Application of random matrix theory to quasiperiodic systems

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.

proceedings of "Percolation98", 5 Elsart pages with 5 figures, to be published in Physica A

References in corpus (2)

• Asymptotics of Universal Probability of Neighboring Level Spacings at the Anderson Transition
• Level-Spacing Distributions of Planar Quasiperiodic Tight-Binding Models

Cited by in corpus (4)

• Universal level-spacing statistics in quasiperiodic tight-binding models
• Energy spectra and eigenstates of quasiperiodic tight-binding Hamiltonians
• Level-spacing distributions of the Gaussian unitary random matrix ensemble
• Gaussian ensembles distributions from mixing quantum systems