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High-resolution, inelastic x-ray scattering measurements of the dynamic structure factor S(Q,\omega) of liquid water have been performed for wave vectors Q between 4 and 30 nm^-1 in distinctly different thermodynamic conditions (T= 263 - 420 K ; at, or close to, ambient pressure and at P = 2 kbar). In agreement with previous inelastic x-ray and neutron studies, the presence of two inelastic contributions (one dispersing with Q and the other almost non-dispersive) is confirmed. The study of their temperature- and Q-dependence provides strong support for a dynamics of liquid water controlled by the structural relaxation process. A viscoelastic analysis of the Q-dispersing mode, associated with the longitudinal dynamics, reveals that the sound velocity undergoes the complete transition from the adiabatic sound velocity (c_0) (viscous limit) to the infinite frequency sound velocity (c_\infinity) (elastic limit). On decreasing Q, as the transition regime is approached from the elastic side, we observe a decrease of the intensity of the second, weakly dispersing feature, which completely disappears when the viscous regime is reached. These findings unambiguously identify the second excitation to be a signature of the transverse dynamics with a longitudinal symmetry component, which becomes visible in the S(Q,\omega) as soon as the purely viscous regime is left., Comment: 28 pages, 12 figures

The dynamic structure factor, S(Q,w), of vitreous silica, has been measured by inelastic X-ray scattering in the exchanged wavevector (Q) region Q=4-16.5 nm-1 and up to energies hw=115 meV in the Stokes side. The unprecedented statistical accuracy in such an extended energy range allows 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 to observe a positive dispersion in the generalized sound velocity that, around Q=5 nm-1, varies from 6500 to 9000 m/s: this phenomenon was never experimentally observed in a glass., Comment: 5 pages, 3 figures. To appear in Phys. Rev. B

Inelastic X-ray Scattering measurements of the dynamics structure factor have bene performed on vitreous Beryllium Fluoride ({\it v-}BeF$_2$) at $T$=297 K in the momentum transfer, $Q$, range $Q$=1.5$\div$10 nm$^{-1}$. We find evidence of well defined high frequency acoustic modes. The energy position and linewidth of the excitations disperse with $Q$ as $\propto Q$ and $\propto Q^2$, respectively up to about one half of the first maximum of the static structure factor. Their magnitude compare favorably with low-frequency sound velocity and absorption data. The results indicate worth mentioning similarities of the high frequency collective dynamics of different network forming glasses such as {\it v-}B$_2$O$_3$ and {\it v-}SiO$_2$., Comment: 17 pages, 5 .ps figs

The dynamic structure factor of glassy and liquid glycerol has been measured by inelastic X-ray scattering in the exchanged momentum ($Q$) region $Q$=2$\div$23 nm$^{-1}$ and in the temperature range 80$\div$570 K. Beside the propagating longitudinal excitations modes, at low temperature the spectra show a second non $Q$-dispersing peak at $\hbar \Omega_T$$\approx$8.5 meV. We assign this peak to the transverse dynamics that, in topologically disordered systems, acquires a longitudinal symmetry component. This assignment is substantiated by the observation that, in the liquid, this peak vanishes when the structural relaxation time $\tau_\alpha$ approaches $\Omega_T^{-1}$, a behavior consistent with the condition $\tau_\alpha \Omega_T^{-1}$$>>$1 required for the existence of a transverse-like dynamics in the liquid state., Comment: 13 pages, 5 PostScript figures