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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Luck, J.M., Petritis, D. Phonon spectra in one-dimensional quasicrystals. J Stat Phys 42, 289–310 (1986). https://doi.org/10.1007/BF01127714
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DOI: https://doi.org/10.1007/BF01127714