2005/01/25 by V. Janiš, V. Janis, J. Kolorenc +1 · 16 citations
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Condensed matter physics #Diffusion #Dynamical mean field theory #Electron #Field (mathematics) #Field theory (psychology) #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Mean field theory #Physics #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum mechanics #Statistical physics #Vertex (graph theory) #cond-mat.dis-nn #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.71.245106
published in Physical Review B 71(24) (American Physical Society) · REVTeX4, 11 pages, no figures
arxiv created 2005/01/25 · openalex publication_date 2005/06/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We discuss conditions to be put on mean-field-like theories to be able to describe fundamental physical phenomena in disordered electron systems. In particular, we investigate options for a consistent mean-field theory of electron localization and for a reliable description of transport properties. We argue that a mean-field theory for the Anderson localization transition must be electron-hole symmetric and self-consistent at the two-particle (vertex) level. We show that such a theory with local equations can be derived from the asymptotic limit to high spatial dimensions. The weight of the diffusion pole, i.e., the number of diffusive states at the Fermi energy, in this mean-field theory decreases with the increasing disorder strength and vanishes in the localized phase. Consequences of the disclosed behavior for our understanding of vanishing of electron diffusion are discussed.