Breakdown of linear response theory in one-dimensional classical diffusion problems (charge transport)

Abstract

The authors examine charge transport in one-dimensional disordered systems which can be described by a master equation. The diffusivity is not a meaningful quantity to study because in general the linear response assumption does not hold. The authors formulate a scaling theory for the current and examine three classes of distribution functions which lead to localised, quasilocalised and delocalised behaviour in the long-time limit. Whereas linear response is valid as t to infinity for delocalised motion (finite DC conductivity), interesting anomalies are found and predicted for the electric field dependence of the current in the first two situations.