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DC electric field effect on the anomalous exponent of the hopping conductionin the disorder model is investigated. First, we explain the model and derivean analytical expression of the effective waiting time for the general case. Weshow that the exponent depends on the external field. Then we focus on aone-dimensional system in order to illustrate the features of the anomalousexponent. We derive approximate expressions of the anomalous exponent of thesystem analytically. For the case of a weak field, the anomalous exponent isconsistent with that of diffusive systems. This is consistent with thetreatments of Barkai et al. [Phys. Rev. E {\bf 63}, 046118 (2001)] and ourresult supports their theory. On the other hand, for the case of a strong fieldand a strong disorder, the time evolution of the exponent clearly differs fromthat in the weak field. The exponent is consistent with the well-knownexpression of the anomalous exponent in the Multiple Trapping Model atmesoscopic time scales. In the long time limit, a transition of the anomalousexponent to the same value of the weak field occurs. For the case of a strongfield and a weak disorder, the exponent is equal to 1 and thus the diffusion isnormal. These findings are verified by the Monte Carlo simulation.

DC electric field effect on the anomalous exponent of the hopping conduction in the one-dimensional disorder model