Dynamics of surface roughening with quenched disorder

We study the dynamical exponent z for the directed percolation depinning (DPD) class of models for surface roughening in the presence of quenched disorder. We argue that z for d + 1 dimensions is equal to the exponent d min characterizing the shortest path between two sites in an isotropic percolation cluster in d dimensions. To test the argument, we perform simulations and calculate z for DPD, and d min for percolation, from d = 1 to d = 6.First author draf