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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2022, Volume 503, Pages 48–53
DOI: https://doi.org/10.31857/S2686954322020102 (Mi danma248) 		 
This article is cited in 3 scientific papers (total in 3 papers)

MATHEMATICS

Markov approximations of the evolution of quantum systems

J. E. Gougha, Yu. N. Orlovb, V. Zh. Sakbaevb, O. G. Smolyanovcd

a Aberystwyth University, Wales, UK
b Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia
c Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
d Lomonosov Moscow State University
Citations (3)
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DOI: https://doi.org/10.31857/S2686954322020102
Abstract: The convergence in probability of a sequence of iterations of independent random quantum dynamical semigroups to a Markov process describing the evolution of an open quantum system is studied. The statistical properties of the dynamics of open quantum systems with random generators of Markovian evolution are described in terms of the law of large numbers for operator-valued random processes. For compositions of independent random semigroups of completely positive operators, the convergence of mean values to a semigroup described by the Gorini–Kossakowski–Sudarshan–Lindblad equation is established. Moreover, a sequence of random operator-valued functions with values in the set of operators without the infinite divisibility property is shown to converge in probability to an operator-valued function with values in the set of infinitely divisible operators.
Keywords: random linear operator, random operator-valued function, operator-valued random process, law of large numbers, open quantum system, Markovian process, Gorini–Kossakowski–Sudarshan–Lindblad equation.
Presented: V. V. Kozlov
Received: 26.08.2021
Revised: 27.01.2022
Accepted: 15.02.2022
English version:
Doklady Mathematics, 2022, Volume 105, Issue 2, Pages 92–96
DOI: https://doi.org/10.1134/S1064562422020107
Bibliographic databases:
Document Type: Article
UDC: 517.63
Language: Russian
Citation: J. E. Gough, Yu. N. Orlov, V. Zh. Sakbaev, O. G. Smolyanov, “Markov approximations of the evolution of quantum systems”, Dokl. RAN. Math. Inf. Proc. Upr., 503 (2022), 48–53; Dokl. Math., 105:2 (2022), 92–96
Citation in format AMSBIB
\Bibitem{GouOrlSak22}
\by J.~E.~Gough, Yu.~N.~Orlov, V.~Zh.~Sakbaev, O.~G.~Smolyanov
\paper Markov approximations of the evolution of quantum systems
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2022
\vol 503
\pages 48--53
\mathnet{http://mi.mathnet.ru/danma248}
\crossref{https://doi.org/10.31857/S2686954322020102}
\elib{https://elibrary.ru/item.asp?id=48506202}
\transl
\jour Dokl. Math.
\yr 2022
\vol 105
\issue 2
\pages 92--96
\crossref{https://doi.org/10.1134/S1064562422020107}
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