Phonon spectrum in a nanoparticle mechanically coupled to a substrate

We calculate the vibrational density-of-states in an insulating nanoparticle that is in weak mechanical contact with a semi-infinite substrate. The work is motivated by a recent experiment by Yang et al., where the low-energy phonon density-of-states of Y2O3 nanoparticles doped with Eu3+ was measured. Preliminary results presented here, based on the conventional quasiparticle-pole approximation for the phonon propagator, are in reasonable agreement with experiment.