Occurrence of normal and anomalous diffusion in polygonal billiard channels

Details Occurrence of normal and anomalous diffusion in polygonal billiard channels Occurrence of normal and anomalous diffusion in polygonal billiard channels

2005-10-25

arxiv.org/abs/cond-mat/0510654v2

Phys. Rev. E 73, 026205 (2006)

Physics

Condensed Matter

Statistical Mechanics

9 pages, 15 figures. Revised after referee reports: redrawn figures, additional comments. Some higher quality figures availabl

Scientific paper

10.1103/PhysRevE.73.026205

From extensive numerical simulations, we find that periodic polygonal billiard channels with angles which are irrational multiples of pi generically exhibit normal diffusion (linear growth of the mean squared displacement) when they have a finite horizon, i.e. when no particle can travel arbitrarily far without colliding. For the infinite horizon case we present numerical tests showing that the mean squared displacement instead grows asymptotically as t log t. When the unit cell contains accessible parallel scatterers, however, we always find anomalous super-diffusion, i.e. power-law growth with an exponent larger than 1. This behavior cannot be accounted for quantitatively by a simple continuous-time random walk model. Instead, we argue that anomalous diffusion correlates with the existence of families of propagating periodic orbits. Finally we show that when a configuration with parallel scatterers is approached there is a crossover from normal to anomalous diffusion, with the diffusion coefficient exhibiting a power-law divergence.

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