Hopping contribution to the AC conductivity in composite media in the presence of a biased electric field

The frequency-dependent hopping conductivity is calculated within the effective medium approximation for a one-dimensional disordered chain as well as for a cubic percolating network in the presence of a biased electric field. In this biased case, there exists a drift-conducting region at low frequencies crossing over to the diffusive behavior at higher frequencies. In the three-dimensional percolation model, one obtains an additional anomalous diffusion region corresponding to short-time diffusive behavior on percolating clusters. Explicit expressions for the conductivity in various regions are presented