Localization from sigma-model geodesics

TL;DR

This paper introduces a semi-classical sigma-model approach to analyze strong localization in quasi-one-dimensional conductors, providing exact results for transmission eigenvalue distributions across various symmetry classes.

Contribution

It presents a novel semi-classical method based on sigma-models to describe localization phenomena, including exact solutions for certain symmetry classes.

Findings

Exact distribution of transmission eigenvalues obtained

Applicable to multiple symmetry classes including superconducting and chiral

Offers a new perspective on the phenomenon of localization

Abstract

We use a novel method based on the semi-classical analysis of sigma-models to describe the phenomenon of strong localization in quasi one-dimensional conductors, obtaining the full distribution of transmission eigenvalues. For several symmetry classes, describing random superconducting and chiral Hamiltonians, the target space of the appropriate sigma-model is a (super)group manifold. In these cases our approach turns out to be exact. The results offer a novel perspective on localization.