Dynamical properties of colloidal systems: II. Correlation- and response functions

For systems of interacting Brownian particles a Fokker-Planck equation is derived for the probability distribution function of the concentration fluctuations, using assumption of a Gaussian static distribution function. The drift- and the diffusion term are determined by static correlation functions. By this approach specific properties of different systems as e.g., suspensions of charged spherical particles or chain polymers are taken into account. Although the diffusion term is fluctuation dependent the properties of detailed balance and both fluctuation dissipation theorems are satisfied. Using the formalism of Martin, Siggia and Rose, Dyson- and vertex-equations for the two-particle correlation functions are derived. An explicit calculation of these functions, together with related quantities as the dynamic structure factor, and of the diffusion coefficients, is given in a mean-field approximation. The results are compared with several earlier theories, which were developed for specific systems.