Anderson localization from the replica formalism
Alexander Altland, Alex Kamenev, Chushun Tian
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 LSZ, we compute the exact density of transmission matrix eigenvalues of superconducting wires (of symmetry class CI.) 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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