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Localization in a System of N Coupled Chains. Recursion Method. I. General Approach
Author(s) -
Weller W.,
Kasner M.
Publication year - 1988
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221480125
Subject(s) - recursion (computer science) , reflection (computer programming) , diagram , amplitude , interpretation (philosophy) , space (punctuation) , chain (unit) , simple (philosophy) , mathematics , diagrammatic reasoning , mathematical analysis , statistical physics , physics , algorithm , computer science , quantum mechanics , programming language , philosophy , statistics , epistemology , operating system
The localization length of an electron is studied, which moves under the influence of a random potential in a system of N coupled chains. First, a closed recursion relation for the reflection amplitude for one chain is derived. It is based on a simple diagrammatic interpretation of this amplitude in the framework of Berezinskii's real space diagram analysis. Then, the method is generalized to the case of N coupled chains. The calculation of the localization length is reduced to the determination of a stationary probability density of some parameters characterizing the reflection properties of such a system in the asymptotic regime for large length. The general method provides a numerical algorithm for the calculation of interesting quantities too.