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We use extensive molecular dynamics simulations to calculate thermal conductivity and thermal diffusivity in two common molten salts, LiF and KCl. Our analysis includes the total thermal conductivity and intrinsic conductivity involving mass currents measured experimentally. The latter shows good agreement with the experimental data. We also calculate their key thermodynamic properties such as constant-pressure and constant-volume specific heats. We subsequently compare the results to the lower bound for thermal diffusivity expressed in terms of fundamental physical constants. Using this comparison and recent theoretical insights into thermodynamic and transport properties in liquids, we interpret thermal properties on the basis of atomistic dynamics and phonon excitations. We finally find that thermal diffusivity of molten salts is close to their kinematic viscosity., Comment: 8 pages, 4 figures

Approaching the problem of understanding fundamental physical constants (FPCs) started with discussing the role these constants play in high-energy nuclear physics and astrophysics. Condensed matter physics was relatively unexplored in this regard. More recently, it was realised that FPCs set lower or upper bounds on key condensed matter properties. In this Perspective, we discuss a wider role played by FPCs in condensed matter physics: at given environmental conditions, FPCs set the observability and operation of entire physical effects and phenomena. We discuss second-order phase transitions including structural and superconducting transitions and first-order transitions including melting and boiling. We also discuss metastable states, transitions between them, chemical reactions and their products. An interesting byproduct of this discussion is that the order of magnitude of the transition temperature can be calculated from FPCs. We show that the new states emerging as a result of various transitions increase the phase space and entropy. Were FPCs to take different values, these transitions would become inoperative at our environmental conditions and the new states due to these transitions would not emerge. This suggests that the current values of FPCs, by enabling various transitions and reactions which give rise to new states, promote entropy increase. We propose that this is a general effect that applies to different levels of structure in the Universe.

Fundamental physical constants govern key effects in high-energy particle physics and astrophysics, including the stability of particles, nuclear reactions, formation and evolution of stars, synthesis of heavy nuclei and emergence of stable molecular structures. Here, we show that fundamental constants also set an upper bound for the frequency of phonons in condensed matter phases, or how rapidly an atom can vibrate. This bound is in agreement with \textit{ab initio} simulations of atomic hydrogen and high-temperature hydride superconductors, and implies an upper limit to the superconducting transition temperature $T_c$ in condensed matter. Fundamental constants set this limit to the order of 10$^2-10^3$ K. This range is consistent with our calculations of $T_c$ from optimal Eliashberg functions. As a corollary, we observe that the very existence of the current research of finding $T_{\mathrm{c}}$ at and above $300$ K is due to the observed values of fundamental constants. We finally discuss how fundamental constants affect the observability and operation of other effects and phenomena including phase transitions.

Recently, it was realised that liquid viscosity has a lower bound which is nearly constant for all liquids and is governed by fundamental physical constants. This was supported by experimental data in noble and molecular liquids. Here, we perform large-scale molecular dynamics simulations to ascertain this bound in two other important liquid types: the ionic molten salt system LiF and metallic Pb. We find that these ionic and metallic systems similarly have lower viscosity bounds corresponding to the minimum of kinematic viscosity of about 10$^{-7}$ $\frac{{\rm m}^2}{\rm s}$. We show that this agrees with experimental data in other systems with different structures and bonding types, including noble, molecular, metallic and covalent liquids. This expands the universality of viscosity bounds into the main system types known., Comment: 6 pages, 7 figures

Our understanding of the three basic states of matter (solids, liquids and gases) is based on temperature and pressure phase diagrams with three phase transition lines: solid-gas, liquid-gas and solid-liquid lines. There are analytical expressions $P(T)$ for the first two lines derived on a purely general-theoretical thermodynamic basis. In contrast, there exists no similar function for the third, melting, line (ML). Here, we develop a general two-phase theory of MLs and their analytical form. This theory predicts the parabolic form of the MLs for normal melting, relates the MLs to thermal and elastic properties of liquid and solid phases and quantitatively agrees with experimental MLs in different system types. We show that the parameters of the ML parabola are governed by fundamental physical constants. In this sense, parabolic MLs possess universality across different systems., Comment: minor additions and closer to the journal version

Physics-based first-principles pressure-volume-temperature equations of state (EOS) exist for solids and gases but not for liquids due to the long-standing fundamental problems involved in liquid theory. Current EOS models that are applicable to liquids and supercritical fluids at liquid-like density under conditions relevant to planetary interiors and industrial processes are complex empirical models with many physically meaningless adjustable parameters. Here, we develop a generally applicable physics-based (GAP) EOS for liquids including supercritical fluids at liquid-like density. The GAP equation is explicit in the internal energy, and hence links the most fundamental macroscopic static property of fluids, the pressure-volume-temperature EOS, to their key microscopic property: the molecular hopping frequency or liquid relaxation time, from which the internal energy can be obtained. We test our GAP equation against available experimental data in several different ways and find good agreement. Our GAP equation, unavoidably and similarly to solid EOS, contains a semi-empirical term giving the energy of the static sample as a function of volume only (E_ST(V)). Our testing includes studies along isochores, in order to examine the validity of the GAP equation independently of the validity of any function we may choose to utilize for E_ST(V). The only other adjustable parameter in the equation is the Gruneisen parameter for the fluid. We observe that the GAP equation is similar to the Mie-Gruneisen solid EOS in a wide range of the liquid phase diagram. This similarity is ultimately related to the condensed state of these two phases. On the other hand, the differences between the GAP equation and EOS for gases are fundamental. Finally, we identify the key gaps in the experimental data that need to be filled in to proceed further with the liquid EOS.

Understanding the values and origin of fundamental physical constants, one of the grandest challenges in modern science, has been discussed in particle physics, astronomy and cosmology. More recently, it was realised that fundamental constants have a bio-friendly window set by life processes involving motion and flow. This window is related to intrinsic fluid properties such as energy and length scales in condensed matter set by fundamental constants. Here, we discuss important extrinsic factors governing the viscosity of complex fluids operating in life processes due to collective effects. We show that both extrinsic and intrinsic factors affecting viscosity need to be taken into account when estimating the bio-friendly range of fundamental constants from life processes, and our discussion provides a straightforward recipe for doing this. We also find that the relative role of extrinsic and intrinsic factors depends on the range of variability of these intrinsic and extrinsic factors. Remarkably, the viscosity of a complex fluid such as blood with significant extrinsic effects is not far from the intrinsic viscosity calculated using the fundamental constants only, and we discuss the reason for this in terms of dynamics of contact points between cells., Comment: arXiv admin note: text overlap with arXiv:2307.05273

Of the three basic states of matter, liquid is perhaps the most complex. While its flow properties are described by fluid mechanics, its thermodynamic properties are often neglected, and for many years it was widely believed that a general theory of liquid thermodynamics was unattainable. In recent decades that view has been challenged, as new advances have finally enabled us to understand and describe the thermodynamic properties of liquids. This book explains the recent developments in theory, experiment and modelling that have enabled us to understand the behaviour of excitations in liquids and the impact of this behaviour on heat capacity and other basic properties. Presented in plain language with a focus on real liquids and their experimental properties, this book is a useful reference text for researchers and graduate students in condensed matter physics and chemistry, as well as for advanced courses covering the theory of liquids., Comment: 35 pages, 3 figures. Preface, Introduction and experimental section

Viewed as one of the grandest questions in modern science, understanding fundamental physical constants has been discussed in high-energy particle physics, astronomy and cosmology. Here, I review how condensed matter and liquid physics gives new insights into fundamental constants and their tuning. This is based on two observations: first, cellular life and the existence of observers depend on viscosity and diffusion. Second, the lower bound on viscosity and upper bound on diffusion are set by fundamental constants, and I briefly review this result and related recent developments in liquid physics. I will subsequently show that bounds on viscosity, diffusion and the newly introduced fundamental velocity gradient in a biochemical machine can all be varied while keeping the fine-structure constant and the proton-to-electron mass ratio intact. This implies that it is possible to produce heavy elements in stars but have a viscous planet where all liquids have very high viscosity (for example that of tar or higher) and where life may not exist. Knowing the range of bio-friendly viscosity and diffusion, we will be able to calculate the range of fundamental constants which favor cellular life and observers and compare this tuning with that discussed in high-energy physics previously. This invites an inter-disciplinary research between condensed matter physics and life sciences, and I formulate several questions that life science can address. I finish with a conjecture of multiple tuning and an evolutionary mechanism.

The problem of understanding fundamental physical constants was discussed in particle physics, astronomy and cosmology. Here, I show that a new insight comes from condensed matter physics and liquid physics in particular: fundamental constants have a bio-friendly window constrained by bio-friendly viscosity and diffusion setting the motion in essential life processes in and across cells. I also show that bounds on viscosity, diffusion and the fundamental velocity gradient in a biochemical machine can all be varied while keeping the fine-structure constant and the proton-to-electron mass ratio intact, with no implication for the production of heavy nuclei in stars. This leads to a conjecture of multiple tuning and an evolutionary mechanism.

Fundamental physical constants play a profound role in physics. For example, they govern nuclear reactions, formation of stars, nuclear synthesis and stability of biologically vital elements. These are high-energy processes discussed in particle physics, astronomy and cosmology. More recently, it was realised that fundamental physical constants extend their governing reach to low-energy processes and properties operating in condensed matter systems, often in an unexpected way. These properties are those we experience daily and can routinely measure, including viscosity, thermal conductivity, elasticity and sound. Here, we review this work. We start with the lower bound on liquid viscosity, its origin and show how to relate the bound to fundamental physical constants. The lower bound of kinematic viscosity represents the global minimum on the phase diagram. We show how this result answers the long-standing question considered by Purcell and Weisskopf, namely why viscosity never falls below a certain value. An accompanying insight is that water viscosity and water-based life are well attuned to fundamental constants, adding another higher-level layer to the anthropic principle. We then discuss viscosity minima in liquid He above and below the $\lambda$-point. We subsequently consider a very different property, thermal diffusivity, and show that it has the same minimum fixed by fundamental physical constants as viscosity. We also discuss bounds related to elastic properties, elastic moduli and their analogues in low-dimensional systems, and show how these bounds are related to the upper bound for the speed of sound. We conclude with listing ways in which the discussion of fundamental constants and bounds advance physical theories.

We review fundamental problems involved in liquid theory including both classical and quantum liquids. Understanding classical liquids involves exploring details of their microscopic dynamics and its consequences. Here, we apply the same general idea to quantum liquids. We discuss momentum condensation in liquid helium which is consistent with microscopic dynamics in liquids and high mobility of liquid atoms. We propose that mobile transit atoms accumulate in the finite-energy state where the transit speed is close to the speed of sound. In this state, the transit energy is close to the zero-point energy. In momentum space, the accumulation operates on a sphere with the radius set by interatomic spacing and corresponds to zero net momentum. We show that this picture is supported by experiments, including the measured kinetic energy of helium atoms below the superfluid transition and sharp peaks of scattered intensity at predicted energy. We discuss the implications of this picture including the macroscopic wave function and superfluidity.

We observe that quantum indistinguishability is a dynamical effect dependent on measurement duration. We propose a quantitative criterion for observing indistinguishability in quantum fluids and its implications including quantum statistics and derive a viscoelastic function capable of describing both long-time and short-time regimes where indistinguishability and its implications are operative and inactive, respectively. On the basis of this discussion, we propose an experiment to observe a transition between two states where the implications of indistinguishability become inoperative, including a transition between statistics-active and statistics-inactive states.

We present a theory of viscoelasticity of amorphous media, which takes into account the effects of confinement along one of three spatial dimensions. The framework is based on the nonaffine extension of lattice dynamics to amorphous systems, or nonaffine response theory. The size effects due to the confinement are taken into account via the nonaffine part of the shear storage modulus $G'$. The nonaffine contribution is written as a sum over modes in $k$-space. With a rigorous argument based on the analysis of the $k$-space integral over modes, it is shown that the confinement size $L$ in one spatial dimension, e.g. the $z$ axis, leads to a infrared cut-off for the modes contributing to the nonaffine (softening) correction to the modulus that scales as $L^{-3}$. Corrections for finite sample size $D$ in the two perpendicular dimensions scale as $\sim (L/D)^4$, and are negligible for $L \ll D$. For liquids it is predicted that $G'\sim L^{-3}$ in agreement with a previous more approximate analysis, whereas for amorphous materials $G' \sim G'_{bulk} + \beta L^{-3}$. For the case of liquids, four different experimental systems are shown to be very well described by the $L^{-3}$ law., Comment: Physical Review Materials, accepted, in press

In 1977, Purcell asked why liquid viscosities all stop at the same place? Liquids are hard to understand, yet today we can answer the Purcell question in terms of fundamental physical constants fixing viscosity minima. With the Planck constant setting the minimal viscosity, water and life appear to be well attuned to the degree of quantumness of the physical world.

We propose an atomistic model for correlated particle dynamics in liquids and glasses predicting both slow stretched-exponential relaxation (SER) and fast compressed-exponential relaxation (CER). The model is based on the key concept of elastically interacting local relaxation events. SER is related to slowing down of dynamics of local relaxation events as a result of this interaction, whereas CER is related to the avalanche-like dynamics in the low-temperature glass state. The model predicts temperature dependence of SER and CER seen experimentally and recovers the simple, Debye, exponential decay at high temperature. Finally, we reproduce SER to CER crossover across the glass transition recently observed in metallic glasses.

Thermal energy can be conducted by different mechanisms including by single particles or collective excitations. Thermal conductivity is system-specific and shows a richness of behaviors currently explored in different systems including insulators, strange metals and cuprate superconductors. Here, we show that despite the seeming complexity of thermal transport, the thermal diffusivity $\alpha$ of liquids and supercritical fluids has a lower bound which is fixed by fundamental physical constants for each system as $\alpha_m=\frac{1}{4\pi}\frac{\hbar}{\sqrt{m_em}}$, where $m_e$ and $m$ are electron and molecule masses. The newly introduced elementary thermal diffusivity has an absolute lower bound dependent on $\hbar$ and the proton-to-electron mass ratio only. We back up this result by a wide range of experimental data. We also show that theoretical minima of $\alpha$ coincide with the fundamental lower limit of kinematic viscosity $\nu_m$. Consistent with experiments, this points to a universal lower bound for two distinct properties, energy and momentum diffusion, and a surprising correlation between the two transport mechanisms at their minima. We observe that $\alpha_m$ gives the minimum on the phase diagram except in the vicinity of the critical point, whereas $\nu_m$ gives the minimum on the entire phase diagram., Comment: arXiv admin note: text overlap with arXiv:1912.06711

The effect of anharmonicity (coupling) in the field theory generally result in dissipation of plane waves. It has been appreciated that anharmonicity and ensuing dissipation of plane waves can be accompanied by the emergence of the gapped momentum state. Here, we show that the same effect can lead to a gapped energy state and a dispersion relation where the frequency (energy) gap emerges explicitly. We discuss several notable properties of gapped energy and momentum states and connections between them.

Two dimensionless fundamental physical constants, the fine structure constant $\alpha$ and the proton-to-electron mass ratio $\frac{m_p}{m_e}$ are attributed a particular importance from the point of view of nuclear synthesis, formation of heavy elements, planets, and life-supporting structures. Here, we show that a combination of these two constants results in a new dimensionless constant which provides the upper bound for the speed of sound in condensed phases, $v_u$. We find that $\frac{v_u}{c}=\alpha\left(\frac{m_e}{2m_p}\right)^{\frac{1}{2}}$, where $c$ is the speed of light in vacuum. We support this result by a large set of experimental data and first principles computations for atomic hydrogen. Our result expands current understanding of how fundamental constants can impose new bounds on important physical properties.

The nature of the amorphous state has been notably difficult to ascertain at the microscopic level. In addition to the fundamental importance of understanding the amorphous state, potential changes to amorphous structures as a result of radiation damage have direct implications for the pressing problem of nuclear waste encapsulation. Here, we develop new methods to identify and quantify the damage produced by high-energy collision cascades that are applicable to amorphous structures and perform large-scale molecular dynamics simulations of high-energy collision cascades in a model zircon system. We find that, whereas the averaged probes of order such as pair distribution function do not indicate structural changes, local coordination analysis shows that the amorphous structure substantially evolves due to radiation damage. Our analysis shows a correlation between the local structural changes and enthalpy. Important implications for the long-term storage of nuclear waste follow from our detection of significant local density inhomogeneities. Although we do not reach the point of convergence where the changes of the amorphous structure saturate, our results imply that the nature of this new converged amorphous state will be of substantial interest in future experimental and modelling work., Comment: 11 pages, 15 figures

Viscosity of fluids is strongly system-dependent, varies across many orders of magnitude and depends on molecular interactions and structure in a complex way not amenable to first-principles theories. Despite the variations and theoretical difficulties, we find a new quantity setting the minimal kinematic viscosity of fluids: $\nu_m=\frac{1}{4\pi}\frac{\hbar}{\sqrt{m_em}}$, where $m_e$ and $m$ are electron and molecule masses. We subsequently introduce a new property, the "elementary" viscosity $\iota$ with the lower bound set by fundamental physical constants and notably involving the proton-to-electron mass ratio: $\iota_m=\frac{\hbar}{4\pi}\left({\frac{m_p}{m_e}}\right)^{\frac{1}{2}}$, where $m_p$ is the proton mass. We discuss the connection of our result to the bound found by Kovtun, Son and Starinets in strongly-interacting field theories.

Understanding quantum dissipation is important from both theoretical perspective and applications. Here, we show how to describe dissipation in a scalar field theory. We treat dissipation non-perturbatively, represent it by a bilinear term in the Lagrangian and quantize the theory. We find that dissipation promotes a gap in momentum space and reduces the particle energy. As a result, particle mass becomes dressed by dissipation due to self-interaction. The underlying mechanism is similar to that governing the propagation of transverse collective modes in liquids. We discuss the interplay between the dissipative and mass terms, the associated different regimes of field dynamics and the emergence of ultraviolet and infrared cutoffs due to dissipation.

A hallmark of a thermodynamic phase transition is the qualitative change of system thermodynamic properties such as energy and heat capacity. On the other hand, no phase transition is thought to operate in the supercritical state of matter and, for this reason, it was believed that supercritical thermodynamic properties vary smoothly and without any qualitative changes. Here, we perform extensive molecular dynamics simulations in a wide temperature range and find that a deeply supercritical state is thermodynamically heterogeneous, as witnessed by different temperature dependence of energy, heat capacity and its derivatives at low and high temperature. The evidence comes from three different methods of analysis, two of which are model-independent. We propose a new definition of the relative width of the thermodynamic crossover and calculate it to be in the fairly narrow relative range of 13-20\%. On the basis of our results, we relate the crossover to the supercritical Frenkel line.

Physical properties of an interacting system are governed by collective excitations, but their nature at extreme supercritical conditions is unknown. Here, we present direct evidence for propagating solid-like longitudinal phonon-like excitations with wavelengths extending to interatomic separations deep in the supercritical state at temperatures up to 3,300 times the critical temperature. We observe that the crossover of dispersion curves develops at $k$ points reducing with temperature. We interpret this effect as the crossover from the collective phonon to the collisional mean-free path regime of particle dynamics and find that the crossover points are close to both the inverse of the shortest available wavelength in the system and to the particle mean free path inferred from experiments and theory. Notably, both the shortest wavelength and mean free path scale with temperature with the same power law, lending further support to our findings.

Theoretical description of liquids has been primarily based on the hydrodynamic approach and its generalization to the solid-like regime. We show that the same liquid properties can be derived starting from solid-like equations and generalizing them to account for the hydrodynamic flow. Both approaches predict propagating shear waves with the notable gap in $k$-space. This gives an important symmetry of liquids regarding their description. We subsequently construct a two-field Lagrangian of liquid dynamics where the dissipative hydrodynamic and solid-like terms are treated on equal footing. The Lagrangian predicts two gapped waves propagating in opposite space-time directions. The dissipative and mass terms compete by promoting gaps in $k$-space and energy, respectively. When bare mass is close to the field hopping frequency, both gaps close and the dissipative term annihilates the bare mass., Comment: Physical Review E 96, 062134 (2017)

We study thermo-mechanical properties of matter at extreme conditions deep in the supercritical state, at temperatures exceeding the critical one up to four orders of magnitude. We calculate the Gr\"{u}neisen parameter {\gamma} and find that it decreases with temperature from 3 to 1 on isochores depending on the density. Our results indicate that from the perspective of thermo-mechanical properties, the supercritical state is characterized by the wide range of {\gamma} which includes the solid-like values - an interesting finding in view of the common perception of the supercritical state as being an intermediate state between gases and liquids. We rationalize this result by considering the relative weights of oscillatory and diffusive components of the supercritical system below the Frenkel line. We also find that {\gamma} is nearly constant at the Frenkel line above the critical point and explain this universality in terms of pressure and temperature scaling of system properties along the lines where particle dynamics changes qualitatively.

The existence of the phonon-roton minimum has been widely observed for both the solid and liquid phases but so far there is no sufficient theoretical explanation of its origin. In this paper we use a range of techniques to study the dynamics and short-range order for a range of simple materials in their crystalline, amorphous and liquid phases. We perform inelastic neutron scattering (INS) experiments of polycrystalline and liquid barium to study the high-frequency dynamics and understand the mechanisms underlying the atomic motion. Moreover we perform INS simulations for crystals and supercooled liquids, compare the collective excitation spectra and identify similarities. We perform molecular dynamics (MD) simulations for the same materials and present results of population and bond angle distribution showing a short-range order dependence of the different phases, expanding the current knowledge in literature. Finally, we support our findings with a theoretical explanation of the origin of the phonon-roton minima which is observed in both solids and liquids. We study this as a classical phenomenon and we base our explanation on short range interatomic interactions.

Fundamental understanding of strongly-interacting systems necessarily involves collective modes, but their nature and evolution is not generally understood in dynamically disordered and strongly-interacting systems such as liquids and supercritical fluids. We report the results of extensive molecular dynamics simulations and provide direct evidence that liquids develop a gap in solid-like transverse spectrum in the reciprocal space, with no propagating modes between zero and a threshold value. In addition to the liquid state, this result importantly applies to the supercritical state of matter. We show that the emerging gap increases with the inverse of liquid relaxation time and discuss how the gap affects properties of liquid and supercritical states.

We develop an approach to liquid thermodynamics based on collective modes. We perform extensive molecular dynamics simulations of noble, molecular and metallic liquids and provide the direct evidence that liquid energy and specific heat are well-described by the temperature dependence of the Frenkel (hopping) frequency. The agreement between predicted and calculated thermodynamic properties is seen in the notably wide range of temperature spanning tens of thousands of Kelvin. The range includes both subcritical liquids and supercritical fluids. We discuss the structural crossover and inter-relationships between structure, dynamics and thermodynamics of liquids and supercritical fluids., Comment: 10 pages, 6 figures

We discuss the mechanism by which the field vacuum energy varies as a result of strong self-interaction. We propose a non-perturbative approach to treat strong interactions and discuss the problem in terms of quasi-particles describing the motion of field modes. The resulting vacuum energy is variable and depends on the state of the system. If the interacting scalar field is related to the cosmological field, an acceleration equation with a stable equilibrium point follows in a simple model, predicting the oscillatory behavior of the scale factor and other cosmological effects.

Recent research suggests that the supercritical state consists of liquidlike and gaslike states where particle dynamics and key system properties are qualitatively different. We report experimental evidence of the structural crossover in supercritical neon at pressure and temperature conditions significantly exceeding the critical point values: 250$\,P_c$ and 6.6$\,T_c$. The experimental results show a crossover of the medium-range order structure evidenced by the change of the structure factor with pressure. We also observe the crossover of the short-range order structure indicated by changes in the coordination number. The relative width of the crossover is fairly narrow and is smaller than 10-12 \% in pressure and temperature. By comparing our experimental results with molecular dynamics simulations, we suggest that the observed crossover can be attributed to the Frenkel line and discuss the relationship between the structural crossover and qualitative changes of dynamical and thermodynamic properties of supercritical matter., Comment: 7 pages, 6 figures

We show that the vacuum (zero-point) energy of a low-temperature quantum liquid is a variable property which changes with the state of the system, in notable contrast to the static vacuum energy in solids commonly considered. We further show that this energy is inherently anomalous: it decreases with temperature and gives negative contribution to system's heat capacity. This effect operates in an equilibrium and macroscopic system, in marked contrast to small or out-of-equilibrium configurations discussed previously. We find that the negative contribution is over-compensated by the positive term from the excitation of longitudinal fluctuations and demonstrate how the overall positive heat capacity is related to the stability of a condensed phase at the microscopic level.

Strongly interacting, dynamically disordered and with no small parameter, liquids took a theoretical status between gases and solids. We review different approaches to liquids and propose that liquids do not need classifying in terms of their proximity to gases and solids. Instead, they are a unique system in their own class with a notably mixed dynamical state in contrast to pure dynamical states of solids and gases. We start with explaining how the first-principles approach to liquids is an intractable, exponentially complex problem of coupled non-linear oscillators with bifurcations. This is followed by a reduction of the problem based on liquid relaxation time $\tau$ representing non-perturbative treatment of strong interactions. On the basis of $\tau$, solid-like high-frequency modes are predicted and we review related recent experiments. We demonstrate how these modes can be derived by generalizing either hydrodynamic or elasticity equations. We comment on the historical trend to approach liquids using hydrodynamics and compare it to an alternative solid-like approach. We subsequently discuss how collective modes evolve with temperature and how this affects liquid energy and other properties such as fast sound. Here, our emphasis is on real, rather than model, liquids. Highlighting the dominant role of high-frequency modes for liquid energy, we review a wide range of liquids: subcritical low-viscous liquids, supercritical state with two different dynamical and thermodynamic regimes separated by the Frenkel line, highly-viscous liquids and liquid-glass transition. We also discuss liquid-liquid phase transitions where the solid-like properties of liquids have become further apparent. We then discuss gas-like and solid-like approaches to quantum liquids and persisting theoretical problems. We list areas where interesting insights may appear and continue the extraordinary liquid story.

Supercritical state has been viewed as an intermediate state between gases and liquids with largely unknown physical properties. Here, we address the important ability of supercritical fluids to sustain collective excitations. We directly study propagating modes on the basis of correlation functions calculated from extensive molecular dynamics simulations, and find that the supercritical system sustains propagating solid-like transverse modes below the Frenkel line but becomes devoid of transverse modes above the line where it supports longitudinal modes only. Important thermodynamic implications of this finding are discussed. We directly detect positive sound dispersion (PSD) below the Frenkel line where transverse modes are operative, quantitatively explain its magnitude on the basis of transverse and longitudinal velocities. PSD disappears above the Frenkel line which therefore demarcates the supercritical phase diagram into two areas where PSD does and does not operate.

We discuss how structural disorder and amorphization affects solid-state diffusion, and consider zirconolite as a currently important case study. By performing extensive molecular dynamics simulations, we disentangle the effects of amorphization and density, and show that a profound increase of solid-state diffusion takes place as a result of amorphization. Importantly, this can take place at the same density as in the crystal, representing an interesting general insight regarding solid-state diffusion. We find that decreasing the density in the amorphous system increases pre-factors of diffusion constants, but not decreasing the activation energy. We also find that atomic species in zirconolite are affected differently by amorphization and density change. Our microscopic insights are relevant for understanding how solid-state diffusion changes due to disorder and for building predictive models of operation of materials to be used to encapsulate nuclear waste.

A new dynamic line, the Frenkel line, has recently been proposed to separate the supercritical state into rigid-liquid and non-rigid gas-like uid. The location of Frenkel line on the phase diagram is unknown for real uids. Here, we map the Frenkel line for three important systems: CO2, H2O and CH4. This provides an important demarcation on the phase diagram of these systems, the demarcation that separates two distinct physical states with liquid-like and gas-like properties. We find that the Frenkel line can have similar trend as the melting line above the critical pressure. Moreover, we discuss the relationship between unexplained solubility maxima and Frenkel line, and propose that the Frenkel line corresponds to the optimal conditions for solubility.

Behavior of supercritical fluids attracts a lot of attention nowadays. It is important both from the point of view of fundamental science and technological applications. However, up to now the progress in the field is rather moderate. In this article we report a computational study of supercritical carbon dioxide which is one of the most important fluids for chemical industry. We study the response functions of $CO_2$ in supercritical regime and calculate the locations of their maxima (Widom lines). We also make preliminary calculations of the line of crossover of microscopic dynamics of particles (Frenkel line). The conclusions on the Frenkel line location can be applied to study of the atmosphere of Venus., Comment: 6 pages, 8 figures

Recent advance in understanding the supercritical state posits the existence of a new line above the critical point separating two physically distinct states of matter: rigid liquid and non-rigid gas-like fluid. The location of this line, the Frenkel line, remains unknown for important real systems. Here, we map the Frenkel line on the phase diagram of supercritical iron using molecular dynamics simulations. On the basis of our data, we propose a general recipe to locate the Frenkel line for any system, the recipe that importantly does not involve system-specific detailed calculations and relies on the knowledge of the melting line only. We further discuss the relationship between the Frenkel line and the metal-insulator transition in supercritical liquid metals. Our results enable predicting the state of supercritical iron in several conditions of interest. In particular, we predict that liquid iron in the Jupiter core is in the "rigid liquid" state and is highly conducting. We finally analyse the evolution of iron conductivity in the core of smaller planets such as Earth and Venus as well as exoplanets: as planets cool off, the supercritical core undergoes the transition to the rigid-liquid conducting state at the Frenkel line., Comment: 5 pages, 5 figures

Slow flow of the viscous liquid is a thought-provoking experiment that challenges students, academics and public to think about some fundamental questions in modern science. In the Queensland demonstration, the world-longest running experiment earning the Ig Nobel prize, one drop of pitch takes about 10 years to fall, leading to problems of actually observing the drops. Here, we describe our recent demonstration of slowly-flowing bitumen where appreciable flow is observed on the time scale of months. The experiment is free from dissipative heating effects and has the potential to improve the accuracy of measurement. Bitumen viscosity was calculated by undergraduate students during the summer project. The worldwide access to the running experiment is provided by webcams uploading the images to a dedicated website, enhancing student education experience and promotion of science. This demonstration serves as an attractive student education exercise and stimulates the discussion of fundamental concepts and hotly debated ideas in modern physics research: difference between solids and liquids, the nature of liquid-glass transition, emergence of long time scales in a physical process, and the conflict between human intuition and physical reality.

We outline a new programme of solving the problem of treating strong interactions in field theories. The programme does not involve perturbation theories and associated problems of divergences. We apply our recent idea of treating strongly interacting liquids to field theories by showing the equivalence of Hamiltonians of liquids and interacting fields. In this approach, the motion of the field results in the disappearance of $n-1$ transverse modes with frequency smaller than the Frenkel frequency $\omega_{\rm F}$, similar to the loss of two transverse modes in a liquid with frequency $\omega<\omega_{\rm F}$. We illustrate the proposed programme with the calculation of the energy and propagator, and show that the results can not be obtained in perturbation theory to any finite order. Importantly, the Frenkel energy gap $E_{\rm F}=\hbar\omega_{\rm F}$ and the associated massive Frenkel particle naturally appear in our consideration, the result that is relevant for current efforts to demonstrate a mass gap in interacting field theories such as Yang-Mills theory. Notably, our mechanism involves a physically sensible starting point in terms of real masses (frequencies) in the harmonic non-interacting field, in contrast to the Higgs effect involving the imaginary mass as a starting point. We further note that the longitudinal mode in our approach remains gapless, implying that both short-range and long-range forces with massive and massless particles naturally emerge and unify in a single interacting field, a result not hitherto anticipated. Finally, we comment on the relationship between our results and hydrodynamic description of the quark-gluon plasma.

Disorder has been long considered as a formidable foe of theoretical physicists in their attempts to understand system's behavior. Here, we review recently accumulated data and propose that from the point of view of calculating thermodynamic properties, the problem of disorder may not be as severe as has been hitherto assumed. We particularly emphasize that contrary to the long-held view, collective excitations do not decay in disordered systems. We subsequently discuss recent experimental, theoretical and modelling results related to collective excitations in disordered media, and show how these results pave the way to understanding thermodynamics of disordered systems: glasses, liquids, supercritical fluids and spin glasses. An interesting insight from the recent work is the realization that most important changes of thermodynamic properties of the disordered system are governed only by its fundamental length, the interatomic separation. We discuss how the proposed theory relates to the previous approaches based on general many-body statistical mechanics framework.

Understanding physics of gas giants requires the knowledge about the behavior of hydrogen at extreme pressures and temperatures. Molecular hydrogen in these planets is supercritical, and has been considered as a physically homogeneous state where no differences can be made between a liquid and a gas and where all properties undergo no marked or distinct changes with pressure and temperature, the picture believed to hold below the dissociation and metallization transition. Here, we show that in Jupiter and Saturn, supercritical molecular hydrogen undergoes a dynamic transition around 10 GPa and 3000 K from the "rigid" liquid state to the "non-rigid" gas-like fluid state at the Frenkel line recently proposed, with accompanying qualitative changes of all major physical properties. The consequences of this finding are discussed, including a physically justified way to demarcate the interior and the atmosphere in gas giants.

The origin of visible light emission from nanostructures has been a subject of an intense debate since the early work by L. E. Brus and A. P. Alivisatos in 1980s. The intense research that followed has paved the way towards applications of quantum structures in optoelectronics and in bio-sensing and contributed to the development of nanotechnology. The major new challenge is in accessing the structural, electronic and optical properties of quantum dots on a nanoparticle scale in order to understand complex relationships between structural motifs and their contributions to the relevant physical (e. g. optical and electronic) properties. Here we demonstrate that a combination of molecular dynamics simulations and optically-detected x-ray absorption spectroscopy shows sufficient sensitivity to distinguish between regions contributing to the luminescence signal in oxygen and hydrogen terminated Ge quantum dots, thus potentially providing a sub-nanoparticle resolution.