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arXiv · 1405.0975

Measuring logarithmic corrections to normal diffusion in infinite-horizon billiards

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

We perform numerical measurements of the moments of the position of a tracer particle in a two-dimensional periodic billiard model (Lorentz gas) with infinite corridors. This model is known to exhibit a weak form of super-diffusion, in the sense that there is a logarithmic correction to the linear growth in time of the mean-squared displacement. We show numerically that this expected asymptotic behavior is easily overwhelmed by the subleading linear growth throughout the time-range accessible to numerical simulations. We compare our simulations to the known analytical results for the variance of the anomalously-rescaled limiting normal distributions.

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Giampaolo Cristadoro, Thomas Gilbert, Marco Lenci, David P. Sanders. 2014-05-05. Measuring logarithmic corrections to normal diffusion in infinite-horizon billiards. https://doi.org/10.1103/physreve.90.022106

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