Anomalous dynamical light scattering in soft glassy gels

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.