Exact and approximate manybody dynamics with stochastic onebody density matrix evolution
Abstract
We show that the dynamics of interacting fermions can be exactly replaced by a quantum jump theory in the manybody 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 Liouvillevon Neumann equation is derived as well as the associated. BogolyubovBornGreenKirwoodYvon hierarchy. Due to the specific form of the manybody density along the path, the presented theory is equivalent to a stochastic theory in onebody density matrix space, in which each density matrix evolves according to its own meanfield augmented by a onebody noise. Guided by the exact reformulation, a stochastic meanfield dynamics valid in the weak coupling approximation is proposed. This theory leads to an approximate treatment of twobody effects similar to the extended timedependent HartreeFock scheme. In this stochastic meanfield dynamics, statistical mixing can be directly considered and jumps occur on a coarsegrained time scale. Accordingly, numerical effort is expected to be significantly reduced for applications.
 Authors:
 Laboratoire de Physique Corpusculaire, ENSICAEN and Universite de Caen, IN2P3CNRS, Blvd. du Marechal Juin, F14050 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; BOLTZMANNVLASOV EQUATION; COUPLING; DENSITY MATRIX; FERMIONS; HARTREEFOCK METHOD; MEANFIELD THEORY; QUANTUM FIELD THEORY; SCHROEDINGER EQUATION; SLATER METHOD; STATISTICAL MODELS; STOCHASTIC PROCESSES; TIME DEPENDENCE; TWOBODY PROBLEM
Citation Formats
Lacroix, Denis. Exact and approximate manybody dynamics with stochastic onebody density matrix evolution. United States: N. p., 2005.
Web. doi:10.1103/PhysRevC.71.064322.
Lacroix, Denis. Exact and approximate manybody dynamics with stochastic onebody density matrix evolution. United States. doi:10.1103/PhysRevC.71.064322.
Lacroix, Denis. 2005.
"Exact and approximate manybody dynamics with stochastic onebody density matrix evolution". United States.
doi:10.1103/PhysRevC.71.064322.
@article{osti_20698750,
title = {Exact and approximate manybody dynamics with stochastic onebody 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 manybody 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 Liouvillevon Neumann equation is derived as well as the associated. BogolyubovBornGreenKirwoodYvon hierarchy. Due to the specific form of the manybody density along the path, the presented theory is equivalent to a stochastic theory in onebody density matrix space, in which each density matrix evolves according to its own meanfield augmented by a onebody noise. Guided by the exact reformulation, a stochastic meanfield dynamics valid in the weak coupling approximation is proposed. This theory leads to an approximate treatment of twobody effects similar to the extended timedependent HartreeFock scheme. In this stochastic meanfield dynamics, statistical mixing can be directly considered and jumps occur on a coarsegrained 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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