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Feynman—Chernoff Iterations and Their Applications in Quantum Dynamics

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Abstract

The notion of Chernoff equivalence for operator-valued functions is generalized to the solutions of quantum evolution equations with respect to the density matrix. A semigroup is constructed that is Chernoff equivalent to the operator function arising as the mean value of random semigroups. As applied to the problems of quantum optics, an operator is constructed that is Chernoff equivalent to a translation operator generating coherent states.

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia

    Yu. N. Orlov

  2. Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141701, Russia

    V. Zh. Sakbaev

Authors
  1. Yu. N. Orlov
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  2. V. Zh. Sakbaev
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Correspondence to Yu. N. Orlov.

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Original Russian Text © Yu.N. Orlov, V.Zh. Sakbaev, 2018, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2018, Vol. 301, pp. 209–218.

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Orlov, Y.N., Sakbaev, V.Z. Feynman—Chernoff Iterations and Their Applications in Quantum Dynamics. Proc. Steklov Inst. Math. 301, 197–206 (2018). https://doi.org/10.1134/S0081543818040156

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  • DOI: https://doi.org/10.1134/S0081543818040156

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