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Application of random matrix theory to quasiperiodic systems

Michael Schreiber·Uwe Grimm·Rudolf A. Roemer·Jian-Xin Zhong
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Abstract

We study statistical properties of energy spectra of a tight-binding model on the two-dimensional quasiperiodic Ammann-Beenker tiling. Taking into account the symmetries of finite approximants, we find that the underlying universal level-spacing distribution is given by the Gaussian orthogonal random matrix ensemble, and thus differs from the critical level-spacing distribution observed at the metal-insulator transition in the three-dimensional Anderson model of disorder. Our data allow us to see the difference to the Wigner surmise.

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Michael Schreiber, Uwe Grimm, Rudolf A. Roemer, Jian-Xin Zhong. 1998-09-28. Application of random matrix theory to quasiperiodic systems. https://doi.org/10.1016/s0378-4371(98)00634-7

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