Phase-shift randomness in one-dimensional disordered conductors in the quasi-metallic domain

Abstract

An invariant imbedding method yields exact analytical results for the distribution of the phase theta (L) of the reflection amplitude and for low-order resistance moments (pⁿ) for a disordered conductor of length L in the quasi-metallic regime L<c (L_c=localisation length). The distribution of theta is significantly non-uniform only for sufficiently small values (2) of the parameter 2k₀L, where k₀ is the incident momentum. For realistic values of 2k₀L, the resistance moments are dominated by the terms obtained previously by arbitrarily assuming uniformly distributed phases. A direct proof of the validity of the random-phase assumption for studying scaling of resistance in one dimension is thus obtained.