Universal Self-Diffusion and Subdiffusion in Colloids at Freezing

We provide a theoretical explanation for the observed quasiuniversality of the ratio of the longtime to short-time self-diffusion coefficients in colloidal liquids at freezing. We also predict that the mean-squared displacement at freezing, plotted against a suitably renormalized time, yields a universal curve showing a short-time subdiffusive regime and a long-time caged diffusion. We obtain $C_s(k,t)$, the intermediate scattering function, for all (k,t) and show that it implies strong non-Gaussian behavior in the probability distribution of the single-particle displacement at short times