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 superdiffusion, 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 analytical results for the variance of the anomalously rescaled limiting normal distributions.
Giampaolo Cristadoro, Thomas Gilbert, Marco Lenci, David P. Sanders (2014). Measuring logarithmic corrections to normal diffusion in infinite-horizon billiards. PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS, 90(2), 022106-1-022106-10 [10.1103/PhysRevE.90.022106].
Measuring logarithmic corrections to normal diffusion in infinite-horizon billiards
CRISTADORO, GIAMPAOLO;LENCI, MARCO;
2014
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 superdiffusion, 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 analytical results for the variance of the anomalously rescaled limiting normal distributions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.