The Open UniversitySkip to content

Energy spectra and eigenstates of quasiperiodic tight-binding Hamiltonians

Grimm, Uwe and Schreiber, Michael (2003). Energy spectra and eigenstates of quasiperiodic tight-binding Hamiltonians. In: Trebin, Hans-Rainer ed. Quasicrystals: Structure and Physical Properties. Weinheim: Wiley-VCH, pp. 210–235.

DOI (Digital Object Identifier) Link:
Google Scholar: Look up in Google Scholar


Analytic and numerical results for quasiperiodic tight-binding models are reviewed, with emphasis on two and three-dimensional models which so far are beyond a mathematically rigorous treatment. In particular, we consider energy spectra of aperiodic tight-binding models and the corresponding level statistics, which are well reproduced by random matrix theory. The eigenstates are characterised by multifractal analysis, and a construction of peculiar multifractal states on the Penrose tiling is discussed. We also consider quantum diffusion, and present some results on interacting electron systems in one dimension.

Item Type: Book Chapter
ISBN: 3-527-40399-X, 978-3-527-40399-8
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 8237
Depositing User: Uwe Grimm
Date Deposited: 28 Jun 2007
Last Modified: 02 Dec 2010 20:00
Share this page:


Scopus Citations

Actions (login may be required)

Policies | Disclaimer

© The Open University   + 44 (0)870 333 4340