## 2 Measurements of the _THz_ Spectrum of Noble Gases up to the 1990s
### The Onset of a Positive Sound Dispersion in Liquid Noble Gases  
In the various works on noble gases reported in literature, it was observed that transport parameters drastically change upon relatively moderate \(P\) and \(T\) variations. This may not be surprising, given that the large compressibility of these systems leads to substantial variations of inter-particle distances and, consequently, of interaction strengths. For instance, clear transformations were observed in the \(Q\)-dependence of the acoustic frequency and damping when measured either in the liquid or in the supercritical phase. In particular, it was generally found that, in liquid Ne and Ar [43; 44; 58; 68]\(\omega_{s}\) systematically exceeds the hydrodynamic prediction at low/intermediate \(Q\)s. A similar effect was also observed in liquid He [48; 69; 70], although the quantum character of this sample makes this finding less straightforward to interpret. Furthermore, in liquid phase samples an \"anomalous\" \(Q\)-dependence was also reported for the sound absorption coefficient, as derived from the width of inelastic peaks, \(z_{s}\). Conversely, all these dispersive effects seem to disappear at extreme supercritical conditions [40; 62; 65; 66]. These trends are clearly exemplified by Figure 9, which compares spectral parameters obtained in supercritical [65] and liquid [71] neon. Overall, data reported therein indicate that, while in liquid Ne the sound frequency (\(\omega_{s}\)) and absorption (\(z_{s}\)) at low \(Q\)s are, respectively, higher and lower than predicted by Equations (3a-c), no substantial discrepancy is instead observed in supercritical Ne. In Figure 9 it can be also noticed that for the latter sample the agreement with the simple hydrodynamic prediction is excellent up to \(Q\approx 7.5\) nm\({}^{-1}\). Figure 8: The relevant transport parameters deduced from the fits of of IXS spectra of deeply supercritical neon [67] and those of \(MD\) spectra from a Lennard Jones model representative of the same sample [65]. The shadowed area roughly locates the transition from the extended hydrodynamics and the mesoscopic regime. Horizontal dashed lines represent the macroscopic (hydrodynamic) values deduced from thermodynamic [59] and US spectroscopy data [28]. As mentioned, \"anomalous\" dispersive effects observed for the liquid sample can be ascribed to the onset of a viscoelastic response induced by the coupling with a relaxation process. To illustrate this point, it is useful to recognize that, in a spectroscopy experiment, the scattering-excited acoustic waves cause a time-dependent perturbation of the local equilibrium of the target sample. As a response, decay channels redistribute the energy carried by the acoustic wave toward some internal degrees of freedom of the fluid. These energy rearrangements ultimately drive the sample to relax in a new local equilibrium within a timescale \(\tau\). Two limiting scenarios can thus occur: (1) the time-dependent acoustic perturbation has period, \(2\pi/\omega_{s}\), much longer than any internal degrees of freedom of the system. Under these conditions, the latter relaxes to equilibrium \"instantaneously\" (_i.e._, within a timescale \(\tau<<1/\omega_{s}\)) and the acoustic propagation essentially takes place over successive equilibrium states (viscous limit); (2) Conversely, if the acoustic wave has an extremely short period, it \"perceives\" internal rearrangements as frozen-like (\(\tau>>1/\omega_{s}\)) and does not couple with them. Consequently, the acoustic propagation is elastic, _i.e._, it occurs with virtually no energy loss (elastic limit). Therefore, when a relaxation is active, the response of a system to the acoustic propagation depends on how the acoustic frequency, \(\omega_{s}\), compares to the relaxation time. When \(\omega_{s}\) increases from the viscous (\(\omega_{s}\tau<<1\)) to the elastic limit (\(\omega_{s}\tau>>1\)), the viscoelastic transition manifests itself through a systematic decrease of acoustic dissipation and a corresponding increase of sound velocity.