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

• Received 1 June 1993

DOI:https://doi.org/10.1103/PhysRevLett.72.234