Vibrational modes in a two-dimensional aperiodic harmonic lattice

We study the nature of collective excitations in classical harmonic lattices with aperiodic and pseudo-random mass distributions. Using a matrix recursive reformulation of the mass displacement equation, we compute the localization length 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. Solving numerically the Hamilton equations for momentum and displacement along the chain, we compute the spreading of an initially localized energy excitation. We find that for sufficient aperiodicity, there is a ballistic propagation of the energy pulse.