Statistical description of interacting Brownian particles

Abstract

An alternative approach to the statistical description of interacting Brownian particles based on the microscopic Langevin equation is presented. Applying the formalism of microscopic phase space densities a stochastic form of the well-known BBGKY-hierarchy for reduced distribution functions in phase space is produced. Special attention is paid to both the particle interaction and the hydrodynamic interaction between the brownons considered on the two-particle level. Assuming fast momentum relaxation we find a hierarchy of diffusion-like equations in configuration space on the Smoluchowski time scale for reduced particle densities and corresponding particle flows. These equations are an extension of the Ebeling-Falkenhagen diffusion equations with respect to hydrodynamics. Finally we formulate the direct correlation force formalism for inhomogeneous non-equilibrium systems in order to break off the hierarchy of coupled equations. Examples for closure relations are given.