Ioffe-Regel crossover for plane-wave vibrational excitations in vitreous silica

The first Ioffe-Regel crossover for vibrational plane waves (when wavelength and mean free path are comparable) has been investigated theoretically for models of vitreous silica $(v-{\mathrm{SiO}}_2)$ constructed by molecular dynamics. The crossover is found to be from a state of weak scattering to one of strong scattering, not vibrational localization. Three methods have been used to investigate the crossover: an analysis of the time evolution of a vibrational plane wave, a spectral-density analysis in frequency space, and an analysis of the final scattered state in momentum space. The first Ioffe-Regel crossover frequency is found by all three methods to be $\sim 1$ THz for $v-{\mathrm{SiO}}_2,$ for both longitudinal and transverse polarizations. A second Ioffe-Regel crossover occurs at $\sim 6$ THz for $v-{\mathrm{SiO}}_2,$ corresponding to the frequency at which the mean free path is minimal (comparable to the interatomic spacing), and the spectral-density width is maximal (comparable to the frequency range of the vibrational density of states).