Generalized Langevin equation for collective diffusion in colloidal suspensions

Using the formalism of the generalized Langevin equation and the procedure of contraction of the description, we derive the time-evolution equations of the collective variables of a colloidal suspension without hydrodynamics interactions at the so-called generalized-hydrodynamic level. In an additional contraction step, we derive the time-evolution equation for the dynamic structure factor of this system, which is shown to have the exact short-time dependence up to order (t/τB)4, where τB is the Brownian relaxation time. We discuss how this approach could be further extended to derive additional short-time exact conditions (Author)