Hamiltonian map approach to 1D Anderson model |
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Authors: | T Kaya |
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Institution: | (1) Physics Department, Yıldız Technical University, Istanbul, 34210 Davutpaşa, Turkey |
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Abstract: | A one-dimensional diagonal tight binding electronic system is analyzed with the Hamiltonian map approach to study analytically
the inverse localization length of an infinite sample. Both the uncorrelated and the dichotomic correlated random potential
sequences are considered in the evaluations of the inverse localization length. Analytical expressions for the invariant measure
or the angle density distribution are the main motivation of this work in order to derive analytical results. The well-known
uncorrelated weak disorder result of the inverse localization length is derived with a clear procedure. In addition, an analytical
expression for high disorder is obtained near the band edge. It is found that the inverse localization length goes to 1 in
this limit. Following the procedure used in the uncorrelated situation, an analytical expression for the inverse localization
length is also obtained for the dichotomic correlated sequence in the small disorder situation. |
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Keywords: | PACS" target="_blank">PACS 05 60 Gg Quantum transport 72 15 Rn Localization effects 72 20 Ee Mobility edges hopping transport 64 60 Cn Order-disorder transformations |
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