Dynamical thermalization in time-dependent billiards

Autor(es)

Hansen, Matheus ^[1] ; Ciro, David ^[2] ; Caldas, Ibere L. ^[1] ; Leonel, Edson D. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Fis, BR-05508090 Sao Paulo, SP - Brazil

^[2] Univ Sao Paulo, Inst Astron Geofis & Ciencias Atmosfer, BR-05508090 Sao Paulo, SP - Brazil

^[3] UNESP, Dept Fis, BR-13506900 Rio Claro, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Chaos; v. 29, n. 10 OCT 2019.
• Citações Web of Science: 0

Resumo

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. Published under license by AIP Publishing. (AU)

• Processo FAPESP: 18/03211-6 - Dinâmica não linear
• Beneficiário: Iberê Luiz Caldas
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 17/14414-2 - Investigação de escala em sistemas dinâmicos
• Beneficiário: Edson Denis Leonel
• Modalidade de apoio: Auxílio à Pesquisa - Regular