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.
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.
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