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arXiv · 1408.0349

Machta-Zwanzig regime of anomalous diffusion in infinite-horizon billiards

Giampaolo Cristadoro·Thomas Gilbert·Marco Lenci·David P. Sanders
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Abstract

We study diffusion on a periodic billiard table with infinite horizon in the limit of narrow corridors. An effective trapping mechanism emerges according to which the process can be modeled by a L\'evy walk combining exponentially-distributed trapping times with free propagation along paths whose precise probabilities we compute. This description yields an approximation of the mean squared displacement of infinite-horizon billiards in terms of two transport coefficients which generalizes to this anomalous regime the Machta-Zwanzig approximation of normal diffusion in finite-horizon billiards [Phys. Rev. Lett. 50, 1959 (1983)].

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BibTeXRIS

Giampaolo Cristadoro, Thomas Gilbert, Marco Lenci, David P. Sanders. 2014-08-02. Machta-Zwanzig regime of anomalous diffusion in infinite-horizon billiards. https://doi.org/10.1103/physreve.90.050102

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