Mean first-passage time for an overdamped particle in a disordered force field

We derive a rigorous expression for the mean first-passage time of an overdamped particle subject to a constant bias in a force field with quenched disorder. Depending on the statistics of the disorder, the disorder-averaged mean first-passage time can undergo a transition from an infinite value for small bias to a finite value for large bias. This corresponds to a depinning transition of the particle. We obtain exact values for the depinning threshold for Gaussian disorder and also for a class of piecewise constant random forces, which we call generalized kangaroo disorder. For Gaussian disorder, we investigate how the correlations of the random force field affect the average motion of the particle. For kangaroo disorder, we apply the general results for the depinning transition to two specific examples, viz., dichotomous disorder and random fractal disorder.