Phonon diffusion in harmonic and anharmonic one-dimensional quasiperiodic lattices

The phonon diffusivity in one-dimensional quasiperiodic lattices is studied using harmonic and inharmonic Hamiltonians. This study is performed by solving the equations of motion using a time discretization and the leap-frog algorithm. For the case of harmonic Hamiltonians, the results show that the variance of a wave packet in quasiperiodic systems is proportional to the time, as in a periodic lattice, but their diffusion constant is lower. This behaviour is qualitatively different from the electronic case, in which the variance increases as a power law of the time, with an exponent that depends upon the strength of the quasiperiodic potential. The difference between the electronic and phonon problems seems to be related to the localization degree of their long wavelength modes. In this limit, we present the time evolution of the phonon wave extension, showing a finite sound velocity given by averaged lattice parameters. Finally, for the inharmonic case, we found that the phonon diffusivity decreases as the nonlinear perturbation grows.