Application of random matrix theory to quasiperiodic systems

Schreiber, Michael; Grimm, Uwe; Roemer, Rudolf A. and Zhong, Jian-Xin (1999). Application of random matrix theory to quasiperiodic systems. Physica A: Statistical and Theoretical Physics, 266(1-4) pp. 477–480.

DOI: https://doi.org/10.1016/S0378-4371(98)00634-7

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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