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

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.