Explaining a changeover from normal to super diffusion in time-dependent billiards. (17th May 2018)

• Record Type: Journal Article
• Authors: Hansen, Matheus; Ciro, David; Caldas, Iberê L.; Leonel, Edson D.
• Is Part Of: Europhysics letters. Volume 121:Number 6(2018:Mar.)
• Publication Date: 2018-05-17
• Subjects: 05.45.-a -- 05.45.Pq -- 05.40.Fb; Physics -- Periodicals; Electronic journals; 530.05
• DOI: 10.1209/0295-5075/121/60003
• Languages: English
• ISSNs: 0295-5075

Abstract

Abstract: 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.