Quantum Transport in Disordered Wires: Equivalence of One-Dimensional Sigma Model and Dorokhov-Mello-Pereyra-Kumar Equation

Abstract

The two known non-perturbative theories of localization in disordered wires, the Fokker-Planck approach due to Dorokhov, Mello, Pereyra, and Kumar, and the field-theoretic approach due to Efetov and Larkin, are shown to be equivalent for all symmetry classes. The equivalence had been questioned as a result of field-theoretic calculations of the average conductance by Zirnbauer [PRL 69, 1584 (1992)], which disagreed with the Fokker-Planck approach in the symplectic symmetry class. We resolve this controversy by pointing to an incorrect implementation of Kramers degeneracy in these calculations, and we derive modified expressions for the first two conductance moments which agree well with existing numerical simulations from the metallic into the localized regime. ***Submitted to Physical Review B.***

21 pages, REVTeX-3.0, 5 postscript figures appended as self-extracting archive. A complete postscript file with figures and text (13 pages) is available from http://rulgm4.LeidenUniv.nl/preprints.html

References in corpus (4)

• Exact Solution for the Distribution of Transmission Eigenvalues in a Disordered Wire and Comparison with Random-Matrix Theory
• On the distribution of transmission eigenvalues in disordered wires
• Equivalence of Fokker-Planck approach and non-linear $\sigma$-model for disordered wires in the unitary symmetry class
• Brownian motion ensembles and parametric correlations of the transmission eigenvalues: Application to coupled quantum billiards and to disordered wires

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