Anderson localization from the replica formalism

Abstract

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.

4 pages, 1 figure

References in corpus (12)

• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Exact Solution for the Distribution of Transmission Eigenvalues in a Disordered Wire and Comparison with Random-Matrix Theory
• Localization and delocalization in dirty superconducting wires
• Wigner-Dyson Statistics from the Replica Method
• Replica field theories, Painleve transcendents, and exact correlation functions
• Level Correlations in Disordered Metals: the Replica sigma-Model
• Equivalence of Fokker-Planck approach and non-linear $\sigma$-model for disordered wires in the unitary symmetry class
• Non-perturbative results for level correlations from the replica nonlinear sigma model
• Localization from sigma-model geodesics
• Phase Transition in a Model with Non-Compact Symmetry on Bethe Lattice and the Replica Limit
• Exploring Level Statistics from Quantum Chaos to Localization with the Autocorrelation Function of Spectral Determinants
• Supersymmetry for disordered systems with interaction

Cited by in corpus (14)

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• Emergence of integer quantum Hall effect from chaos
• Field theory of non-Hermitian disordered systems
• Transmission eigenvalues in random media with surface reflection
• Controlling transmission eigenchannels in random media by edge reflection
• Semiclassical electron transport at the edge of a 2D topological insulator: Interplay of protected and unprotected modes
• Generating Functionals for Quantum Field Theories with Random Potentials
• Dynamics of Anderson localization in disordered wires
• A route from maximal chaoticity to integrability
• Transmission eigenvalue distribution in disordered media from radiant field theory
• Semiclassical spectral correlator in quasi one-dimensional systems