Measuring logarithmic corrections to normal diffusion in infinite-horizon billiards
Statistical Mechanics
2014-10-21 v2 Dynamical Systems
Chaotic Dynamics
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.
Cite
@article{arxiv.1405.0975,
title = {Measuring logarithmic corrections to normal diffusion in infinite-horizon billiards},
author = {Giampaolo Cristadoro and Thomas Gilbert and Marco Lenci and David P. Sanders},
journal= {arXiv preprint arXiv:1405.0975},
year = {2014}
}
Comments
10 pages, 4 figures