Conservation laws in disordered electron systems: Thermodynamic limit and configurational averaging

Abstract

AbstractWe 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)