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 overd amped particle subject to a constant bias in a force field with quenched di sorder. Depending on the statistics of the disorder, the disorder-averaged mean first-passage time can undergo a transition from an infinite Value far small bias to a finite value for large bias. This corresponds to a depinni ng transition of the particle. We obtain exact values for the depinning thr eshold for Gaussian disorder and also for a class of piecewise constant ran dom forces, which we call generalized kangaroo disorder. For Gaussian disor der, we investigate how the correlations of the random force field affect t he average motion of the particle. For kangaroo disorder, we apply the gene ral results for the depinning transition to two specific examples, viz., di chotomous disorder and random fractal disorder.