Anomalous band center localization in the one-dimensional Anderson model with a disordered distribution of infinite variance.

Abstract

We perform a detailed numerical study of the influence of distributions without a finite second moment on the Lyapunov exponent through the one-dimensional tight-binding Anderson model with diagonal disorder. Using the transfer matrix parametrization method and considering a specific distribution function, we calculate the Lyapunov exponent numerically and demonstrate its relation with the fractional lower order moments of the disorder probability density function. For the lower order of moments of disorder distribution with an infinite variance, we obtain the anomalous behavior near the band center.