Volume 121, Number 6, March 2018
|Number of page(s)||7|
|Published online||17 May 2018|
Explaining a changeover from normal to super diffusion in time-dependent billiards
1 Instituto de Física, Universidade de São Paulo - São Paulo - CEP 05314-970 SP, Brazil
2 Instituto de Física, Universidade Federal do Paraná - Curitiba - CEP 81531-990 PR, Brazil
3 Departamento de Física, UNESP - Rio Claro - CEP 13506-900 SP, Brazil
Received: 29 January 2018
Accepted: 25 April 2018
The changeover from normal to super diffusion in time-dependent billiards is explained analytically. The unlimited energy growth for an ensemble of bouncing particles in time-dependent billiards is obtained by means of a two-dimensional mapping of the first and second moments of the speed distribution function. We prove that, for low initial speeds the average speed of the ensemble grows with exponent of the number of collisions with the boundary, therefore exhibiting normal diffusion. Eventually, this regime changes to a faster growth characterized by an exponent corresponding to super diffusion. For larger initial energies, the temporary symmetry in the diffusion of speeds explains an initial plateau of the average speed.
PACS: 05.45.-a – Nonlinear dynamics and chaos / 05.45.Pq – Numerical simulations of chaotic systems / 05.40.Fb – Random walks and Levy flights
© EPLA, 2018
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