Force Relaxation in the q-Model for Granular Media

We study the relaxation of force distributions in the q-model, assuming a uniform q-distribution. We show that diffusion of correlations makes this relaxation very slow. On a d-dimensional lattice, the asymptotic state is approached as l ^(1–d)/2, where l is the number of layers from the top. Furthermore, we derive asymptotic modes of decay, along which an arbitrary short-range correlated initial distribution will decay towards the stationary state.