A theory for the vibrational dynamics in disordered solids [W. Schirmacher, Europhys. Lett. 73, 892 (2006), based on the random spatial variation of the shear modulus, has been applied to determine the wave vector (k) dependence of the Brillouin peak position (Omega(k)) and width (Gamma(k)), as well as the density of vibrational states [g(omega)], in disordered systems. As a result, we give a firm theoretical ground to the ubiquitous k2 dependence of Gamma(k) observed in glasses. Moreover, we derive a quantitative relation between the excess of the density of states (the boson peak) and Gamma(k), two quantities that were not considered related before. The successful comparison of this relation with the outcome of experiments and numerical simulations gives further support to the theory.

According to textbook definitions 1 , there exists no physical observable able to distinguish a liquid from a gas beyond the critical point, and hence only a single fluid phase is defined. There are, however, some thermophysical quantities, having maxima that define a line emanating from the critical point, named 'the Widom line' 2 in the case of the constant-pressure specific heat. We determined the velocity of nanometric acoustic waves in supercritical fluid argon at high pressures by inelastic X-ray scattering and molecular dynamics simulations. Our study reveals a sharp transition on crossing the Widom line demonstrating how the supercritical region is actually divided into two regions that, although not connected by a first-order singularity, can be identified by different dynamical regimes: gas-like and liquid-like, reminiscent of the subcritical domains. These findings will pave the way to a deeper understanding of hot dense fluids, which are of paramount importance in fundamental and applied sciences. Throughout the past century great effort was devoted to the investigation of the physics of fluid systems: all of their thermodynamical properties in the phase diagram below the critical point are nowadays well known 3. On the other hand, experimental studies in the supercritical region have been limited so far, owing to technical difficulties. The fluid pressure-temperature (P-T) phase diagram includes a subcritical region with two different phases (liquid and gas, separated by the liquid-vapour coexistence line) and a single-phase supercritical region. Structural and dynamical investigations, aiming to extend the study of the fluid phase diagram well beyond the critical point play a crucial role in many fundamental and applied research fields, such as condensedmatter physics, Earth and planetary science, nanotechnology and waste management 4-8. From an experimental point of view, the challenge is to close the gap between studies on fluid and solid phases using diamond anvil cell (DAC) techniques 9-12 and studies on hot dense fluids by shock waves 13,14. As this gap typically overlaps with the supercritical fluid region, it is crucial to track the evolution of transport properties of fluids beyond the critical point. In the specific case of acoustic waves, most of the liquids show the so-called positive dispersion. This is an increase of the speed of sound as a function of wavelength from the continuum limit (λ → ∞)-in which the acoustic waves propagate adiabatically-to the short-wavelength limit, that is, on approaching the interparticle distances 15-17. The ultimate origin of this effect can be traced back to the presence of one (or more)

The experimental results relevant for the understanding of the microscopic dynamics in liquid metals are reviewed, with special regards to the ones achieved in the last two decades. Inelastic Neutron Scattering played a major role since the development of neutron facilities in the sixties. The last ten years, however, saw the development of third generation radiation sources, which opened the possibility of performing Inelastic Scattering with X rays, thus disclosing previously unaccessible energy-momentum regions. The purely coherent response of X rays, moreover, combined with the mixed coherent/incoherent response typical of neutron scattering, provides enormous potentialities to disentangle aspects related to the collectivity of motion from the single particle dynamics. If the last twenty years saw major experimental developments, on the theoretical side fresh ideas came up to the side of the most traditional and established theories. Beside the raw experimental results, therefore, we review models and theoretical approaches for the description of microscopic dynamics over different length-scales, from the hydrodynamic region down to the single particle regime, walking the perilous and sometimes uncharted path of the generalized hydrodynamics extension. Approaches peculiar of conductive systems, based on the ionic plasma theory, are also considered, as well as kinetic and mode coupling theory applied to hard sphere systems, which turn out to mimic with remarkable detail the atomic dynamics of liquid metals. Finally, cutting edges issues and open problems, such as the ultimate origin of the anomalous acoustic dispersion or the relevance of transport properties of a conductive systems in ruling the ionic dynamic structure factor are discussed.

When a liquid is cooled below its melting temperature, it usually crystallizes. However, if the quenching rate is fast enough, the system may remain in a disordered state, progressively losing its fluidity upon further cooling. When the time needed for the rearrangement of the local atomic structure reaches approximately 100 seconds, the system becomes "solid" for any practical purpose, and this defines the glass transition temperature Tg. Approaching this transition from the liquid side, different systems show qualitatively different temperature dependencies of the viscosity, and accordingly they have been classified by introducing the concept of "fragility." We report experimental observations that relate the microscopic properties of the glassy phase to the fragility. We find that the vibrational properties of the glass well below Tg are correlated with the fragility value. Consequently, we extend the fragility concept to the glassy state and indicate how to determine the fragility uniquely from glass properties well below Tg.