Band-center anomaly of the conductance distribution in one-dimensional Anderson localization

TL;DR

This paper investigates how the conductance distribution in one-dimensional Anderson localization deviates at the band center, revealing a breakdown of the random-phase approximation and confirming results through numerical simulations.

Contribution

It identifies the band-center anomaly in conductance distribution and links it to the failure of the random-phase approximation, providing a deeper understanding of localization phenomena.

Findings

Deviation from universal conductance distribution at band center

Breakdown of the random-phase approximation at specific energies

Numerical simulations confirm theoretical predictions

Abstract

We analyze the conductance distribution function in the one-dimensional Anderson model of localization, for arbitrary energy. For energy at the band center the distribution function deviates from the universal form assumed in single-parameter scaling theory. A direct link to the break-down of the random-phase approximation is established. Our findings are confirmed by a parameter-free comparison to the results of numerical simulations.