Application of random matrix theory to quasiperiodic systems

Michael Schreiber, Uwe Grimm, Rudolf A Römer and Jian-Xin Zhong

Physica A: Statistical Mechanics and its Applications, 1999, vol. 266, issue 1, 477-480

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.

Keywords: Random matrix theory; Wigner surmise; Level-spacing distribution; Quasiperiodic systems (search for similar items in EconPapers)
Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:266:y:1999:i:1:p:477-480

DOI: 10.1016/S0378-4371(98)00634-7

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