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

Schreiber, Michael; Grimm, Uwe; Roemer, Rudolf A. and Zhong, Jianxin (1999). Energy levels of quasiperiodic Hamiltonians, spectral unfolding, and random matrix theory. Computer Physics Communications, 121-122 pp. 499–501.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1016/S0010-4655(99)00391-4
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Abstract

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 unfolding. The effect of unfolding on the integrated level-spacing distribution 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 random matrix ensemble (GOE) even without unfolding. For energy ranges with fluctuating DOS, we observe deviations from the GOE result. After unfolding, we always recover the GOE distribution.

Item Type: Journal Article
ISSN: 0010-4655
Extra Information: Proceedings of the Europhysics Conference on Computational Physics CCP 1998
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 12359
Depositing User: Uwe Grimm
Date Deposited: 20 Nov 2008 12:43
Last Modified: 02 Dec 2010 20:15
URI: http://oro.open.ac.uk/id/eprint/12359
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