We introduce an unified approach to states of matter (solid, liquid and gas) and describe the thermodynamics of the pressure-temperature phase diagram in terms of phonon excitations. We derive the effective Hamiltonian with low-energy cutoff in two transverse phonon polarisations (phononic band gaps) by breaking the symmetry in phonon interactions. Further, we construct the statistical mechanics of states of aggregation employing the Debye approximation. The introduced formalism covers the Debye theory of solids, the phonon theory of liquids, and thermodynamic limits such as the Delong-Petit thermodynamic limit (cV = 3kB), the ideal gas limit (cV = 3 2 kB) and the new thermodynamic limit (cV = 2kB), dubbed here the Frenkel line thermodynamic limit. We discuss the phonon propagation and localisation effects in liquids above and below the Frenkel line, and explain the "fast sound" phenomenon. As a test for our theory we calculate velocity-velocity autocorrelation and pair distribution functions within the Green-Kubo formalism. We show the consistency between dynamics of phonons and pair correlations in the framework of the unified approach. New directions towards advancements in phononic band gaps engineering, hypersound manipulation technologies and exploration of exotic behaviour of fluids relevant to geo-and planetary sciences are discussed. The presented results are equally important both for practical implications and for fundamental research.*email: bolmatov@bnl.gov arXiv:1512.07191v1 [cond-mat.stat-mech]

In this work we report on inelastic X-ray scattering experiments combined with the molecular dynamics simulations on deeply supercritical Ar. The presented results unveil the mechanism and regimes of sound propagation in the liquid matter, and provide a compelling evidence for the adiabatic-to-isothermal longitudinal sound propagation transition. We introduce a Hamiltonian predicting low-frequency transverse sound propagation gaps which is confirmed by experimental findings and molecular dynamics calculations. As a result, a universal link is established between the positive sound dispersion (PSD) phenomenon and the origin of transverse sound propagation revealing the viscous-to-elastic crossover in liquids. The PSD and transverse phononic excitations evolve consistently with theoretical predictions. Both can be considered as a universal fingerprint of the dynamic response of a liquid which is also observable in a sub-domain of supercritical phase. The simultaneous disappearance of both these effects at elevated temperatures is a manifestation of the Frenkel line. We expect that these findings will advance the current understanding of fluids under extreme thermodynamic conditions.

Supercritical fluids play a significant role in elucidating fundamental aspects of liquid matter under extreme conditions. They have been extensively studied at pressures and temperatures relevant to various industrial applications. However, much less is known about the structural behaviour of supercritical fluids and no structural crossovers have been observed in static compression experiments in any temperature and pressure ranges beyond the critical point. The structure of supercritical state is currently perceived to be uniform everywhere on the pressure-temperature phase diagram, and to change only in a monotonic way even moving around the critical point, not only along isotherms or isobars. Conversely, we observe structural crossovers for the first time in a deeply supercritical sample through diffraction measurements in a diamond anvil cell and discover a new thermodynamic boundary on the pressure-temperature diagram. We explain the existence of these crossovers in the framework of the phonon theory of liquids using molecular dynamics simulations. The obtained results are of prime importance since they imply a global reconsideration of the mere essence of the supercritical phase. Furthermore, this discovery may pave the way to new unexpected applications and to the exploration of exotic behaviour of confined fluids relevant to geo- and planetary sciences.

In this paper we present inelastic X-ray scattering experiments in a diamond anvil cell and molecular dynamic simulations to investigate the behavior of phononic excitations in liquid Ar. The spectra calculated using molecular dynamics were found to be in a good agreement with the experimental data. Furthermore, we observe that, upon temperature increases, a low-frequency transverse phononic gap emerges while high-frequency propagating modes become evanescent at the THz scale. The effect of strong localization of a longitudinal phononic mode in the supercritical phase is observed for the first time. The evidence for the high-frequency transverse phononic gap due to the transition from an oscillatory to a ballistic dynamic regimes of motion is presented and supported by molecular dynamics simulations. This transition takes place across the Frenkel line thermodynamic limit which demarcates compressed liquid and non-compressed fluid domains on the phase diagram and is supported by calculations within the Green-Kubo phenomenological formalism. These results are crucial to advance the development of novel terahertz thermal devices, phononic lenses, mirrors, and other THz metamaterials.

The supercritical state is currently viewed as uniform and homogeneous on the pressuretemperature phase diagram in terms of physical properties. Here, we study structural properties of the supercritical carbon dioxide, and discover the existence of persistent medium-range order correlations which make supercritical carbon dioxide non-uniform and heterogeneous on an intermediate length scale, a result not hitherto anticipated. We report on the carbon dioxide heterogeneity shell structure where, in the first shell, both carbon and oxygen atoms experience gas-like type interactions with short range order correlations, while within the second shell oxygen atoms essentially exhibit liquid-like type of interactions with medium range order correlations due to localisation of transverse-like phonon packets. We show that the local order heterogeneity remains in the three phase-like equilibrium within very wide temperature range. Importantly, we highlight a catalytic role of atoms inside the nearest neighbor heterogeneity shell in providing a mechanism for diffusion in the supercritical carbon dioxide on an intermediate length scale. Finally, we discuss important implications for answering the intriguing question whether Venus may have had carbon dioxide oceans and urge for an experimental detection of this persistent local order heterogeneity.PACS numbers: 05.20. Jj,5.70.Fh, 05.70.+a Unlike the long-range order of ideal crystalline structures, local order is an intrinsic characteristic of soft matter materials and often serves as the key to the tuning of their properties and their possible applications [1][2][3][4][5][6][7][8]. Liquid materials often exhibit medium and/or short range order, such as nanoscale structural motifs, clustering, or local ordering at the level of the atomic coordination spheres. Describing this local order of soft matter systems and supercritical fluids in particular is crucial for understanding the origins of their material properties [9][10][11][12][13][14].