TY - JOUR

T1 - Quasiprobability distributions in stochastic wave-function methods

AU - Polyakov, E.A.

AU - Vorontsov-Velyaminov, P.N.

PY - 2015

Y1 - 2015

N2 - Quasiprobability distributions emerging in the stochastic wave-function method of Carusotto et al. [Phys. Rev. A 63, 023606 (2001)] are investigated. We show that there are actually two types of quasiprobabilities. The first one, the “diagonal Hartree-Fock state projection” representation, is useful in representing the initial conditions for stochastic simulation in the most compact form. It defines antinormally ordered expansion of the density operator and normally ordered mapping of the observables to be averaged. We completely characterize the equivalence classes of this phase-space representation. The second quasiprobability distribution, the “nondiagonal Hartree-Fock state projection” representation, extends the first one in order to achieve stochastic representation of the quantum dynamics. We demonstrate how the differential identities of the stochastic ansatz generate the automorphisms of this phase-space representation. These automorphisms turn the stochastic representation into a gauge theory. The g

AB - Quasiprobability distributions emerging in the stochastic wave-function method of Carusotto et al. [Phys. Rev. A 63, 023606 (2001)] are investigated. We show that there are actually two types of quasiprobabilities. The first one, the “diagonal Hartree-Fock state projection” representation, is useful in representing the initial conditions for stochastic simulation in the most compact form. It defines antinormally ordered expansion of the density operator and normally ordered mapping of the observables to be averaged. We completely characterize the equivalence classes of this phase-space representation. The second quasiprobability distribution, the “nondiagonal Hartree-Fock state projection” representation, extends the first one in order to achieve stochastic representation of the quantum dynamics. We demonstrate how the differential identities of the stochastic ansatz generate the automorphisms of this phase-space representation. These automorphisms turn the stochastic representation into a gauge theory. The g

KW - Phase Space Formulation

KW - Stochastic Differential Equations

KW - Quasiprobability Distributions

U2 - 10.1103/PhysRevA.91.042107

DO - 10.1103/PhysRevA.91.042107

M3 - Article

VL - 91

SP - 042107_1-18

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 4

ER -