Memory function approach to the dynamics of interacting Brownian particles

We investigate some of the dynamic properties of diffusing particles described by a many-body Smoluchowski equation. The dynamic structure factor is expressed in terms of a memory function which is evaluated in the cases of i) weak interaction and ii) low particle density, but arbitrary interaction. A one-dimensional system with a hard-core pair potential is treated explicitly. Furthermore, by including a periodic single-particle potential, a model is obtained which has relevance to superionic conductors. For this case we discuss how the frequency-dependent conductivity is affected by the correlated motion of particles.