Self-consistent generalized Langevin equation for colloid dynamics

We present a general self-consistent theory of colloid dynamics which, for a system without hydrodynamic interactions. allows us to calculate F(k,t), and its self-diffusion counterpart F-S(k t), given the effective interaction pair potential u(r) between colloidal particles, and the corresponding equilibrium static structural properties. This theory is build upon the exact results for F(k,t) and F-S(k,t) in terms of a hierarchy of memory functions. derived from the application of the generalized Langevin equation formalism, plus the proposal of Vineyard-like connections between F(k,t) and F-S(k,t) through their respective memory functions, and a closure relation between these memory functions and the time-dependent friction function Delta zeta (t). As an illustrative application, we present and analyze a selection of numerical results of this theory in the short- and intermediate-time regimes, as applied to a two-dimensional repulsive Yukawa Brownian fluid. For this system. we find that our theory accurately describes the dynamic properties contained in F(k,t) in a wide range of conditions, including strongly correlated systems, at the longest times available from our computer simulations.