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Vineyard-like approximations for colloid dynamics

In this paper we propose a hierarchy of higher-order Vineyard-like approximations for colloidal systems. These consist of approximate expressions for the intermediate scattering function F(k,t) in terms of the self-intermediate scattering function F(s)(k,t) (or some memory function associated with it), and of other static structural properties of the suspension. In order to assess the accuracy of the proposed approximations, we perform Brownian dynamics simulations in a simple model system (a two-dimensional Yukawa Brownian fluid), in which we determine F(k,t), F(s)(k,t), and the required static structural properties. We study proposals for "second-order" and "third-order" Vineyard-like approximations. We find that the detailed structure of the relationship between the corresponding collective and self-memory functions turns out to be most important, as quantified by our simulation results.