Relaxation times for Hamiltonian systems

Details Relaxation times for Hamiltonian systems Relaxation times for Hamiltonian systems

2009-04-08

arxiv.org/abs/0904.1322v2

Commun. Math. Phys. 297 (2010), 427-445

Physics

Mathematical Physics

26 pages

Scientific paper

10.1007/s00220-010-1039-2

Usually, the relaxation times of a gas are estimated in the frame of the Boltzmann equation. In this paper, instead, we deal with the relaxation problem in the frame of the dynamical theory of Hamiltonian systems, in which the definition itself of a relaxation time is an open question. We introduce a lower bound for the relaxation time, and give a general theorem for estimating it. Then we give an application to a concrete model of an interacting gas, in which the lower bound turns out to be of the order of magnitude of the relaxation times observed in dilute gases.

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