Phonon spectra in one-dimensional quasicrystals |
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Authors: | J M Luck D Petritis |
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Institution: | (1) Service de Physique Théorique, CEN-Saclay, B.P. 2, 91191 Gif-sur-Yvette Cedex, France;(2) CPT, Ecole Polytechnique, 91128 Palaiseaux Cedex, France |
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Abstract: | The propagation of phonons in one-dimensional quasicrystals is investigated. We use the projection method which has been recently proposed to generate almost periodic tilings of the line. We define a natural Laplace operator on these structures, which models phonon (and also tight-binding electron) propagation. The selfsimilarity properties of the spectrum are discussed, as well as some characteristic features of the eigenstates, which are neither extended nor localized. The long-wavelength limit is examined in more detail; it is argued that one is the lower critical dimension for this type of models. |
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Keywords: | Quasicrystals quasiperiodic structures Cantor spectrum density of states critical wave functions |
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