Critical quantum chaos and the one dimensional Harper model

Details Critical quantum chaos and the one dimensional Harper model Critical quantum chaos and the one dimensional Harper model

1999-02-24

arxiv.org/abs/cond-mat/9902321v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 4 eps figures

Scientific paper

10.1103/PhysRevLett.84.1643

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 $\Sigma_{2}(E)\propto 0.041E$.

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