In the Q range where inelastic x-ray and neutron scattering are applied to the study of acoustic collective excitations in fluids, various models of the dynamic structure factor S(Q, omega) generalize in different ways the results obtained from linearized-hydrodynamics theory in the Q-->0 limit. Here we show that the models most commonly fitted to experimental S(Q, omega) spectra can be given a unified formulation. In this way, direct comparisons among the results obtained by fitting different models become now possible to a much larger extent than ever. We also show that a consistent determination of the dispersion curve and of the propagation Q range of the excitations is possible, whichever model is used. We derive an exact formula which describes in all cases the dispersion curve and allows for the first quantitative understanding of its shape, by assigning specific and distinct roles to the various structural, thermal, and damping effects that determine the Q dependence of the mode frequencies. The emerging picture describes the acoustic modes as Q-dependent harmonic oscillators whose characteristic frequency is explicitly renormalized in an exact way by the relaxation processes, which also determine, through the widths of both the inelastic and the elastic lines, the whole shape of collective-excitation spectra.

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The ion dynamics of liquid mercury was investigated by inelastic neutron scattering. By exploiting an optimized high-resolution ( approximately 1 meV) experimental configuration, the dynamic response function was accurately measured. Collective excitations extending up to 0.6 A(-1) were observed with an associated velocity of 2100+/-80 m/s. This value is notably greater than the sound velocity, but it is provided by a simple Bohm-Staver calculation. The latter finding emphasizes those electron-related features in the ion dynamics, which are common to systems as different as polyvalent and alkali metals.

The microscopic ion dynamics of liquid gallium was investigated at 320 K-that is, just above the melting point-and 970 K by inelastic neutron scattering experiments and molecular dynamics simulations. The high quality of the experimental data allowed the observation of density fluctuation modes extending up to 1.0 Å −1 and existing at both temperatures. At melting, an acousticlike mode propagating with a velocity definitely exceeding the sound velocity was observed, in agreement with the results of a recent inelastic x-ray scattering experiment. The mode velocity and damping were found to be almost temperature independent. The experimental response function was compared with the results of a molecular dynamics simulation, based on a simple model for the effective ion-ion potential which, however, did not contain any temperature-dependent parameter. The result worth noting is that, despite the simple potential, the simulation was capable to reproduce all the observed features of the measured dynamicstructure factor quantitatively and at both the temperatures.

The velocity autocorrelation function (VAF), a key quantity in the atomic-scale dynamics of fluids, has been the first paradigmatic example of a long-time tail phenomenon, and much work has been devoted to detecting such long-lasting correlations and understanding their nature. There is, however, much more to the VAF than simply the evidence of this long-time dynamics. A unified description of the VAF from very short to long times, and of the way it changes with varying density, is still missing. Here we show that an approach based on very general principles makes such a study possible and opens the way to a detailed quantitative characterization of the dynamical processes involved at all time scales. From the analysis of molecular dynamics simulations for a slightly supercritical Lennard-Jones fluid at various densities, we are able to evidence the presence of distinct fast and slow decay channels for the velocity correlation on the time scale set by the collision rate. The density evolution of these decay processes is also highlighted. The method presented here is very general, and its application to the VAF can be considered as an important example.