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Analytic perturbation theory and localization phenomena
Author(s) -
Brändas E. J.,
Obcemea C. H.
Publication year - 1979
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560160506
Subject(s) - randomness , statistical physics , perturbation (astronomy) , perturbation theory (quantum mechanics) , mathematics , cluster (spacecraft) , kernel (algebra) , physics , quantum mechanics , pure mathematics , computer science , statistics , programming language
This paper attempts to apply the results of analytic perturbation theory to systems exhibiting some degree of randomness in their state variables. In particular, we focus on the localization problem in the Anderson model. It is shown that this approach proves the existence of bound states as a result of the statistical treatment of the Weinberg–van Winter–Hunziker irreducible N ‐particle kernel. The analysis is extended beyond the one‐particle cluster approach and the occurrence of higher‐order clusters is discussed in relation to the diluteness criterion and the conditions set on the interaction potential V .