Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
1999-12-10
Phys. Rev. B 62 (2000) 15569-15578
Physics
Condensed Matter
Disordered Systems and Neural Networks
24 pages, REVTeX, 10 PostScript figures included, major revision, new results added
Scientific paper
10.1103/PhysRevB.62.15569
We study energy spectra, eigenstates and quantum diffusion for one- and two-dimensional quasiperiodic tight-binding models. As our one-dimensional model system we choose the silver mean or `octonacci' chain. The two-dimensional labyrinth tiling, which is related to the octagonal tiling, is derived from a product of two octonacci chains. This makes it possible to treat rather large systems numerically. For the octonacci chain, one finds singular continuous energy spectra and critical eigenstates which is the typical behaviour for one-dimensional Schr"odinger operators based on substitution sequences. The energy spectra for the labyrinth tiling can, depending on the strength of the quasiperiodic modulation, be either band-like or fractal-like. However, the eigenstates are multifractal. The temporal spreading of a wavepacket is described in terms of the autocorrelation function C(t) and the mean square displacement d(t). In all cases, we observe power laws for C(t) and d(t) with exponents -delta and beta, respectively. For the octonacci chain, 0
Grimm Uwe
Repetowicz Przemyslaw
Schreiber Michael
Yuan Huiqiu
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