A selfconsistent theory of localization

1973/05/24 by R Abou-Chacra, R. Abou-Chacra, D. J. Thouless +3 · 22 citations
Physics and Astronomy · #Quantum and electron transport phenomena #Spectroscopy and Quantum Chemical Studies #Theoretical and Computational Physics

paper · doi:10.1088/0022-3719/6/10/009

crossref issued 1973/05/24 · crossref published 1973/05/24 · crossref published-print 1973/05/24 · openalex publication_date 1973/05/24 · crossref created 2002/07/26 · crossref deposited 2023/04/23 · openalex created_date 2025/10/10 · crossref indexed 2026/08/01 · openalex updated_date 2026/08/01

Abstract

A new basis has been found for the theory of localization of electrons in disordered systems. The method is based on a selfconsistent solution of the equation for the self energy in second order perturbation theory, whose solution may be purely real almost everywhere (localized states) or complex everywhere (nonlocalized states). The equations used are exact for a Bethe lattice. The selfconsistency condition gives a nonlinear integral equation in two variables for the probability distribution of the real and imaginary parts of the self energy. A simple approximation for the stability limit of localized states gives Anderson's 'upper limit approximation'. Exact solution of the stability problem in a special case gives results very close to Anderson's best estimate.

Citations

• The theory of impurity conduction
• Numerical studies of localization in disordered systems

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