Explaining a changeover from normal to super diffusion in time-dependent billiards

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 distributi...

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Bibliographic Details
Published in:Europhysics letters 2018-03, Vol.121 (6), p.60003
Main Authors: Hansen, Matheus, Ciro, David, Caldas, Iberê L., Leonel, Edson D.
Format: Article
Language:English
Subjects:
05.40.Fb
05.45.-a
05.45.Pq
Diffusion rate
Distribution functions
Energy distribution
Time dependence
Two dimensional analysis
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Summary: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.
ISSN:0295-5075
1286-4854
DOI:10.1209/0295-5075/121/60003