Theoretical and Mathematical Physics

, Volume 171, Issue 1, pp 531–540 | Cite as

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



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.


Anderson localization one-dimensional disordered system Green’s function 


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© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Fock Institute of PhysicsSt. Petersburg State UniversitySt. PetersburgRussia

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