Driven classical diffusion with strong correlated disorder
  We analyze one-dimensional motion of an overdamped classical particle in the presence of external disorder potential and an arbitrary driving force F. In thermodynamical limit the effective force-dependent mobility mu(F) is self-averaging, although the required system size may be exponentially large for strong disorder. We calculate the mobility mu(F) exactly, generalizing the known results in linear response (weak driving force) and the perturbation theory in powers of the disorder amplitude. For a strong disorder potential with power-law correlations we identify a non-linear regime with a prominent power-law dependence of the logarithm of mu(F) on the driving force. 
Leonid P. Pryadko and Jing-Xian Lin