On the distribution of transmission eigenvalues in disordered wires

TL;DR

This paper analytically solves the Dorokhov-Mello-Pereyra-Kumar equation for disordered wires across three symmetry classes, using a Calogero-Sutherland model, confirming previous results for the β=2 case.

Contribution

It provides an exact solution to the evolution of transmission eigenvalues in disordered wires for all three symmetry classes using a novel mapping to a Calogero-Sutherland model.

Findings

Exact solutions for β=1,2,4 cases

Agreement with previous results for β=2

Advances understanding of disordered wire conductance

Abstract

We solve the Dorokhov-Mello-Pereyra-Kumar equation which describes the evolution of an ensamble of disordered wires of increasing length in the three cases $\beta=1,2,4$. The solution is obtained by mapping the problem in that of a suitable Calogero-Sutherland model. In the $\beta=2$ case our solution is in complete agreement with that recently found by Beenakker and Rejaei.