2002/12/06 by Uwe Grimm, Michael Schreiber
Physics and Astronomy · #cond-mat.dis-nn #cond-mat.mtrl-sci #cond-mat.str-el
published as In: Quasicrystals - Structure and Physical Properties, ed. H.-R. Trebin (Wiley-VCH, Weinheim, 2003), pp. 210-235 · 27 pages, 27 PostScript figures, LaTeX using vch-book.cls
arxiv created 2002/12/06 · arxiv updated 2009/11/30
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.