Anomalies and non-log-normal tails in one-dimensional localization with power-law disorder

M. Titov; H. Schomerus

doi:10.1103/physrevlett.91.176601

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Anomalies and non-log-normal tails in one-dimensional localization with power-law disorder

M. Titov·H. Schomerus

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Abstract

Within a general framework, we discuss the wave function statistics in the Lloyd model of Anderson localization on a one-dimensional lattice with a Cauchy distribution for the random on-site potential. We demonstrate that already in leading order in the disorder strength, there exists a hierarchy of anomalies in the probability distributions of the wave function, the conductance, and the local density of states, for every energy which corresponds to a rational ratio of wave length to the lattice constant. We also show that these distribution functions do have power-law rather then log-normal tails and do not display universal single-parameter scaling. These peculiarities persist in any model with power-law tails of the disorder distribution function.

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BibTeX RIS

M. Titov, H. Schomerus. 2003-02-27. Anomalies and non-log-normal tails in one-dimensional localization with power-law disorder. https://doi.org/10.1103/physrevlett.91.176601

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