Spectral and thermodynamic properties of a Fibonacci quasicrystal

R. K. Pattnaik, E. A. Whittaker

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Abstract

The authors present calculations leading to the phonon density of states in a Fibonacci quasicrystal with fixed end-points. The method is based on a selective elimination process and the results show that the system at low frequencies has the behaviour of a periodic lattice. The high-frequency end of the spectrum is found to have large forbidden bands and in the limit of longer chains the higher-frequency modes are seen to be suppressed. The density of state function has further been used to calculate the heat capacity which is found to be lower than its periodic counterpart. The electronic energy has been calculated from the associated transmission coefficient and the results show that the spectrum is largely band-like, in contrast to the uniform scaling structure which has been reported. It is also shown that in the limit the quasicrystal reduces to a periodic structure: the calculations reproduce the usual results.

Original languageEnglish
Article number016
Pages (from-to)577-588
Number of pages12
JournalJournal of Physics A: Mathematical and General
Volume25
Issue number3
DOIs
StatePublished - 1992

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