Email this article Randomizes hamiltonian mechanics
- Authors: Orlov Y.N.1, Sakbaev V.Z.2, Smolyanov O.G.2,3
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Affiliations:
- Institute for Applied Mathematics of the Russian Academy of Sciences
- Moscow Institute of Physics and Technology
- Lomonosov Moscow State University
- Issue: Vol 486, No 6 (2019)
- Pages: 653-658
- Section: Mathematics
- URL: https://journals.eco-vector.com/0869-5652/article/view/14488
- DOI: https://doi.org/10.31857/S0869-56524866653-658
- ID: 14488
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Abstract
Randomized Hamiltonian mechanics is the Hamiltonian mechanics which is determined by a time-dependent random Hamiltonian function. Corresponding Hamiltonian system is called random Hamiltonian system. The Feynman formulas for the random Hamiltonian systems are obtained. This Feynman formulas describe the solutions of Hamilton equation whose Hamiltonian is the mean value of random Hamiltonian function. The analogs of the above results is obtained for a random quantum system (which is a random infinite dimensional Hamiltonian system). This random quantum Hamiltonians are the part of Hamiltonians of open quantum system.
About the authors
Yu. N. Orlov
Institute for Applied Mathematics of the Russian Academy of Sciences
Email: fumi2003@mail.ru
Russian Federation, 4, Miusskaya square, Moscow, 125047
V. Zh. Sakbaev
Moscow Institute of Physics and Technology
Author for correspondence.
Email: fumi2003@mail.ru
Russian Federation, 9, Institutskij, Dolgoprudny, Moscow region, 141701
O. G. Smolyanov
Moscow Institute of Physics and Technology; Lomonosov Moscow State University
Email: fumi2003@mail.ru
Russian Federation, 9, Institutskij, Dolgoprudny, Moscow region, 141701; 1, Leninskie gory, Moscow, 119991
References
- Богачев В.И., Смолянов O.Г. Действительный и функциональный анализ: университетский курс. М.; Ижевск: РХД, 2011.
- Козлов В.В., Смолянов О.Г. Гамильтонов подход к вторичному квантованию // ДАН. 2018. Т. 483. № 2. С. 138-142.
- Козлов В.В., Смолянов О.Г. Инвариантные и квазиинвариантные меры на бесконечномерных пространствах // ДАН. 2015. Т. 465. № 5. С. 527-531.
- Орлов Ю.Н., Сакбаев В.Ж., Смолянов О.Г. // Изв. РАН. Сер. мат. 2016. Т. 80. № 6. С. 141-172.
- Sakbaev V.Zh. Averaging of Random Walks and Shift-Invariant Measures on a Hilbert Space // Theoret. and Math. Phys. 2017. V. 191. № 3. P. 886-909.
- Козлов В.В., Смолянов О.Г. // ДАН. 2012. Т. 444. № 6. С. 607-611.
- Смолянов О.Г., Шавгулидзе Е.Т. Континуальные интегралы. М., 2015.
- Орлов Ю.Н., Сакбаев В.Ж., Смолянов О.Г. // ДАН. 2017. Т. 477. № 3. С. 271-275.
- Сакбаев В.Ж. О законе больших чисел для композиций независимых случайных полугрупп // Изв. вузов. Сер. мат. 2016. № 10. С. 72-76.
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