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Localization from sigma-model geodesics

A. Lamacraft·B. D. Simons·M. R. Zirnbauer
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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.

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A. Lamacraft, B. D. Simons, M. R. Zirnbauer. 2004-09-09. Localization from sigma-model geodesics. https://doi.org/10.1103/physrevb.70.075412

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