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

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Abstract

For a one-dimensional diagonally disordered half-infinite chain, we consider the problem of finding the limit value as t → ∞ 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.

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Authors and Affiliations

  1. Vavilov State Optical Institute, St. Petersburg, Russia

    G. G. Kozlov

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  1. G. G. Kozlov
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Correspondence to G. G. Kozlov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 162, No. 2, pp. 285–303, February, 2010.

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Kozlov, G.G. Computation of localization degree in the sense of the Anderson criterion for a one-dimensional diagonally disordered system. Theor Math Phys 162, 238–253 (2010). https://doi.org/10.1007/s11232-010-0019-1

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  • DOI: https://doi.org/10.1007/s11232-010-0019-1

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