Quantum energy spectra and one-dimensional quasiperiodic systems

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Abstract
Statistical properties of energy spectra in one-dimensional quasiperiodic systems are studied numerically. We find three distinctive level distributions: the Poisson, inverse-power-law (IPL), and cosine-band-like behaviors in the Harper model with an incommensurate potential. These depend on whether the electronic state is localized, critical, or extended, respectively. Energy spectra of electrons on the quasiperiodic Fibonacci lattice are also characterized by the IPL irrespective of the strength of the modulation, indicating that the state is always critical.