  The impact of an electric field on the electron localization problem is
studied within the framework of a field-theoretic formulation. The
investigation shows that the impact of the electric field on the localization
corrections is governed by the interplay between two time scales, one set by
the electric field, and the other by the phase relaxation rate. At very low
temperatures the scaling of the conductivity is governed by the electric field.
In this regime the conductivity depends logarithmically on the field, and an
arbitrarily small electric field delocalizes the electron states. At higher
temperatures the behavior of the conductivity is governed by the temperature
scaling. In this regime the field has no impact on the observable leading
localization corrections.
