EVIDENCE FOR UNIVERSAL ASYMPTOTIC DECAY OF VELOCITY FLUCTUATIONS IN LORENTZ GASES

We report a numerical study of the velocity autocorrelation function (VACF) in a lattice model of a Lorentz gas with scatterers that have a finite excluded volume. We observe that, at scatterer densities below the percolation threshold, the VACF decays as t-2. As the percolation density is approached, the onset of the asymptotic t-2 -decay shifts to increasingly longer times but the asymptotic exponent itself remains unaffected. Such behaviour appears to contrast with that of off-lattice Lorentz-gas simulations, where the asymptotic exponent was found to vary strongly with scatterer density. Our findings are, however, consistent with percolation-related crossover scenarios proposed by Gotze et al. (Phys. Rev. A, 23 (1981) 2634) and van Velzen et al. (Physica A, 154 (1988) 34).