Multifractality and quantum diffusion from self-consistent theory of localization
Journal Article
·
· Journal of Experimental and Theoretical Physics
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.
- OSTI ID:
- 22471994
- Journal Information:
- Journal of Experimental and Theoretical Physics, Journal Name: Journal of Experimental and Theoretical Physics Journal Issue: 5 Vol. 121; ISSN JTPHES; ISSN 1063-7761
- Country of Publication:
- United States
- Language:
- English
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