Feynman—Chernoff Iterations and Their Applications in Quantum Dynamics

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 appli...

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Bibliographic Details
Published inProceedings of the Steklov Institute of Mathematics Vol. 301; no. 1; pp. 197 - 206
Main Authors Orlov, Yu. N., Sakbaev, V. Zh
Format Journal Article Conference Proceeding
LanguageEnglish
Published Moscow Pleiades Publishing 01.05.2018
Springer Nature B.V
Subjects
Equivalence
Mathematics
Mathematics and Statistics
Operators (mathematics)
Quantum optics
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Summary: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.
ISSN:0081-5438
1531-8605
DOI:10.1134/S0081543818040156