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Randomized Hamiltonian Mechanics

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Abstract

Hamiltonian mechanics determined by time-dependent random Hamiltonian functions is called randomized Hamiltonian mechanics. The corresponding Hamiltonian systems are called random. Feynman formulas for random Hamiltonian systems are obtained. It is shown that these formulas describe solutions of a Hamiltonian equation whose Hamiltonian is the mean value of the random Hamiltonian function. Analogous results are obtained for random quantum systems (which are known to be infinite-dimensional random Hamiltonian systems). The random quantum Hamiltonians can be used to describe the so-called open quantum systems (which are part of some lager quantum systems).

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ACKNOWLEDGMENTS

This work was performed at the Laboratory of Infinite-Dimensional Analysis and Mathematical Physics of the Faculty of Mechanics and Mathematics of Lomonosov Moscow State University.

Funding

Smolyanov’s work was supported by a grant of MIPT visit professor and by Lomonosov Moscow State University within the framework of the grant “Fundamental Problems in Mathematics and Mechanics.”

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Authors and Affiliations

  1. Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 125047, Moscow, Russia

    Yu. N. Orlov

  2. Moscow Institute of Physics and Technology (National Research University), 141700, Dolgoprudnyi, Moscow oblast, Russia

    V. Zh. Sakbaev & O. G. Smolyanov

  3. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, 119991, Moscow, Russia

    O. G. Smolyanov

Authors
  1. Yu. N. Orlov
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  2. V. Zh. Sakbaev
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  3. O. G. Smolyanov
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Corresponding author

Correspondence to V. Zh. Sakbaev.

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Translated by I. Ruzanova

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Orlov, Y.N., Sakbaev, V.Z. & Smolyanov, O.G. Randomized Hamiltonian Mechanics. Dokl. Math. 99, 313–316 (2019). https://doi.org/10.1134/S1064562419030207

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  • DOI: https://doi.org/10.1134/S1064562419030207

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