Frequency dependence of hopping conductivity of a one-dimensional system in the framework of the effective medium technique

The technique of the effective medium for calculation of the frequency dependence of conductivity in the hopping regime has been developed for the systems with random disposition of points in the space and for jumps between near neighbours as applied to one-dimensional systems. This technique allows to calculate the electric conductivity dependence on frequency within the whole frequency range in the framework of the unified approach. In all known limiting cases (low and high frequences, models of cut grid) the results are in good agreement with earlier data and also with computer calculations. The limits of application of two-point and multiplet models are discussed