Abstract
We use large-scale computer simulations to explore the non-equilibrium aging dynamics in a microscopic model for colloidal gels. We find that gelation resulting from a kinetically-arrested phase separation is accompanied by `anomalous' particle dynamics revealed by superdiffusive particle motion and compressed exponential relaxation of time correlation functions. Spatio-temporal analysis of the dynamics reveals intermittent heterogeneities producing spatial correlations over extremely large length scales. Our study is the first microscopically-resolved model reproducing all features of the spontaneous aging dynamics observed experimentally in soft materials.