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Anderson localization from the replica formalism

Alexander Altland·Alex Kamenev·Chushun Tian
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Abstract

We study Anderson localization in quasi--one--dimensional disordered wires within the framework of the replica $σ$--model. Applying a semiclassical approach (geodesic action plus Gaussian fluctuations) recently introduced within the context of supersymmetry by Lamacraft, Simons and Zirnbauer \cite{LSZ}, we compute the {\em exact} density of transmission matrix eigenvalues of superconducting wires (of symmetry class $C$I.) For the unitary class of metallic systems (class $A$) we are able to obtain the density function, save for its large transmission tail.

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Alexander Altland, Alex Kamenev, Chushun Tian. 2005-05-12. Anderson localization from the replica formalism. https://doi.org/10.1103/physrevlett.95.206601

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