  DC electric field effect on the anomalous exponent of the hopping conduction
in the disorder model is investigated. First, we explain the model and derive
an analytical expression of the effective waiting time for the general case. We
show that the exponent depends on the external field. Then we focus on a
one-dimensional system in order to illustrate the features of the anomalous
exponent. We derive approximate expressions of the anomalous exponent of the
system analytically. For the case of a weak field, the anomalous exponent is
consistent with that of diffusive systems. This is consistent with the
treatments of Barkai et al. [Phys. Rev. E {\bf 63}, 046118 (2001)] and our
result supports their theory. On the other hand, for the case of a strong field
and a strong disorder, the time evolution of the exponent clearly differs from
that in the weak field. The exponent is consistent with the well-known
expression of the anomalous exponent in the Multiple Trapping Model at
mesoscopic time scales. In the long time limit, a transition of the anomalous
exponent to the same value of the weak field occurs. For the case of a strong
field and a weak disorder, the exponent is equal to 1 and thus the diffusion is
normal. These findings are verified by the Monte Carlo simulation.
