Randomized Hamiltonian Mechanics
- Authors: Orlov Y.N.1, Sakbaev V.Z.2, Smolyanov O.G.2,3
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Affiliations:
- Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences
- Moscow Institute of Physics and Technology (National Research University)
- Faculty of Mechanics and Mathematics, Lomonosov Moscow State University
- Issue: Vol 99, No 3 (2019)
- Pages: 313-316
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225684
- DOI: https://doi.org/10.1134/S1064562419030207
- ID: 225684
Cite item
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).
About the authors
Yu. N. Orlov
Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences
Email: fumi2003@mail.ru
Russian Federation, Moscow,
125047
V. Zh. Sakbaev
Moscow Institute of Physics and Technology (National Research University)
Author for correspondence.
Email: fumi2003@mail.ru
Russian Federation, Dolgoprudnyi, Moscow oblast, 141700
O. G. Smolyanov
Moscow Institute of Physics and Technology (National Research University); Faculty of Mechanics and Mathematics, Lomonosov Moscow State University
Email: fumi2003@mail.ru
Russian Federation, Dolgoprudnyi, Moscow oblast, 141700; Moscow, 119991