Simulation of diffusion in a two-dimensional lattice-gas cellular automaton: A test of mode-coupling theory

Abstract

We compute the velocity autocorrelation function of a tagged particle in a two-dimensional lattice-gas cellular automaton using a method that is about a million times more efficient than existing techniques. A ${\mathrm{t}}^{\mathrm{-}1}$ algebraic tail in the tagged-particle velocity autocorrelation function is clearly observed. The amplitude of this tail is predicted to within a few percent by a lattice-gas version of mode-coupling theory. The magnitude of logarithmic corrections to the ${\mathrm{t}}^{\mathrm{-}1}$ tail is much smaller than expected for continuous fluids.