Theoretical and Mathematical Physics

, Volume 191, Issue 1, pp 537–557 | Cite as

Dissipation effects in infinite-dimensional Hamiltonian systems

  • S. M. Saulin


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 finitedimensional 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).


Lagrange system system with infinite number of degrees of freedom final dynamics 


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© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia

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