Death and Resurrection of a Current by Disorder,Interaction or Periodic Driving

We present several models of biased transport on (random) comb-like structures and on percolating backbones, that allow full mathematical control. We show how power-law corrections in the distribution of trap sizes may lead to a discontinuity in the current-field characteristic: the current jumps to zero when the driving exceeds a threshold. The current may resurrect when the field is modulated in time, also discontinuously: a little shaking enables the current to jump up. Finally, exclusion between particles postpones or even prevents the current from dying, while attraction such as modeled in zero range processes may expedite it.