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<<Lc (Lc=localisation length). The distribution of theta is significantly non-uniform only for sufficiently small values (<or approximately=102) 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.