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Application of random matrix theory to quasiperiodic systems

1998/09/28 by Michael Schreiber, Uwe Grimm, Rudolf A. Römer +3
Materials Science · Mathematics · Physics and Astronomy · #Condensed matter physics #Distribution (mathematics) #Gaussian #Geometry #Homogeneous space #Mathematical analysis #Mathematics #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Quasicrystal #Quasicrystal Structures and Properties #Quasiperiodic function #Random matrix #Statistical physics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.mtrl-sci

paper · pdf · doi:10.1016/s0378-4371(98)00634-7

published as Physica A 266, 477-480 (1999) · proceedings of "Percolation98", 5 Elsart pages with 5 figures, to be published in Physica A

arxiv created 1998/09/28 · openalex publication_date 1999/04/01 · arxiv updated 2015/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations