Dynamical thermalization in time-dependent billiards

Numerical experiments of the statistical evolution of an ensemble of noninteracting particles in a time-dependent billiard with inelastic collisions reveals the existence of three statistical regimes for the evolution of the speed ensemble, namely, diffusion plateau, normal growth/exponential decay,...

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2019-10, Vol.29 (10), p.103122-103122
Main Authors: Hansen, Matheus, Ciro, David, Caldas, Iberê L., Leonel, Edson D.
Format: Article
Language:English
Subjects:
Decay rate
Diffusion rate
Distribution functions
Evolution
Inelastic collisions
Thermalization (energy absorption)
Time dependence
Velocity
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Summary:Numerical experiments of the statistical evolution of an ensemble of noninteracting particles in a time-dependent billiard with inelastic collisions reveals the existence of three statistical regimes for the evolution of the speed 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. Furthermore, 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 an 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 toward a stationary distribution function with a kind of “reservoir temperature” determined by the boundary oscillation amplitude and the restitution coefficient.
ISSN:1054-1500
1089-7682
DOI:10.1063/1.5120023