Evidence of anomalous dispersion of the generalized sound velocity in glasses

The dynamic structure factor $S(Q,\omega ),$ of vitreous silica, has been measured by inelastic x-ray scattering in the exchanged wave-vector (Q) region $Q=4\mathrm{}–16.5{\mathrm{nm}}^{-1}$ and up to energies $ħ\omega =115\mathrm{}\mathrm{meV}$ in the Stokes side. The unprecedented statistical accuracy in such an extended energy range allows us to accurately determine the longitudinal current spectra and the energies of the vibrational excitations. The simultaneous observation of two excitations in the acoustic region and the persistence of propagating sound waves up to Q values comparable with the (pseudo-)Brillouin-zone edge allow us to observe a positive dispersion in the generalized sound velocity that, around $Q\approx 5{\mathrm{nm}}^{-1},$ varies from $\approx 6500$ to $\approx 9000\mathrm{m}/\mathrm{s};$ this phenomenon was never experimentally observed in a glass.