Decay of the Velocity Autocorrelation Function

Abstract

Molecular-dynamic studies of the behavior of the diffusion coefficient after a long time $s$ have shown that the velocity autocorrelation function decays as ${s}^{\ensuremath{-}1}$ for hard disks and as ${s}^{\ensuremath{-}\frac{3}{2}}$ 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 ${(\ensuremath{\eta}s)}^{\ensuremath{-}\frac{d}{2}}$, where $\ensuremath{\eta}$ 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.