It is shown that the memory function of concentration fluctuations M̃(k, t), derived from the generalized Smoluchowski equation, is not a one-particle irreducible quantity. A new function M(k, t), which is one-particle irreducible, is derived and the relation between both functions is...

The N-particle Smoluchowski equation is solved exactly for a system of spherical Brownian particles interacting through hard-core potentials to first order in the volume concentration φ. The self-diffusion coefficient is found to be given by Ds = D0(1−2φ), where D0 is the free diffusion...