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Critical quantum chaos and the one dimensional Harper model

S. N. Evangelou·J. -L. Pichard
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Abstract

We study the quasiperiodic Harper's model in order to give further support for a possible universality of the critical spectral statistics. At the mobility edge we numerically obtain a scale-invariant distribution of the bands $S$, which is closely described by a semi-Poisson $P(S)=4S \exp(-2S)$ curve. The $\exp (-2S)$ tail appears when the mobility edge is approached from the metal while $P(S)$ is asymptotically log-normal for the insulator. The multifractal critical density of states also leads to a sub-Poisson linear number variance $Σ_{2}(E)\propto 0.041E$.

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S. N. Evangelou, J. -L. Pichard. 1999-02-24. Critical quantum chaos and the one dimensional Harper model. https://doi.org/10.1103/physrevlett.84.1643

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