Exact classical stochastic representations of the many-body quantum dynamics

Research output

Abstract

In this work we investigate the exact classical stochastic representations of many-body quantum dynamics. We focus on the representations in which the quantum states and the observables are linearly mapped onto classical quasiprobability distributions and functions in a certain (abstract) phase space. We demonstrate that when such representations have regular mathematical properties, they are reduced to the expansions of the density operator over a certain overcomplete operator basis. Our conclusions are supported by the fact that all the stochastic representations currently known in the literature (quantum mechanics in generalized phase space and, as it recently has been shown by us, the stochastic wave-function methods) have the mathematical structure of the above-mentioned type. We illustrate our considerations by presenting the recently derived operator mappings for the stochastic wave-function method.
Original languageEnglish
Pages (from-to)501-512
JournalNanosystems: Physics, Chemistry, Mathematics
Volume6
Issue number4
DOIs
Publication statusPublished - 2015
Externally publishedYes

Fingerprint

operators
wave functions
quantum mechanics
expansion

Cite this

@article{f550310a71af452b8f5f5192291c0a98,
title = "Exact classical stochastic representations of the many-body quantum dynamics",
abstract = "In this work we investigate the exact classical stochastic representations of many-body quantum dynamics. We focus on the representations in which the quantum states and the observables are linearly mapped onto classical quasiprobability distributions and functions in a certain (abstract) phase space. We demonstrate that when such representations have regular mathematical properties, they are reduced to the expansions of the density operator over a certain overcomplete operator basis. Our conclusions are supported by the fact that all the stochastic representations currently known in the literature (quantum mechanics in generalized phase space and, as it recently has been shown by us, the stochastic wave-function methods) have the mathematical structure of the above-mentioned type. We illustrate our considerations by presenting the recently derived operator mappings for the stochastic wave-function method.",
keywords = "quantum ensemble theory, quantum noise, stochastic equations",
author = "Polyakov, {E. A.} and Vorontsov-Velyaminov, {P. N.}",
year = "2015",
doi = "10.17586/2220-8054-2015-6-4-501-512",
language = "English",
volume = "6",
pages = "501--512",
journal = "Nanosystems: Physics, Chemistry, Mathematics",
issn = "2220-8054",
publisher = "НИУ ИТМО",
number = "4",

}

TY - JOUR

T1 - Exact classical stochastic representations of the many-body quantum dynamics

AU - Polyakov, E. A.

AU - Vorontsov-Velyaminov, P. N.

PY - 2015

Y1 - 2015

N2 - In this work we investigate the exact classical stochastic representations of many-body quantum dynamics. We focus on the representations in which the quantum states and the observables are linearly mapped onto classical quasiprobability distributions and functions in a certain (abstract) phase space. We demonstrate that when such representations have regular mathematical properties, they are reduced to the expansions of the density operator over a certain overcomplete operator basis. Our conclusions are supported by the fact that all the stochastic representations currently known in the literature (quantum mechanics in generalized phase space and, as it recently has been shown by us, the stochastic wave-function methods) have the mathematical structure of the above-mentioned type. We illustrate our considerations by presenting the recently derived operator mappings for the stochastic wave-function method.

AB - In this work we investigate the exact classical stochastic representations of many-body quantum dynamics. We focus on the representations in which the quantum states and the observables are linearly mapped onto classical quasiprobability distributions and functions in a certain (abstract) phase space. We demonstrate that when such representations have regular mathematical properties, they are reduced to the expansions of the density operator over a certain overcomplete operator basis. Our conclusions are supported by the fact that all the stochastic representations currently known in the literature (quantum mechanics in generalized phase space and, as it recently has been shown by us, the stochastic wave-function methods) have the mathematical structure of the above-mentioned type. We illustrate our considerations by presenting the recently derived operator mappings for the stochastic wave-function method.

KW - quantum ensemble theory

KW - quantum noise

KW - stochastic equations

U2 - 10.17586/2220-8054-2015-6-4-501-512

DO - 10.17586/2220-8054-2015-6-4-501-512

M3 - Article

VL - 6

SP - 501

EP - 512

JO - Nanosystems: Physics, Chemistry, Mathematics

JF - Nanosystems: Physics, Chemistry, Mathematics

SN - 2220-8054

IS - 4

ER -