%0 Journal Article
%T Measuring logarithmic corrections to normal diffusion in infinite-horizon billiards
%A Giampaolo Cristadoro
%A Thomas Gilbert
%A Marco Lenci
%A David P. Sanders
%J Mathematics
%D 2014
%I arXiv
%R 10.1103/PhysRevE.90.022106
%X 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.
%U http://arxiv.org/abs/1405.0975v2