingly, numerical effort is expected to be significantly reduced for applications.},
doi = {10.1103/PhysRevC.71.064322},
journal = {Physical Review. C, Nuclear Physics},
number = 6,
volume = 71,
place = {United States},
year = 2005,
month = 6
}
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