2004/03/24 by V. Janiš, V. Janis, J. Kolorenc +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Combinatorics #Conservation law #Electron #Generalization #Law #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Norm (philosophy) #Physics #Quantum and electron transport phenomena #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #Statistical physics #Thermodynamic limit #Vertex (graph theory) #Wave function #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1002/pssb.200404786
published as Phys. Stat. Sol. (B) 241, 2032 (2004) · REVTeX4, 8 pages, no figures
arxiv created 2004/03/24 · openalex publication_date 2004/06/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract We discuss conservation of probability in noninteracting disordered electron systems. We argue that although the norm of the electron wave function is conserved in individual realizations of the random potential, we cannot extend this conservation law easily to configurationally averaged systems in the thermodynamic limit. A direct generalization of the norm conservation to averaged functions is hindered by the existence of localized states breaking translational invariance. Such states are elusive to the description with periodic Bloch waves. Mathematically this difficulty manifests itself via the diffusion pole in the electron–hole irreducible vertex. The pole leads to a clash with analyticity of the self‐energy, reflecting causality of the theory, when norm conservation is enforced by a Ward identity. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)