Off-Equilibrium Dynamics in a Singular Diffusion Model

We introduce a schematic nonlinear diffusion model where density fluctuations induce a rich out-of-equilibrium dynamics. The properties of the model are studied by numerical simulations and analytically in a mean field approximation. At low temperatures and high densities we find a long off-equilibrium glassy region, where the system evolves out of an initially pinned state showing aging and a slow decay of the autocorrelation as an enhanced power law, along with strong spatial heterogeneities and violation of the fluctuation-dissipation theorem.