Dresden 2000 – scientific programme
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MP: Theoretische und Mathematische Grundlagen der Physik
MP 1: Quantenchaos
MP 1.5: Talk
Monday, March 20, 2000, 15:00–15:15, W A317
Energy spectra, wavefunctions, and quantum diffusion for quasiperiodic tight-binding models — •U. Grimm1, H. Q. Yuan1,2, P. Repetowicz1, and M. Schreiber1 — 1Institut für Physik, Technische Universität, 09107 Chemnitz, Germany — 2Department of Physics, Xiangtan University, Xiangtan 411105, P. R. China
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 Schrödinger 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 C(t)∼ t−δ and d(t) ∼ tβ. For the octonacci chain, 0<δ<1, whereas for the labyrinth tiling a crossover is observed from δ=1 to 0<δ<1 with increasing modulation strength. Corresponding to the multifractal eigenstates, we obtain anomalous diffusion with 0<β<1 for both systems. Moreover, we find that the behavior of C(t) and d(t) is independent of the shape and the location of the initial wavepacket.