Phonon transport in strong-scattering media

We study phonon transport in random 3D lattices when the mean free path l becomes comparable to the lattice spacing a. Through numerical simulation, it is shown that in contrast to the electronic case, here the Ioffe-Regel criterion is inaccurate in the prediction of phonon localization. By using the Thouless criterion to pinpoint the mobility edge ωc, a broad frequency regime is found below ωc where kl{≤}1 but the phonon transport is still diffusive. The diffusion constant in this regime is given quantitatively by νEa/3, where νE is an energy transport velocity derived from a continuity relation.