Velocity auto-correlation functions in a 2d lattice Lorentz gas: Comparison of theory and computer simulation

Abstract

We present Monte Carlo simulations of the hopping motion of a particle in a two-dimensional square lattice Lorentz gas. The long time tail of the velocity autocorrelation function in this system is computed with an accuracy of 1:5X10 5. At low densities the Monte Carlo results agree quantitatively at all times with the predictions of kinetic theory. The theoretical predictions for the second order density corrections to the diffusion constant and the asymptotic behavior of the velocity autocorrelation function are found to be compatible with the Monte Carlo results. To our knowledge, this is the first example of quantitative agreement between kinetic theory and computer simulation for the long time tail of the velocity ACF in a Lorentz gas.