Abstract

We use a method based on the semiclassical analysis of $\ensuremath{\sigma}$ 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 $\ensuremath{\sigma}$ model is a (super)group manifold. In these cases our approach turns out to be exact. The results offer a perspective on localization.

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