Exactly Solvable Scaling Theory of Conduction in Disordered Wires

TL;DR

This paper presents an exact solution to the scaling theory of phase-coherent conduction in disordered wires, clarifying discrepancies between random-matrix theory predictions and microscopic calculations.

Contribution

It provides an exact solution to the Dorokhov-Mello-Pereyra-Kumar equation without time-reversal symmetry, refining previous theoretical predictions.

Findings

Exact solution confirms the accuracy of random-matrix theory predictions with a correction factor.

Resolves discrepancies in conductance fluctuation magnitudes.

Improves understanding of conductance distribution in disordered wires.

Abstract

Recent developments are reviewed in the scaling theory of phase-coherent conduction through a disordered wire. The Dorokhov-Mello-Pereyra-Kumar equation for the distribution of transmission eigenvalues has been solved exactly, in the absence of time-reversal symmetry. Comparison with the previous prediction of random-matrix theory shows that this prediction was highly accurate --- but not exact: The repulsion of the smallest eigenvalues was overestimated by a factor of two. This factor of two resolves several disturbing discrepancies between random-matrix theory and microscopic calculations, notably in the magnitude of the universal conductance fluctuations in the metallic regime, and in the width of the log-normal conductance distribution in the insulating regime. ***To be published as a "Brief Review" in Modern Physics Letters B.****