Velocity autocorrelation function in a four-dimensional lattice gas

Abstract

We report simulations of the velocity autocorrelation function (VACF) of a tagged particle in a four-dimensional lattice gas cellular automaton (LGCA). We observe a hydrodynamic tail in the VACF, which decays as t-‘, in agreement with the theoretical predictions. However, in a quantitative comparison, the simulations show that mode-coupling theory underestimates the amplitude of the hydrodynamic tail by (15 + 60)%. The artificial correlations, previously observed in the projected three-dimensional lattice gas model, are found to be absent in this truly 4D model.