Titov, M. and Schomerus, H. (2003) Anomalous wavefunction statistics on a one-dimensional lattice with power-law disorder . Physical Review Letters, 91. p. 176601.
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 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 wavelength to lattice constant. Power-law rather than log-normal tails dominate the short-distance wave-function statistics.
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