Energy spectra and eigenstates of quasiperiodic tight-binding Hamiltonians

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.

27 pages, 27 PostScript figures, LaTeX using vch-book.cls

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