The band-centre anomaly in the 1D Anderson model with correlated disorder

We study the band-centre anomaly in the one-dimensional Anderson model with weak correlated disorder. Our analysis is based on the Hamiltonian map approach; the correspondence between the discrete model and its continuous counterpart is discussed in detail. We obtain analytical expressions of the lo...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2015-08, Vol.48 (35), p.355001-30
Main Authors: Tessieri, L, Herrera-González, I F, Izrailev, F M
Format: Article
Language:English
Subjects:
Anderson model
Anomalies
band-centre anomaly
correlated disorder
Correlation
Disorders
Exact solutions
Invariants
Localization
Mathematical analysis
Mathematical models
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Summary:We study the band-centre anomaly in the one-dimensional Anderson model with weak correlated disorder. Our analysis is based on the Hamiltonian map approach; the correspondence between the discrete model and its continuous counterpart is discussed in detail. We obtain analytical expressions of the localization length and of the invariant measure of the phase variable, valid for energies in a neighbourhood of the band centre. By applying these general results to specific forms of correlated disorder, we show how correlations can enhance or suppress the anomaly at the band centre.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/48/35/355001