Velocity autocorrelation function of a Brownian particle

In this article, we present molecular dynamics study of the velocity autocorrelation function (VACF) of a Brownian particle. We compare the results of the simulation with the exact analytic predictions for a compressible fluid from [6] and an approximate result combining the predictions from hydrodynamics at short and long times. The physical quantities which determine the decay were determined from separate bulk simulations of the Lennard-Jones fluid at the same thermodynamic state point.We observe that the long-time regime of the VACF compares well the predictions from the macroscopic hydrodynamics, but the intermediate decay is sensitive to the viscoelastic nature of the solvent.