Exact Solution for the Distribution of Transmission Eigenvalues in a Disordered Wire and Comparison with Random-Matrix Theory

TL;DR

This paper derives an exact probability distribution for transmission eigenvalues in disordered wires, revealing deviations from random-matrix theory predictions for certain eigenvalues, and compares these findings with theoretical models.

Contribution

It provides an exact solution to the Fokker-Planck equation for disordered wires, connecting it to a free-fermion problem and analyzing eigenvalue distributions.

Findings

Exact distribution function obtained for transmission eigenvalues.

Eigenvalue repulsion from random-matrix theory breaks down away from unity.

Comparison with theoretical models highlights deviations in eigenvalue behavior.

Abstract

An exact solution is presented of the Fokker-Planck equation which governs the evolution of an ensemble of disordered metal wires of increasing length, in a magnetic field. By a mapping onto a free-fermion problem, the complete probability distribution function of the transmission eigenvalues is obtained. The logarithmic eigenvalue repulsion of random-matrix theory is shown to break down for transmission eigenvalues which are not close to unity. ***Submitted to Physical Review B.****