Multifractality and quantum diffusion from self-consistent theory of localization
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.
- Authors:
- Kapitza Institute for Physical Problems (Russian Federation)
- Publication Date:
- OSTI Identifier:
- 22471994
- Resource Type:
- Journal Article
- Journal Name:
- Journal of Experimental and Theoretical Physics
- Additional Journal Information:
- Journal Volume: 121; Journal Issue: 5; Other Information: Copyright (c) 2015 Pleiades Publishing, Inc.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1063-7761
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPARATIVE EVALUATIONS; CONVERGENCE; DIFFUSION; DISPERSIONS; QUANTUM MECHANICS; SPACE; WAVE FUNCTIONS
Citation Formats
Suslov, I. M., E-mail: suslov@kapitza.ras.ru. Multifractality and quantum diffusion from self-consistent theory of localization. United States: N. p., 2015.
Web. doi:10.1134/S1063776115110096.
Suslov, I. M., E-mail: suslov@kapitza.ras.ru. Multifractality and quantum diffusion from self-consistent theory of localization. United States. https://doi.org/10.1134/S1063776115110096
Suslov, I. M., E-mail: suslov@kapitza.ras.ru. 2015.
"Multifractality and quantum diffusion from self-consistent theory of localization". United States. https://doi.org/10.1134/S1063776115110096.
@article{osti_22471994,
title = {Multifractality and quantum diffusion from self-consistent theory of localization},
author = {Suslov, I. M., E-mail: suslov@kapitza.ras.ru},
abstractNote = {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.},
doi = {10.1134/S1063776115110096},
url = {https://www.osti.gov/biblio/22471994},
journal = {Journal of Experimental and Theoretical Physics},
issn = {1063-7761},
number = 5,
volume = 121,
place = {United States},
year = {Sun Nov 15 00:00:00 EST 2015},
month = {Sun Nov 15 00:00:00 EST 2015}
}