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Quasi-crystals are often alloys of 2-3 metals with a non-periodic arrangement of atoms. Still, they show the highly-peaked diffraction pattern of crystals while also possessing exotic electronic properties such as self-similar electronic spectra and multifractal wave functions usually associated with disordered materials. The level-spacing statistics of energy levels, P(s), with s the difference of adjacent energy levels, is known to be a marker that can distinguish ordered/periodic/metallic from disordered/non-periodic/insulating materials with ordered materials following a so-called Gaussian ensemble statistics. In a recent paper, Grimm and Roemer have shown that the Gaussian ensemble statistics also holds for quasi-periodic systems. Hence quasi-periodic systems seem to defy the usual classification where only ordered/periodic/metallic should show such a Gaussian statistics.

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