Cluster expansion of the diffusion kernel of a suspension of interacting Brownian particles

We derive a cluster expansion for the wavenumber- and frequency-dependent diffusion coefficient of a suspension of interacting Brownian particles. The diffusion coefficient is expressed in terms of evolution operators of progressively increasing complexity. We expect that at low frequency only the low-order terms contribute effectively. We propose an expression for the wavenumber-dependent collective diffusion coefficient at zero frequency which involves the dynamics of only two particles. A similar expression is obtained for the wave-number dependent self-diffusion coefficient.