  We study the nature of collective excitations in harmonic chains with masses
exhibiting long-range correlated disorder with power spectrum proportional to
$1/k^{\alpha}$, 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 $\alpha > 1$. 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 $\alpha>1$
due to the presence of extended vibrational modes.
