Macroscopic approach to the theory of one-dimensional disordered conductors

Abstract

We propose the following requirements that have to be satisfied by an ensemble of transfer matrices associated with disordered one-dimensional conductors of macroscopic length l: (1) flux conservation, (2) time-reversal invariance, (3) the appropriate combination law when two wires are put together, and (4) for samples of very small l, the average resistance is required to depend linearly in l and the statistical distribution is selected on the basis of a maximum information-entropy criterion. The present approach gives, for the resistance, results that are consistent with those of microscopic calculations.