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TMF, 2010, Volume 162, Number 2, Pages 285–303 (Mi tmf6471)  

This article is cited in 2 scientific papers (total in 2 papers)

Computation of localization degree in the sense of the Anderson criterion for a one-dimensional diagonally disordered system

G. G. Kozlov

Vavilov State Optical Institute, St. Petersburg, Russia

Abstract: For a one-dimensional diagonally disordered half-infinite chain, we consider the problem of finding the limit value as $t\to\infty$ of the average excitation density $D$ at the edge site of the chain under the condition that the excitation is localized at this site at $t=0$. For a binary disordered chain, we obtain an expression for $D$ that is exact in the small defect concentration limit for an arbitrary defect energy. In this case, the density $D$ depends nonanalytically on the energy. We obtain an expression for $D$ in the case of an arbitrary small diagonal disorder. We also calculate the relative contribution to $D$ from states with a given energy. All the obtained results agree well with the computer simulation data.

Keywords: disordered system, random matrix, state localization, Anderson criterion

DOI: https://doi.org/10.4213/tmf6471

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English version:
Theoretical and Mathematical Physics, 2010, 162:2, 238–253

Bibliographic databases:

Received: 11.02.2010

Citation: G. G. Kozlov, “Computation of localization degree in the sense of the Anderson criterion for a one-dimensional diagonally disordered system”, TMF, 162:2 (2010), 285–303; Theoret. and Math. Phys., 162:2 (2010), 238–253

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf6471
  • http://mi.mathnet.ru/eng/tmf/v162/i2/p285

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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, “Spectral dependence of the localization degree in the one-dimensional disordered Lloyd model”, Theoret. and Math. Phys., 171:1 (2012), 531–540  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    2. 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
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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