Delocalization in harmonic chains with long-range correlated random masses

We study the nature of collective excitations in harmonic chains with masses exhibiting long-range correlated disorder with a power spectrum proportional to ${1/k}^{\ensuremath{\alpha}},$ where k is the wave vector of the modulations on the random masses landscape. Using a transfer-matrix method and exact diagonalization, we compute the localization length and participation ratio of eigenmodes within the band of allowed energies. We find extended vibrational modes in the low-energy region for $\ensuremath{\alpha}g1.$ In order to study the time evolution of an initially localized energy input, we calculate the second moment ${M}_{2}(t)$ of the energy spatial distribution. We show that ${M}_{2}(t),$ besides being dependent of the specific initial excitation and exhibiting an anomalous diffusion for weakly correlated disorder, assumes a ballistic spread in the regime $\ensuremath{\alpha}g1$ due to the presence of extended vibrational modes.