Vibrational modes in aperiodic one-dimensional harmonic chains

The present paper addresses the effect of aperiodicity in one-dimensional oscillatory systems. We study the nature of collective excitations in harmonic chains in the presence of aperiodic and pseudorandom mass distributions. Using the transfer matrix method and exact diagonalization on finite chains, we compute the localization length and the participation number of eigenmodes within the band of allowed frequencies. Our numerical calculations indicate that, for aperiodic arrays of masses, a new phase of extended states appears in this model. For pseudorandom masses distribution, all eigenstates remain localized except the uniform mode (omega=0). Solving numerically the Hamilton equations for momentum and displacement of the chain, we compute the spreading of an initially localized energy excitation. We show that, independent of the kind of initial excitation, an aperiodic structure of masses can induce ballistic transport of energy.