Long-time tails of the velocity autocorrelation function in two- and three-dimensional lattice-gas cellular automata: A test of mode-coupling theory

We report simulations of the velocity autocorrelation function (VACF) of a tagged particle in two- and three-dimensional lattice-gas cellular automata, using a new technique that is about a million times more efficient than the conventional techniques. The simulations clearly show the algebraic ${\mathit{t}}^{\mathrm{-}\mathit{D}/2\mathrm{}}$ tail of the VACF. We compare the observed long-time tail with the predictions of mode-coupling theory. In three dimensions, the amplitude of this tail is found to agree within the (small) statistical error with these predictions. In two dimensions small but significant deviations from mode-coupling theory of up to 5% are observed.