Quasiprobability distributions in stochastic wave-function methods

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3 Citations (Scopus)

Abstract

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
Original languageEnglish
Pages (from-to)042107_1-18
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume91
Issue number4
DOIs
Publication statusPublished - 2015

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wave functions
automorphisms
projection
equivalence
gauge theory
emerging
operators
expansion
simulation

Cite this

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T1 - Quasiprobability distributions in stochastic wave-function methods

AU - Polyakov, E.A.

AU - Vorontsov-Velyaminov, P.N.

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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

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KW - Stochastic Differential Equations

KW - Quasiprobability Distributions

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