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TMF, 2012, Volume 171, Number 1, Pages 124–134 (Mi tmf6916)  

This article is cited in 4 scientific papers (total in 4 papers)

Spectral dependence of the localization degree in the one-dimensional disordered Lloyd model

G. G. Kozlov

Fock Institute of Physics, St. Petersburg State University, St. Petersburg, Russia

Abstract: We calculate the Anderson criterion and the spectral dependence of the degree of localization in the first nonvanishing approximation with respect to disorder for one-dimensional diagonally disordered models with a site energy distribution function that has no finite even moments higher than the zeroth. For this class of models (for which the usual perturbation theory is inapplicable), we show that the perturbation theory can be consistently constructed for the joint statistics of advanced and retarded Green's functions. Calculations for the Lloyd model show that the Anderson criterion in this case is a linear (not quadratic as usual) function of the disorder degree. We illustrate the calculations with computer experiments.

Keywords: Anderson localization, one-dimensional disordered system, Green's function

DOI: https://doi.org/10.4213/tmf6916

Full text: PDF file (495 kB)
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English version:
Theoretical and Mathematical Physics, 2012, 171:1, 531–540

Bibliographic databases:

Document Type: Article
Received: 19.05.2011

Citation: G. G. Kozlov, “Spectral dependence of the localization degree in the one-dimensional disordered Lloyd model”, TMF, 171:1 (2012), 124–134; Theoret. and Math. Phys., 171:1 (2012), 531–540

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  • https://doi.org/10.4213/tmf6916
  • http://mi.mathnet.ru/eng/tmf/v171/i1/p124

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. G. G. Kozlov, “Calculation of spectral dependence of Anderson criterion for 1D system with correlated diagonal disorder”, Theoret. and Math. Phys., 179:1 (2014), 500–508  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. G. G. Kozlov, “Correlated Lloyd model: Exact solution”, Theoret. and Math. Phys., 181:2 (2014), 1396–1404  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    3. Mendez-Bermudez J.A., Martinez-Mendoza A.J., Gopar V.A., Varga I., “Lloyd-Model Generalization: Conductance Fluctuations in One-Dimensional Disordered Systems”, Phys. Rev. E, 93:1 (2016), 012135  crossref  adsnasa  isi
    4. Mendez-Bermudez J.A., Aguilar-Sanchez R., “Information-Length Scaling in a Generalized One-Dimensional Lloyd'S Model”, Entropy, 20:4 (2018), 300  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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