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arXiv · 1905.02267

Dynamical thermalization in time-dependent Billiards

M. Hansen·D. Ciro·I. L. Caldas·E. D. Leonel
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Abstract

Numerical experiments of the statistical evolution of an ensemble of non-interacting particles in a time-dependent billiard with inelastic collisions, reveals the existence of three statistical regimes for the evolution of the speeds ensemble, namely, diffusion plateau, normal growth/exponential decay and stagnation. These regimes are linked numerically to the transition from Gauss-like to Boltzmann-like speed distributions. Further, the different evolution regimes are obtained analytically through velocity-space diffusion analysis. From these calculations the asymptotic root mean square of speed, initial plateau, and the growth/decay rates for intermediate number of collisions are determined in terms of the system parameters. The analytical calculations match the numerical experiments and point to a dynamical mechanism for thermalization, where inelastic collisions and a high-dimensional phase space lead to a bounded diffusion in the velocity space towards a stationary distribution function with a kind of reservoir temperature determined by the boundary oscillation amplitude and the restitution coefficient.

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M. Hansen, D. Ciro, I. L. Caldas, E. D. Leonel. 2019-05-06. Dynamical thermalization in time-dependent Billiards. https://doi.org/10.1063/1.5120023

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