Phonon localization in quasiperiodic systems

The effects of anharmonic interactions on the localization of phonons in quasiperiodic systems are studied by looking at the transmittance, Lyapunov exponent, participation ratio and energy-level-spacing distribution, within the rotating-wave approximation and first-order perturbation theory. For Fibonacci chains, a power-law distribution is found in the small-spacing region, since the eigenstates are critical. Even within first perturbation stages, anharmonic contributions do clearly manifest, weakening the level clustering behavior, contrary to the periodic case where the distribution is insensitive to weak anharmonic interactions. These results suggest a structural instability of the self-similar vibrational spectrum in quasiperiodic systems.