## 5 2006-Present: Toward a New Vision of the Supercritical Phase  
Based on the results previously discussed, it may be natural to conclude that the viscoelastic behavior is a dynamic fingerprint of the liquid phase, which disappears when supercritical conditions are reached. Indeed, the _PSD_ has often been considered an almost universal feature of liquid aggregates, since almost ubiquitously observed in liquid systems as disparate as, for instance hard sphere [102] and Lennard-Jones models [103], noble gases [43; 46; 71], as well as diatomic [8], associated [12; 13] and glass forming [15; 17] systems. Its disappearance at deeply supercritical conditions was considered as an indication that supercritical fluids do not exhibit a high frequency viscoelasticity. The actual test of this conjecture requires a thorough investigation of the _THz_ spectral shape of supercritical fluid at extreme \(P\) and \(T\) values. For many decades, this has been an almost prohibitive task, owing to a number of experimental difficulties. As mentioned, the development of _IXS_ brought about a substantial narrowing of the beam cross section, while the improved performance of undulators and crystal optics have dramatically enhanced the flux achievable in ordinary _THz_ spectroscopy measurements. This paved the way to new class of _IXS_ experiments at extreme pressures based upon the use of diamond anvil cells (_DACs_). Taking advantage of this opportunity, an _IXS_ _DACs_ measurement on deeply supercritical oxygen demonstrated that a _PSD_ of about \(20\%\) in amplitude is visible at temperatures as high as nearly twice the critical one [104]. The results of this measurement imposed a global revision of the previous idea that _THz_ viscoelasticity phenomena could represent a dynamical fingerprint of the liquid phase. Another breakthrough came from a successive joint _IXS_ and _MD_ work on Ar at extreme pressures [105], which showed the occurrence of a dynamic transition upon crossing a boundary in the supercritical domain. A dramatic reduction in the amplitude of _PSD_ was, in fact, observed upon crossing the Widom line [106] and was interpreted as a crossover between a \"liquid like\" and a \"gas like\" sub-regions of the supercritical phase. As a reminder, the Widom line is defined as the locus of specific heat maxima, which emanates from the critical point toward the supercritical domain with essentially the same slope as the coexistence line. For this reason, the Widom line is often considered a \"prosecution\" of the coexistence line beyond the critical point. Perhaps the most intriguing aspect of these results is that the mere existence of a boundary in the thermodynamic plane challenges the long-standing vision of the supercritical phase as intrinsically uniform [107], thus opening up unexplored theoretical scenarios and novel investigation opportunities. Another important result came from the recent conclusion that PSD effects are intimately related to the onset of shear propagation. The occurrence of a shear mode propagation in argon was first demonstrated by a _MD_ simulation on a Lennard Jones Ar [41; 42]. As a common result, it was observed that at some wavelengths transverse current spectra bore evidence for a well-defined maximum, indicating the occurrence of a shear mode propagation. More recently, a joint _IXS_ and _MD_ simulation work on deeply supercritical argon [108] evidenced a close connection between the ability of a fluid system to support shear mode propagation and the presence of a sizeable _PSD_. In this work _IXS_ spectra were measured along a nearly isobaric path (with \(P\approx 1\) GPa) with \(T\) spanning the 300 K-436 K temperature range, while _MD_ data spanned the same isobar within a larger \(T\)-interval (up to 800 K). As a result, it was there shown that the disappearance of the _PSD_ in deep supercritical conditions is accompanied by a parallel shear modes overdamping (see Figure 14).