Transport and localization of waves in one-dimensional disordered media: Random phase approximation and beyond

TL;DR

This paper provides a comprehensive numerical analysis of wave reflection and phase statistics in one-dimensional disordered media, extending beyond the random phase approximation to better understand localization and transport properties.

Contribution

It introduces a full numerical solution of the Fokker-Planck equation for reflection and phase distributions in 1D disordered systems beyond the RPA, enhancing understanding of localization effects.

Findings

Phase distribution significantly influences transport averages.

Beyond RPA, reflection statistics differ from traditional models.

Results impact the one-parameter scaling theory of localization.

Abstract

We report a systematic and detailed numerical study of statistics of the reflection coefficient $(|R(L)|^2)$ and its associated phase ($\theta$) for a plane wave reflected from a one-dimensional (1D) disordered medium beyond the random phase approximation (RPA) for Gaussian white-noise disorder. We solve numerically the full Fokker-Planck (FP) equation for the probability distribution in the ($|R(L)|^2,\theta(L)$)-space for different lengths of the sample with different "disorder strengths". The statistical electronic transport properties of 1D disordered conductors are calculated using the Landauer four-probe resistance formula and the FP equation. This constitutes a complete solution for the reflection statistics and many aspects of electron transport in a 1D Gaussian white-noise potential. Our calculation shows the contribution of the phase distribution to the different averages and its effects on the one-parameter scaling theory of localization.