Anomalous localization in low-dimensional systems with correlated disorder |
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Authors: | F.M. Izrailev A.A. Krokhin N.M. Makarov |
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Affiliation: | 1. Instituto de Física, Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico;2. Department of Physics, University of North Texas, P.O. Box 311427, Denton, TX 76203, United States;3. Instituto de Ciencias, Universidad Autónoma de Puebla, Privada 17 Norte No. 3417, Col. San Miguel Hueyotlipan, Puebla 72050, Mexico |
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Abstract: | This review presents a unified view on the problem of Anderson localization in one-dimensional weakly disordered systems with short-range and long-range statistical correlations in random potentials. The following models are analyzed: the models with continuous potentials, the tight-binding models of the Anderson type, and various Kronig–Penney models with different types of perturbations. Main attention is paid to the methods of obtaining the localization length in dependence on the controlling parameters of the models. Specific interest is in an emergence of effective mobility edges due to certain long-range correlations in a disorder. The predictions of the theoretical and numerical analysis are compared to recent experiments on microwave transmission through randomly filled waveguides. |
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Keywords: | Anderson localization Low-dimensional systems Correlated disorder |
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