Abstract
We compute the dynamical structure factor S(q,tau) of an elastic medium where force dipoles appear at random in space and in time, due to `micro-collapses' of the structure. Various regimes are found, depending on the wave vector q and the collapse time. In an early time regime, the logarithm of the structure factor behaves as (q tau)^{3/2}, as predicted by Cipelletti et al. [1] using heuristic arguments. However, in an intermediate time regime we rather obtain a q tau)^{5/4} behaviour. Finally, the asymptotic long time regime is found to behave as q^{3/2} tau. We also give a plausible scenario for aging, in terms of a strain dependent energy barrier for micro-collapses. The relaxation time is found to grow with the age t_w, quasi-exponentially at first, and then as t_w^{4/5} with logarithmic corrections.
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