Correlations for interacting Brownian particles. II

Abstract

The generalized Smoluchowski equation is used in a projection operator formalism to find an equation for the intermediate scattering function. Several different approximations are made to investigate the behavior of the intermediate scattering function for intermediate and long times. The generalized Stokes–Einstein relation is not given exactly by the formalism in the hydrodynamic regime. The hydrodynamic interaction is needed to produce a separation between the intermediate and long time scales in the small k limit.