Localization from sigma-model geodesics

A. Lamacraft, B. D. Simons, and M. R. Zirnbauer 2004. Physical Review B

Abstract

We use a method based on the semiclassical analysis of \(\sigma\)-models to describe the phenomenon of strong localization in quasi one-dimensional conductors, obtaining the density 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 perspective on localization.