Exact BCS stochastic schemes for a time-dependent many-body fermionic system

Journal Article · Sun Jan 15 04:00:00 EST 2006 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.73.0· OSTI ID:20786760

Montina, A; Castin, Yvan ^[1]

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1. Dipartimento di Fisica, Universita di Firenze, Via Sansone 1, 50019 Sesto Fiorentino (Finland) (Italy)

A common approximate way to study the time evolution of a superfluid Fermi gas is to consider the mean-field time-dependent BCS equations. We show that, by inclusion of an appropriate fluctuating term in these mean-field equations, the exact quantum evolution of the Fermi gas is recovered, after an average over all possible realizations of the noise term: this leads to an exact quantum Monte Carlo technique for the real-time evolution of an interacting fermionic system. In practice, we derive the general conditions on the noise term, ensuring that the exact dynamics is reproduced, and we explore several explicit realizations of this noise term, trying to minimize the statistical spreading of the quantum Monte Carlo simulations. The convergence issue is discussed in detail, with upper bounds obtained on the statistical spreading, and the relation between the stochastic and the mean-field equations is analyzed. Finally, we apply the method to a simple two-site model, to exemplify that the simulations can display effects out of reach of the mean-field approximation.

• OSTI ID: 20786760
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 1 Vol. 73; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
APPROXIMATIONS
BCS THEORY
COMPUTERIZED SIMULATION
CONVERGENCE
FERMI GAS
FERMIONS
FIELD EQUATIONS
MANY-BODY PROBLEM
MEAN-FIELD THEORY
MONTE CARLO METHOD
NOISE
STOCHASTIC PROCESSES
SUPERFLUIDITY
TIME DEPENDENCE