Scaling properties of vibrational spectra and eigenstates for tilings models of icosahedral quasicrystals

Joop Los, Ted Janssen & Franz Gähler
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...
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