Long-time tail of the velocity-autocorrelation function in the Lorentz lattice gas.

Abstract

We present numerical results for the first and second moments of the distribution of collision times of the d=2 Lorentz lattice gas with density q in the range 0.2\char21{}0.8. They are used to calculate the mean-square displacement 〈${\mathit{X}}^{2}$(${\mathit{T}}_{\mathit{k}}$)〉 as a function of the number of collisions k. Using an asymptotic relation the mean-square displacement 〈${\mathit{X}}^{2}$(t)〉 as function of time is obtained from the latter quantity. As a result we are able to predict in an accurate numerical way the long-time tail of the velocity-autocorrelation function.