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 $Q\to 0$ 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.

We have measured the intermolecular structure factor and its thermodynamic derivatives in the vicinity of the triple point of liquid deuterium, using two different neutron sources. We have also derived the same quantities by using path integral Monte Carlo computer simulations. For the structure factor, we find good agreement between the experiments and the simulation results, using either the Lennard-Jones or a more realistic phenomenological potential. However, when the comparison is extended to the thermodynamic derivatives, a clear difference is observed between the two different intermolecular potentials.

A detailed inelastic neutron scattering investigation of the THz dynamics of liquid zinc is presented. The observed $Q$ dependence clearly reveals the existence of a complex dynamics made up of two distinct excitations. The highest energy mode is the prolongation of the longitudinal acoustic density fluctuations whereas the comparison with the phonon dynamics of crystalline hcp zinc suggests a transverse acousticlike nature for the second one. This mode seems related to peculiar anisotropic interactions, possibly connected to the behavior of the crystalline phase.

We performed a neutron Brillouin scattering determination of the dynamic structure factor of liquid gold in the wave-vector range $6<Q<16$ nm${}^{$-${}1}$. Despite the experimental difficulties due to the considerable neutron absorption and the high melting temperature of the sample, a non-negligible coherent signal could successfully be extracted and revealed the presence of underdamped ion density-fluctuation modes in the whole $Q$ range of the experiment. The quality of the data further enabled a significant comparison with the results of ab initio simulations for liquid gold. The agreement found between neutron and simulation data not only provides a necessary test of ab initio methods still limited to the use of few hundreds atoms, but also reasonably justifies a thorough analysis of the simulated dynamics in the extended $Q$ range that can be more comfortably accessed by calculations. A viscoelastic modeling of the simulated spectra proves to be appropriate and, surprisingly, the so-derived salient dynamic features of liquid gold show an overall $Q$ behavior globally similar to that already found for insulating liquids. The present and recent results on the collective properties of simple liquids thus lead us to embrace the concept that simple liquid metals and insulators, at the nanometer length scale, are dynamically much less different than expected.

Extending a preceding study of the velocity autocorrelation function (VAF) in a simulated Lennard-Jones fluid [ Phys. Rev. E 92, 042166 (2015)] to cover higher-density and lower-temperature states, we show that the recently demonstrated multiexponential expansion method allows for a full account and understanding of the basic dynamical processes encompassed by a fundamental quantity as the VAF. In particular, besides obtaining evidence of a persisting long-time tail, we assign specific and unambiguous physical meanings to groups of exponential modes related to the longitudinal and transverse collective dynamics, respectively. We have made this possible by consistently introducing the interpretation of the VAF frequency spectrum as a global density of states in fluids, generalizing a solid-state concept, and by giving to specific spectral components, obtained through the VAF exponential expansion, the corresponding meaning of partial densities of states relative to specific dynamical processes. The clear identification of a high-frequency oscillation of the VAF with the near-top excitation frequency in the dispersion curve of acoustic waves is a neat example of the power of the method. As for the transverse mode contribution, its analysis turns out to be particularly important, because the multiexponential expansion reveals a transition marking the onset of propagating excitations when the density is increased beyond a threshold value. While this finding agrees with the recent literature debating the issue of dynamical crossover boundaries, such as the one identified with the Frenkel line, we can add detailed information on the modes involved in this specific process in the domains of both time and frequency. This will help obtain a still missing full account of transverse dynamics, in both its nonpropagating and propagating aspects which are linked through dynamical transitions depending on both the thermodynamic states and the excitation wave vectors.