Interface motion in a random medium: mean field theory

The motion of an interface in a random medium is studied by a stochastic differential equation, with terms corresponding to an external driving field, interface elasticity, and a (quenched) random background field. For driving fields F smaller than a threshold field F c the interface is pinned, i.e. the velocity v=0. F c and v are calculated within a discretized mean field theory. For F close to the threshold field the author finds that v grows linearly with F-F c . Simulations of the mean field equations are in agreement with the analytical results.