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Application of random matrix theory to quasiperiodic systems

Author

Listed:
  • Schreiber, Michael
  • Grimm, Uwe
  • Römer, Rudolf A
  • Zhong, Jian-Xin

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.

Suggested Citation

  • Schreiber, Michael & Grimm, Uwe & Römer, Rudolf A & Zhong, Jian-Xin, 1999. "Application of random matrix theory to quasiperiodic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 266(1), pages 477-480.
    • Handle: RePEc:eee:phsmap:v:266:y:1999:i:1:p:477-480
    DOI: 10.1016/S0378-4371(98)00634-7
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