Universal self-diffusion and subdiffusion in colloids at freezing

We provide a theoretical explanation for the observed quasiuniversality of the ratio of the long-time to short-time self-diffusion coefficients in the 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 ${\mathit{C}}_{\mathit{s}}$(k,t), the intermediate scattering function, for all (k,t) and show that it implies strong non-Gaussian behavior in the probablity distribution of the single-particle displacement at short times.