It is well known that particles can get trapped by randomly placed obstacles when they are pushed too much. We present a model where the current in a disordered medium dies at a large external field, but is reborn when the activity is increased. By activity we mean the time-variation of the external driving at a constant time-averaged field. A different interpretation of the resurgence of the current is that the particles are capable of taking an infinite sequence of potential barriers via a mechanism similar to stochastic resonance. We add a discussion regarding the role of shaking in processes of relaxation.
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