Long-time tails in two-dimensional fluids by molecular dynamics

We report on molecular dynamics simulation of long-time tails in the velocity and stress autocorrelation functions of a dense two-dimensional fluid. Large systems of the order of hundred thousand particles have been investigated, performing canonical averages over an ensemble of trajectories generated on a parallel computer. We find the well-known t−1 decay for the velocity autocorrelation function at two different densities of the fluid, together with a faster than linear time dependence for the mean-square displacement at long times. Although there are indications of an asymptotically faster decay, the data are not precise enough to discriminate whether the decay is in agreement with the (tlnt)−1 prediction of consistent mode-coupling theory or it is due to finite size effects. No evidence, within the statistical errors, is found for a long-time tail in the stress autocorrelation function. This finding is in agreement with recent NEMD results [Hoover et al., Phys. Rev. E 51 (1995) 273; Gravina et al., Phys. Rev. E 52 (1995) 6123], who find an analytical dependence of the shear viscosity upon the shear rate with no evidence for divergence in the Green-Kubo value.