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Multifractality and quantum diffusion from self-consistent theory of localization

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Abstract

Multifractal properties of wave functions in a disordered system can be derived from self-consistent theory of localization by Vollhardt and Wölfle. A diagrammatic interpretation of results allows to obtain all scaling relations used in numerical experiments. The arguments are given that the one-loop Wegner result for a space dimension d = 2 + ϵ is exact, so the multifractal spectrum is strictly parabolical. The σ-models are shown to be deficient at the four-loop level and the possible reasons of that are discussed. The extremely slow convergence to the thermodynamic limit is demonstrated. The open question on the relation between multifractality and a spatial dispersion of the diffusion coefficient D(ω, q) is resolved in the compromise manner due to ambiguity of the D(ω, q) definition. Comparison is made with the extensive numerical material.

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  1. Kapitza Institute for Physical Problems, Moscow, Russia

    I. M. Suslov

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Original Russian Text © I.M. Suslov, 2015, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2015, Vol. 148, No. 5, pp. 1012–1030.

The article was translated by the authors.

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Suslov, I.M. Multifractality and quantum diffusion from self-consistent theory of localization. J. Exp. Theor. Phys. 121, 885–901 (2015). https://doi.org/10.1134/S1063776115110096

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