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...

The relaxation of density fluctuations is characterized by the experimentally accessible dynamic structure factor S(k,t). Whereas the short-time behaviour of this quantity is well understood, its long-time characteristics are more difficult to determine since memory effects become important...