Localization behavior induced by asymmetric disorder for the one-dimensional Anderson model.

Abstract

The behavior of the Lyapunov exponent under a small asymmetric disorder distribution is investigated for the one-dimensional Anderson model in the vicinity of the band center and for finite in-band energies. The special effect that could be found in systems with an asymmetric disorder distribution is shown to be small through a perturbation calculation. We obtain a quadratic formula for the Lyapunov exponent and show the enhancement of localization close to the band center induced by asymmetric disorder distribution. We find zero correction for an asymmetric disorder distribution with finite in-band energies. This quantitative behavior of the Lyapunov exponent explains why various asymmetric factors could be neglected in weakly disordered real systems. It also shows in what situation the asymmetric property of the disorder distribution should be considered during study of the localization behavior with a higher accuracy.