Hydrodynamic Theory of the Velocity Correlation Function

The velocity correlation function of an atom in a simple liquid is calculated using a frequency-dependent version of the Stokes-Einstein formula. Stokes's law for the frictional force on a moving sphere is generalized to arbitrary frequency, compressibility, and visco-elasticity, with arbitrary slip of the fluid on the surface of the sphere. This frequency-dependent friction coefficient is then used in a generalized Stokes-Einstein formula, and the velocity correlation function is found by Fourier inversion. By using physically reasonable values for viscoelastic parameters, good agreement is obtained with the velocity correlation function determined by Rahman using computer experiments.