Geodesic
Computation of localization degree in the~sense of the~Anderson criterion for a~one-dimensional diagonally disordered system
Teoretičeskaâ i matematičeskaâ fizika, Tome 162 (2010) no. 2, pp. 285-303

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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, state localization, Anderson criterion.
Mots-clés : random matrix 
@article{TMF_2010_162_2_a9,
     author = {G. G. Kozlov},
     title = {Computation of localization degree in the~sense of {the~Anderson} criterion for a~one-dimensional diagonally disordered system},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {285--303},
     publisher = {mathdoc},
     volume = {162},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2010_162_2_a9/}
}
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G. G. Kozlov. Computation of localization degree in the~sense of the~Anderson criterion for a~one-dimensional diagonally disordered system. Teoretičeskaâ i matematičeskaâ fizika, Tome 162 (2010) no. 2, pp. 285-303. http://geodesic.mathdoc.fr/item/TMF_2010_162_2_a9/