LEVEL-SPACING DISTRIBUTIONS OF PLANAR QUASI-PERIODIC TIGHT-BINDING MODELS

We study statistical properties of energy spectra of two-dimensional q uasiperiodic tight-binding models. Taking into account the symmetries of models defined on various finite approximants of quasiperiodic tili ngs, we find that the underlying universal level-spacing distribution is given by the Gaussian orthogonal random matrix ensemble. Our data a llow us to see the difference to the Wigner surmise. In particular, ou r result differs from the critical level-spacing distribution observed at the metal-insulator transition in the three-dimensional Anderson m odel of disorder.