Generalized hydrodynamics of systems of Brownian particles

A generalized hydrodynamic theory is developed for systems of interacting Brownian particles on the basis of a Fokker-Planck equation. General results are derived for correlation functions, frequency- and wave-vector dependent transport coefficients. Explicit expressions for moments, cumulants and the hydrodynamic limits of the transport coefficients are given. For the special cases of overdamped systems with and without hydrodynamic interaction the general results are simplified. As an example for the application of this approach the system of charged spherical polystyrene spheres in aqueous solution is treated in detail. The generalized transport functions are evaluated in mode-mode coupling approximation and detailed numerical results are presented for various collective and single-particle properties. Finally, the relationship to a corresponding Smoluchowski approach is discussed.