Exact transmission moments in one-dimensional weak localization and single-parameter scaling

TL;DR

This paper derives exact expressions for the mean and variance of the transmission coefficient in a one-dimensional Anderson chain under weak localization, confirming single-parameter scaling theory's validity in this regime.

Contribution

It provides the first exact formulas for transmission moments in weak localization, expanding understanding beyond previous phase randomization assumptions.

Findings

Confirmed the validity of single-parameter scaling in weak localization

Derived exact expressions for transmission mean and variance

Compared results with earlier phase randomization-based findings

Abstract

We obtain for the first time the expressions for the mean and the variance of the transmission coefficient for an Anderson chain in the weak localization regime, using exact expansions of the complex transmission- and reflection coefficients to fourth order in the weakly disordered site energies. These results confirm the validity of single-parameter scaling theory in a domain where the higher transmission cumulants may be neglected. We compare our results with earlier results for transmission cumulants in the weak localization domain based on the phase randomization hypothesis.