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 $F_S\mathrm{}(k,t),$ given the effective interaction pair potential $u\left(r\right)\mathrm{}$ between colloidal particles, and the corresponding equilibrium static structural properties. This theory is build upon the exact results for $F(k,t)\mathrm{}$ and $F_S\mathrm{}(k,t)\mathrm{}$ 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 $F(k,t)\mathrm{}$ and $F_S\mathrm{}(k,t)\mathrm{}$ through their respective memory functions, and a closure relation between these memory functions and the time-dependent friction function $\Delta \zeta \mathrm{}\left(t\right).$ 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 $F(k,t)\mathrm{}$ in a wide range of conditions, including strongly correlated systems, at the longest times available from our computer simulations.

• Received 21 February 2001

DOI:https://doi.org/10.1103/PhysRevE.64.066114