Anomalous Diffusion in Infinite Horizon Billiards

Details Anomalous Diffusion in Infinite Horizon Billiards Anomalous Diffusion in Infinite Horizon Billiards

2002-10-28

arxiv.org/abs/nlin/0210062v1

Nonlinear Sciences

Cellular Automata and Lattice Gases

11 pages, 7 figures Submitted to Physical Review E

Scientific paper

10.1103/PhysRevE.67.021110

We consider the long time dependence for the moments of displacement < |r|^q > of infinite horizon billiards, given a bounded initial distribution of particles. For a variety of billiard models we find <|r|^q> ~ t^g(q) (up to factors of log t). The time exponent, g(q), is piecewise linear and equal to q/2 for q<2 and q-1 for q>2. We discuss the lack of dependence of this result on the initial distribution of particles and resolve apparent discrepancies between this time dependence and a prior result. The lack of dependence on initial distribution follows from a remarkable scaling result that we obtain for the time evolution of the distribution function of the angle of a particle's velocity vector.

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