Geodesic
Spectral dependence of the~localization degree in the~one-dimensional disordered Lloyd model
Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 1, pp. 124-134

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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. 
@article{TMF_2012_171_1_a10,
     author = {G. G. Kozlov},
     title = {Spectral dependence of the~localization degree in the~one-dimensional disordered {Lloyd} model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {124--134},
     publisher = {mathdoc},
     volume = {171},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_171_1_a10/}
}
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G. G. Kozlov. Spectral dependence of the~localization degree in the~one-dimensional disordered Lloyd model. Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 1, pp. 124-134. http://geodesic.mathdoc.fr/item/TMF_2012_171_1_a10/