Numéro |
J. Phys. I France
Volume 3, Numéro 1, January 1993
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Page(s) | 107 - 134 | |
DOI | https://doi.org/10.1051/jp1:1993120 |
J. Phys. I France 3 (1993) 107-134
Scaling properties of vibrational spectra and eigenstates for tiling models of icosahedral quasicrystals
J. Los1, Janssen1 and F. Gähler21 Institute for Theoretical Physics, University of Nijmegen, 6525 ED Nijmegen, The Netherlands
2 Département de Physique Théorique, Université de Genève, 24 quai Ernest Ansermet, CH-1211 Genève, Switzerland
(Received 11 August 1992, accepted in final form 1 October 1992)
Abstract
A study of the lattice dynamics of 3-dimensional tilings modelling icosahedral quasicrystals is presented, both in commensurate
approximations and cluster approximations. In the commensurate approximation this is done for three different types of tilings,
namely: perfect, symmetrized and randomized approximants. It turns out that the density of states as a function of frequency
is smoothed by randomization. A multifractal analysis of the spectrum shows that mainly at high frequencies the scaling behaviour
of the spectrum is different from that for periodic structures. Also the eigenvectors are examined and it appears that only
the states at the very upper end of the spectrum have a relatively small participation fraction, i.e. are more localized.
The majority of the states scale as normal extended states, as is shown by a multifractal analysis of the eigenvectors for
systematic approximants. Also, for most of the states localization is not enhanced by randomization. Throughout the paper
the results are compared with those for a 1-dimensional quasicrystal, the Fibonacci chain.
63.20D
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