Energy levels of quasiperiodic Hamiltonians, spectral unfolding, and random matrix theory

We consider a tight-binding Hamiltonian defined on the quasiperiodic Ammann -Beenker tiling. Although the density of states (DOS) is rather spiky, the integrated DOS (IDOS) is quite smooth and can be used to perform spectral u nfolding. The effect of unfolding on the integrated level-spacing distribut ion is investigated for various parts of the spectrum which show different behaviour of the DOS. For energy intervals with approximately constant DOS, we find good agreement with the distribution of the Gaussian orthogonal ra ndom matrix ensemble (GOE) even without unfolding. For energy ranges with f luctuating DOS, we observe deviations from the GOE result. After unfolding, we always recover the GOE distribution. (C) 1999 Elsevier Science B.V. All rights reserved.