Anomalous diffusion in infinite horizon billiards

We consider the long time dependence for the moments of displacement of infinite horizon billiards, given a bounded initial distribution of particles. For a variety of billiard models we find approximately t(gamma(q)) (up to factors of ln t). The time exponent, gamma(q), is piecewise linear and eq...

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Bibliographic Details
Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2003-02, Vol.67 (2 Pt 1), p.021110-021110
Main Authors: Armstead, Douglas N, Hunt, Brian R, Ott, Edward
Format: Article
Language:English
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Summary:We consider the long time dependence for the moments of displacement of infinite horizon billiards, given a bounded initial distribution of particles. For a variety of billiard models we find approximately t(gamma(q)) (up to factors of ln t). The time exponent, gamma(q), is piecewise linear and equal to q/2 for q2. 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.
ISSN:1539-3755
DOI:10.1103/PhysRevE.67.021110