Decay of the Velocity Autocorrelation Function

Molecular-dynamic studies of the behavior of the diffusion coefficient after a long time s have shown that the velocity autocorrelation function decays as s^-1 for hard disks and as s^{-3 / 2} for hard spheres, at least at intermediate fluid densities. A hydrodynamic similarity solution of the decay in velocity of an initially moving volume element in an otherwise stationary compressible viscous fluid agrees with a decay of (ηs)^{-d / 2}, where η is the viscosity and d is the dimensionality of the system. The slow decay, which would lead to a divergent diffusion coefficient in two dimensions, is caused by a vortex flow pattern which has been quantitatively compared for the hydrodynamic and molecular-dynamic calculations.