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TMF, 2017, Volume 191, Number 1, Pages 78–99 (Mi tmf9062)  

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

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-03747
This research was supported by the Russian Foundation for Basic Research (Grant No. 15-01-03747).


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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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