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On the Limiting Markov Process of Energy Exchanges in a Rarely Interacting Ball-Piston Gas

par Bálint, Péter;Gilbert, Thomas ;Nándori, Péter;Szász, Domokos;Tóth, Imre Péter
Référence Journal of statistical physics, page (1-23)
Publication Publié, 2016

Article révisé par les pairs

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Résumé :

We analyse the process of energy exchanges generated by the elastic collisions between a point-particle, confined to a two-dimensional cell with convex boundaries, and a `piston', i.e. a line-segment, which moves back and forth along a one-dimensional interval partially intersecting the cell. This model can be considered as the elementary building block of a spatially extended high-dimensional billiard modeling heat transport in a class of hybrid materials exhibiting the kinetics of gases and spatial structure of solids. Using heuristic arguments and numerical analysis, we argue that, in a regime of rare interactions, the billiard process converges to a Markov jump process for the energy exchanges and obtain the expression of its generator.