Crossover behaviour in one-dimensional disordered systems in external electric fields

A method formulated by Felderhof (1986), is extended to the treatment of the conduction problem of disordered systems in external electric fields. The authors apply it to calculate averages and fluctuations for two models: model A consists of a sequence of delta -barriers with random position and amplitude, and model B of a sequence of square barriers with random position, height and width. The two models have qualitatively different behaviours, which can be explained by the fact that the square barriers are bounded. They calculate the ratios of incident to transmitted energy and of incident to transmitted current, which are expressed in terms of the scattering coefficients. The electric field produces a power-law dependence of the averages of those quantities, as opposed to the exponential dependence found for zero field. Further, in model A, there are two qualitatively different regimes at finite fields. Two different critical fields defined in terms of the behaviour of the transmission coefficient have been proposed in the literature. The study of the transmission of energy and current allows the authors to give them a well defined physical interpretation, as the fields at which the energy and current transmissions, respectively, switch from tending to zero to tending to infinity. In the zero-field case, the fluctuations are known to dominate exponentially over the averages. In the presence of an electric field, they find that in model A the fluctuations still dominate, but only algebraically, whereas in model B the relative fluctuations saturate to a constant.