The nature of the phonon eigenstates in quasiperiodic chains (the role of Fibonacci lattices)

Using the forced oscillator method (FOM) and the transfer-matrix technique, we numerically investigate the nature of the phonon states and the wave propagation, in the presence of an external force, in the chains composed of Fibonacci lattices of type site, bond and mixing models, as the quasiperiodic systems. Calculating the Lyapunov exponent and the participation ratio, we also study the localization properties of phonon eigenstates in these chains. The focus is on the significant relationship between the transmission spectra and the nature of the phonon states. Our results show that in the presence of the Fibonacci lattices, at low and medium frequencies the spectra of the quasiperiodic systems are not much different from those of the periodic ones and the corresponding phonon eigenstates are extended. However, the numerical results of the calculations of the transmission coefficient T(ω), the inverse Lyapunov exponent Γ(ω)-1 and the participation ratio PR(ω) show that at high frequencies, in contrast with similar ones in disordered systems, the phonon eigenstates are delocalized.