Markov Approximations of the Evolution of Quantum Systems

J Gough, Yu. N. Orlov, V. Zh. Sakbaev, O. G. Smolyanov

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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.
Original languageEnglish
Pages (from-to)92-96
Number of pages5
JournalDoklady Mathematics
Issue number2
Publication statusPublished - 06 Jul 2022


  • Gorini–Kossakowski–Sudarshan–Lindblad equation
  • Markovian process
  • Mathematics
  • law of large numbers
  • open quantum system
  • operator-valued random process
  • random linear operator
  • random operator-valued function


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  • Erratum to: Several Articles in Doklady Mathematics

    Volkov, N. A., Dmitriev, D. I., Zhukovskii, M. E., Gough, J., Orlov, Y. N., Sakbaev, V. Z., Smolyanov, O. G., Bogdanov, I. I., Grigoryan, O. R., Alekseev, V. A., Smetanin, Y. G., Amaglobeli, M. G., Miasnikov, A. G. & Remeslennikov, V. N., 27 Dec 2022, In: Doklady Mathematics. 106, 2, p. 402-403 2 p.

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