Multifractality and quantum diffusion from self-consistent theory of localization
- Kapitza Institute for Physical Problems (Russian Federation)
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, Vol. 121, Issue 5; Other Information: Copyright (c) 2015 Pleiades Publishing, Inc.; Country of input: International Atomic Energy Agency (IAEA); ISSN 1063-7761
- Country of Publication:
- United States
- Language:
- English
Similar Records
Strict parabolicity of the multifractal spectrum at the Anderson transition
Radiation singularities, multiple scattering and diffusion in multifractal clouds