Evidence for faster-than-t-1 decay of the velocity autocorrelation function in a 2D fluid

Abstract

We report very accurate simulations of the velocity autocorrelation function of a tagged particle in a two-dimensional lattice-gas cellular automaton. We observe, for the first time, that the hydrodynamic long-time tail of the velocity autocorrelation function decays significantly faster than t-1. The simulation results are compatible with the predictions of self-consistent mode-coupling theory. However, observation of a true (t √lnt )-1 decay, which is predicted by the latter theory as t→∞, would require simulations that are 15 orders of magnitude longer than is currently feasible.