Weak-disorder expansion for localization lengths ofquasi-1D systems

A perturbative formula for the lowest Lyapunov exponent of an Anderson model on a strip is presented. It is expressed in terms of an energy-dependent doubly stochastic matrix, the size of which is proportional to the strip width. This matrix and the resulting perturbative expression for the Lyapunov...

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Bibliographic Details
Published in:Europhysics letters 2004-10, Vol.68 (2), p.247-253
Main Authors: Römer, R. A., Schulz-Baldes, H.
Format: Article
Language:English
Subjects:
72.15.Rn
73.20.Fz
73.23.-b
Online Access:Get full text
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Summary:A perturbative formula for the lowest Lyapunov exponent of an Anderson model on a strip is presented. It is expressed in terms of an energy-dependent doubly stochastic matrix, the size of which is proportional to the strip width. This matrix and the resulting perturbative expression for the Lyapunov exponent are evaluated numerically. Dependence on energy, strip width and disorder strength are thoroughly compared with the results obtained by the standard transfer matrix method. Good agreement is found for all energies in the band of the free operator and this even for quite large values of the disorder strength.
ISSN:0295-5075
1286-4854
DOI:10.1209/epl/i2004-10190-9