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.

URL:	http://uk.arxiv.org/abs/cond-mat/0212140
DOI (Digital Object Identifier) Link:	https://doi.org/10.1002/3527606572.ch3
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Abstract

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 Section
ISBN:	3-527-40399-X, 978-3-527-40399-8
Academic Unit/School:	Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID:	8237
Depositing User:	Uwe Grimm
Date Deposited:	28 Jun 2007
Last Modified:	15 Sep 2017 10:01
URI:	http://oro.open.ac.uk/id/eprint/8237
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