On the use of separation of scales in the solution of hopping transport problems

In the paper we show how separation of scales can be used for the calculation of the critical hopping length and its dispersion in the whole range of frequencies. The separation of scales that we use is already present in the pair approximation of Pollak and Geballe. In fact, with decreasing frequency the hopping length increases compared with the localization length. If we use this fact, we obtain a general method that can be applied to systems with and without inelastic scattering both close to and far from equilibrium. We demonstrate the applicability of the method for several examples and discuss the relation of the method to our previous effective-medium method.