Regensburg 2004 – scientific programme
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M: Metallphysik
M 29: Quasikristalle I
M 29.3: Talk
Thursday, March 11, 2004, 15:15–15:30, H16
Spectral Properties and Anomalous Diffusion in Octonacci Quasicrystals — •Viktor Cerovski1, Uwe Grimm2, and Michael Schreiber1 — 1Institute für Physik, Technische Universität, D-09107 — 2The Open University, Applied Mathematics Dept., Milton Keynes, MK7 6AA, UK
Properties of the spectrum and characteristics of the eigenstates as well as the anomalous diffusion in octonacci quasicrystals in d=1,2, and 3 dimensions are studied using large-scale numerical calculations of the return probability C(t) and the spreading of the wavepacket d(t) for various values of the hopping strength v. In all dimensions we find C(t)∼ t−δ, with δ < 1 in d=1 and a crossover from δ<1 to δ=1 when v is varied in d=2,3, which is related to the change of spectrum from singular continuous to absolute continuous. The obtained scaling d(t)∼ t−β with 0<β(v)<1 corresponds to the anomalous diffusion, and the values of the exponent suggest that β is dimensionally independent. We show a numerical experiment illustrating some unusual features of the anomalous diffusion of a particle in quasiperiodic systems, such as spreading of the wave packet via a hierarchical sequence of stages in which the packet almost remains localized, as well as the system sensitivity to the position at which a single impurity is added.