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

Journal Article · Wed Jun 01 04:00:00 EDT 2005 · Physical Review. C, Nuclear Physics

DOI:https://doi.org/10.1103/PhysRevC.71.064322· OSTI ID:20698750

Lacroix, Denis ^[1]

---

1. Laboratoire de Physique Corpusculaire, ENSICAEN and Universite de Caen, IN2P3-CNRS, Blvd. du Marechal Juin, F-14050 Caen (France)

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.

• OSTI ID: 20698750
• Journal Information: Physical Review. C, Nuclear Physics, Journal Name: Physical Review. C, Nuclear Physics Journal Issue: 6 Vol. 71; ISSN 0556-2813; ISSN PRVCAN
• Country of Publication: United States
• Language: English

Related Subjects

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