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Keldysh Institute preprints, 2014, 019, 28 pp. (Mi ipmp1871)  

This article is cited in 1 scientific paper (total in 1 paper)

Averaging of random semigroups and the ambiguity of quantization of Hamiltonian systems

M. H. Numan Elsheikh, J. O. Ogun, Yu. N. Orlov, R. V. Pleshakov, V. Zh. Sakbaev


Abstract: The properties of mean values of random variable with values in the set of semigroups of unitary operators are investigated. The mean value of random semigroup has no semigroup property. But it is equivalent (in Chernoff sense) to the semigroup with generator which is the result of averaging of generators of values of random semigroup. The problem of ambiguity of quantization of Hamiltonian systems is studied by using of semigroup averaging procedure. In particular the wide class of Shchrodinger operators on the graph is described by using of semigroups averaging procedure.

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Citation: M. H. Numan Elsheikh, J. O. Ogun, Yu. N. Orlov, R. V. Pleshakov, V. Zh. Sakbaev, “Averaging of random semigroups and the ambiguity of quantization of Hamiltonian systems”, Keldysh Institute preprints, 2014, 019, 28 pp.

Citation in format AMSBIB
\Bibitem{NumOguOrl14}
\by M.~H.~Numan Elsheikh, J.~O.~Ogun, Yu.~N.~Orlov, R.~V.~Pleshakov, V.~Zh.~Sakbaev
\paper Averaging of random semigroups and the ambiguity of quantization of Hamiltonian systems
\jour Keldysh Institute preprints
\yr 2014
\papernumber 019
\totalpages 28
\mathnet{http://mi.mathnet.ru/ipmp1871}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. N. Orlov, R. V. Pleshakov, “Programmnyi kompleks dlya modelirovaniya nestatsionarnykh neekvidistantnykh vremennykh ryadov”, Preprinty IPM im. M. V. Keldysha, 2017, 036, 15 pp.  mathnet
  • Препринты Института прикладной математики им. М. В. Келдыша РАН
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