Vibrational modes in harmonic chains with diluted disorder

We study the nature of collective excitations in harmonic chains with diluted disorder. Using a transfer matrix method, we compute the localization length of eigenmodes within the band of allowed energies in order to investigate the new extended states which appear in this model. To follow the time evolution of an initially localized energy input, we calculate the second moment M2(t) of the energy spatial distribution. We found that for an impulse initial excitation, the super-diffusive energy spread is not affected by the presence of new resonant modes. However, the energy spread becomes faster for a displacement excitation.