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Relaxation Times for Hamiltonian Systems

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Abstract

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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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Milano, Via Saldini 50, 20133, Milano, Italy

    Alberto Mario Maiocchi & Andrea Carati

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  1. Alberto Mario Maiocchi
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  2. Andrea Carati
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Correspondence to Alberto Mario Maiocchi.

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Communicated by G. Gallavotti

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Maiocchi, A.M., Carati, A. Relaxation Times for Hamiltonian Systems. Commun. Math. Phys. 297, 427–445 (2010). https://doi.org/10.1007/s00220-010-1039-2

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  • DOI: https://doi.org/10.1007/s00220-010-1039-2

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