Stochastic mean-field dynamics for fermions in the weak-coupling limit

Journal Article · Sat Apr 15 00:00:00 EDT 2006 · Physical Review. C, Nuclear Physics

DOI:https://doi.org/10.1103/PhysRevC.73.044311· OSTI ID:20771437

Lacroix, Denis ^[1]

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1. Laboratoire de Physique Corpusculaire, ENSICAEN and Universite de Caen, IN2P3-CNRS, 6 Blvd du Marechal Juin, F-14050 Caen (France)

Assuming that the effect of the residual interaction beyond the mean field is weak and has a short memory time, two approximate treatments of correlation in fermionic systems by means of the Markovian quantum jump are presented. A simplified scenario for the introduction of fluctuations beyond the mean field is presented first. In this theory, part of the quantum correlations between the residual interaction and the one-body density matrix are neglected and jumps occur between many-body densities formed of pairs of states D={phi}{sub a}><{phi}{sub b}/<{phi}{sub b}{phi}{sub a}>, where {phi}{sub a}> and {phi}{sub b}> are antisymmetrized products of single-particle states. The underlying stochastic mean-field theory is discussed and is applied to the monopole vibration of a spherical {sup 40}Ca nucleus under the influence of a statistical ensemble of two-body contact interactions. This framework is however too simplistic to account for both fluctuation and dissipation. In the second part of this work, an alternative quantum jump method is obtained without making the approximation on quantum correlations. By restricting to two-particle-two-hole residual interactions, the evolution of the one-body density matrix of a correlated system is transformed into a Lindblad equation. The associated dissipative dynamics can be simulated by quantum jumps between densities written as D=|{phi}><{phi}|, where |{phi}> is a normalized Slater determinant. The associated stochastic Schroedinger equation for single-particle wave functions is given.

• OSTI ID: 20771437
• Journal Information: Physical Review. C, Nuclear Physics, Vol. 73, Issue 4; Other Information: DOI: 10.1103/PhysRevC.73.044311; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2813
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
APPROXIMATIONS
CALCIUM 40
CORRELATIONS
COUPLING
DENSITY
DENSITY MATRIX
FERMIONS
FLUCTUATIONS
MARKOV PROCESS
MEAN-FIELD THEORY
PARTICLE-HOLE MODEL
QUANTUM FIELD THEORY
RESIDUAL INTERACTIONS
SCHROEDINGER EQUATION
SLATER METHOD
SPHERICAL CONFIGURATION
STATISTICAL MODELS
TWO-BODY PROBLEM
VIBRATIONAL STATES
WAVE FUNCTIONS