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This article is cited in 1 scientific paper (total in 1 paper)
Dissipation effects in infinite-dimensional Hamiltonian systems.
S. M. Saulin Lomonosov Moscow State University, Moscow, Russia
Abstract:
We show that the potential coupling of classical mechanical systems (an oscillator and a heat bath), one of which (the heat bath) is linear and infinite-dimensional, can provoke energy dissipation in a finite-dimensional subsystem (the oscillator). Under natural assumptions, the final dynamics of an oscillator thus reduces to a tendency toward equilibrium. D. V. Treschev previously obtained results concerning the dynamics of an oscillator with one degree of freedom and a quadratic or (under some additional assumptions) polynomial potential. Later, A. V. Dymov considered the case of a linear oscillator with an arbitrary (finite) number of degrees of freedom. We generalize these results to the case of a heat bath (consisting of several components) and a multidimensional oscillator (either linear or nonlinear).
Keywords:
Lagrange system, system with infinite number of degrees of freedom,
final dynamics
DOI:
https://doi.org/10.4213/tmf9062
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English version:
Theoretical and Mathematical Physics, 2017, 191:1, 537–557
Bibliographic databases:
Received: 07.10.2015 Revised: 28.03.2016
Citation:
S. M. Saulin, “Dissipation effects in infinite-dimensional Hamiltonian systems.”, TMF, 191:1 (2017), 78–99; Theoret. and Math. Phys., 191:1 (2017), 537–557
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/tmf9062https://doi.org/10.4213/tmf9062 http://mi.mathnet.ru/eng/tmf/v191/i1/p78
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This publication is cited in the following articles:
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A. V. Dymov, “Asymptotic behavior of a network of oscillators coupled to thermostats of finite energy”, Russ. J. Math. Phys., 25:2 (2018), 183–199
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