Anderson localization from the replica formalism

Details Anderson localization from the replica formalism Anderson localization from the replica formalism

2005-05-12

arxiv.org/abs/cond-mat/0505328v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 1 figure

Scientific paper

10.1103/PhysRevLett.95.206601

We study Anderson localization in quasi--one--dimensional disordered wires within the framework of the replica $\sigma$--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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