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 ${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$, a broad frequency regime is found below ${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$ where kl\ensuremath{\le}1 but the phonon transport is still diffusive. The diffusion constant in this regime is given quantitatively by ${\ensuremath{\nu}}_{\mathit{E}}$a/3, where ${\ensuremath{\nu}}_{\mathit{E}}$ is an energy transport velocity derived from a continuity relation.

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