Markov Approximations of the Evolution of Quantum Systems

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 evol...

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Bibliographic Details
Published in:Doklady. Mathematics 2022-04, Vol.105 (2), p.92-96
Main Authors: Gough, J., Orlov, Yu. N., Sakbaev, V. Zh, Smolyanov, O. G.
Format: Article
Language:English
Subjects:
Convergence
Evolution
Markov processes
Mathematics
Mathematics and Statistics
Operators (mathematics)
Probability theory
Quantum theory
Random processes
Semigroups
Statistical analysis
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Summary: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.
ISSN:1064-5624
1531-8362
DOI:10.1134/S1064562422020107