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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.

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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
Mathematics, Computing and Technology
Item ID: 8237
Depositing User: Uwe Grimm
Date Deposited: 28 Jun 2007
Last Modified: 14 Jan 2016 16:37
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