Phonon properties of a class of one-dimensional quasiperiodic systems

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Abstract
The Kohmoto-Kadanoff-Tang renormalization-group method is extended to study the phonon properties of a class of one-dimensional quasiperiodic systems. Two models are employed, which correspond to the equation of motion for phonon problems with spring constants equal and two types of masses arranged successively in generalized Fibonacci sequences, and that for phonon problems with masses equal and two types of spring constants in generalized Fibonacci sequences. It is shown that the phonon spectra of the quasiperiodic systems are Cantor-like and do not have uniform scalings. Particularly the low-lying phonon excitations tend to be extended in the low-frequency limit.