Transverse excitations in liquid Fe, Cu and Zn

Generally applicable physics-based equation of state for liquids

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 (EST(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 forEST(V). The only other adjustable parameter in the equation is the Grüneisen parameter for the fluid. We observe that the GAP equation is similar to the Mie-Grüneisen 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.

Universal scaling of transverse sound speed and its isomorphic property in Yukawa fluids

Molecular dynamical simulations are performed to investigate the scaling of the transverse sound speed in two-dimensional (2D) and 3D Yukawa fluids. From the calculated diagnostics of the radial distribution function, the mean-squared displacement, and the Pearson correlation coefficient, the approximate isomorphic curves for 2D and 3D liquidlike Yukawa systems are obtained. It is found that the structure and dynamics of 2D and 3D liquidlike Yukawa systems exhibit the isomorphic property under the conditions of the same relative coupling parameter Γ/Γ_{m}=const. It is demonstrated that the reduced transverse sound speed, i.e., the ratio of the transverse sound speed to the thermal speed, is an isomorph invariant, which is a quasiuniversal function of Γ/Γ_{m}. The obtained isomorph invariant of the reduced transverse sound speed can be useful to estimate the transverse sound speed, or determine the coupling strength, with applications to dusty (complex) plasma or colloidal systems.

Theory of melting lines

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.

Vibrational model for thermal conductivity of Lennard-Jones fluids: Applicability domain and accuracy level

Exact mechanisms of thermal conductivity in liquids are not well understood, despite a rich research history. A vibrational model of energy transfer in dense simple liquids with soft pairwise interactions seems adequate to partially fill this gap. The purpose of the present paper is to define its applicability domain and to demonstrate how well it works within the identified applicability domain in the important case of the Lennard-Jones model system. The existing results from molecular dynamics simulations are used for this purpose. Additionally, we show that a freezing density scaling approach represents a very powerful tool to estimate the thermal conductivity coefficient across essentially the entire gas-liquid region of the phase diagram, including metastable regions. A simple practical expression serving this purpose is proposed.

Viscosity and diffusion in life processes and tuning of fundamental constants

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 favour 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.

Fast dynamics and high effective dimensionality of liquid fluidity

Fluidity, the ability of liquids to flow, is the key property distinguishing liquids from solids. This fluidity is set by the mobile transit atoms moving from one quasi-equilibrium point to the next. The nature of this transit motion is unknown. Here, we show that flow-enabling transits form a dynamically distinct sub-ensemble where atoms move on average faster than the overall system, with a manifestly non-Maxwellian velocity distribution. This is in contrast to solids and gases where no distinction of different ensembles can be made and where the distribution is always Maxwellian. The non-Maxwellian distribution is described by an exponent [Formula: see text] corresponding to high dimensionality of space. This is generally similar to extra synthetic dimensions in topological quantum matter, albeit higher dimensionality in liquids is not integer but is fractional. The dimensionality is close to 4 at melting and exceeds 4 at high temperature. [Formula: see text] has a maximum as a function of temperature and pressure in liquid and supercritical states, returning to its Maxwell value in the solid and gas states.

Collective excitations in a melt of fast phase change material GeCu2Te3

Inelastic x-ray scattering measurements have been carried out to investigate atomic dynamics in a melt of fast phase change material GeCu₂Te₃. The dynamic structure factor was analysed using the model function with three damped harmonic oscillator components. By investigating the correlation between the excitation energy and the linewidth, and that between the excitation energy and the intensity on contour maps of a relative approximate probability distribution function proportional toexp(-χ2/N), we could judge the reliability of each inelastic excitation in the dynamic structure factor. The results indicate that there are two inelastic excitation modes besides the longitudinal acoustic one in the liquid. The lower energy excitation could be assigned to the transverse acoustic one whereas the higher energy one disperses like fast sound. The latter result may imply that the liquid ternary alloy exhibits a microscopic phase separation tendency.

Phonon dispersion curves in the type-I crystalline and molten clathrate compound Eu8Ga16Ge30

The dynamic structure factorS(Q,E), whereQandEare momentum and energy transfer, respectively, has been measured for liquid Eu₈Ga₁₆Ge₃₀(EGG), using inelastic x-ray scattering. The excitation energy of the longitudinal acoustic mode in the liquid was scaled to that in liquid Ba₈Ga₁₆Sn₃₀(BGS) with the effective mass. This result means that the local structure in both liquids are similar. The longitudinal acoustic excitation energy of type-I clathrate compound EGG disperses faster than that in the liquid, suggesting that the interatomic force is weakened on melting. The lower energy excitation was observed in both liquid EGG and liquid BGS. In comparison with the longitudinal phonon dispersion in crystalline clathrate compound EGG obtained by density functional theory-based calculations, the lower energy in the liquid was found to be near the optical mode energy. The result indicates that the lower energy mode arises from the relative motion between Eu and (Ga, Ge) atoms.

Interacting Oscillators with Fluctuating Coupling: Mode Mixing without Cross-Correlations

Coupled oscillators are one of the basic models in nonlinear dynamics. Here, we study numerically and analytically the spectra of two harmonic oscillators with stochastically fluctuating coupling and driving forces reproducing a thermostat. We show that, even at small coupling, vanishing on average, the oscillation spectra exhibit mixing, even though no cross-correlations exists between the oscillators. Our results reveal a new mechanism of mode mixing for stochastically uncorrelated systems that is crucial for analysis of spectra in various systems, from simple liquids to living systems.

Deformations, relaxation, and broken symmetries in liquids, solids, and glasses: A unified topological field theory

We combine hydrodynamic and field theoretic methods to develop a general theory of phonons as Goldstone bosons in crystals, glasses, and liquids based on nonaffine displacements and the consequent Goldstone phase relaxation. We relate the conservation, or lack thereof, of specific higher-form currents with properties of the underlying deformation field-nonaffinity-which dictates how molecules move under an applied stress or deformation. In particular, the single-valuedness of the deformation field is associated with conservation of higher-form charges that count the number of topological defects. Our formalism predicts, from first principles, the presence of propagating shear waves above a critical wave vector in liquids, thus giving a formal derivation of the phenomenon in terms of fundamental symmetries. The same picture provides also a theoretical explanation of the corresponding "positive sound dispersion" phenomenon for longitudinal sound. Importantly, accordingly to our theory, the main collective relaxation timescale of a liquid or a glass (known as the α relaxation for the latter) is given by the phase relaxation time, which is not necessarily related to the Maxwell time. Finally, we build a nonequilibrium effective action using the in-in formalism defined on the Schwinger-Keldysh contour, that further supports the emerging picture. In summary, our work suggests that the fundamental difference between solids, fluids, and glasses has to be identified with the associated generalized higher-form global symmetries and their topological structure, and that the Burgers vector for the displacement fields serves as a suitable topological order parameter distinguishing the solid (ordered) phase and the amorphous ones (fluids, glasses).

Low energy excitation in liquid Sb and liquid Bi observed in inelastic x-ray scattering spectra

The dynamic structure factorS(Q,E), whereQandEare momentum and energy transfer, respectively, has been measured for liquid Sb, using inelastic x-ray scattering. A modified damped harmonic oscillator model function was applied to analyseS(Q,E) of liquid Sb and also to that of liquid Bi by Inuiet al(2015Phys. Rev.B92, 054206). The obtained excitation energy was in fairly good agreement with that predicted byab initiomolecular dynamics simulations on these liquid semi-metals. The excitation energy of the longitudinal acoustic mode in liquid Sb and liquid Bi exhibits flat-toppedQdependence whereas the lower excitation energy below the longitudinal acoustic excitation showsQ-gap behaviour. From the viscosity estimated from theQ-gap experimentally obtained, it is inferred that the lower energy excitation arises from the transverse acoustic excitation in the liquids.

Universal interrelation between dynamics and thermodynamics and a dynamically driven "c" transition in fluids

Our very wide survey of the supercritical phase diagram and its key properties reveals a universal interrelation between dynamics and thermodynamics and an unambiguous transition between liquidlike and gaslike states. This is seen in the master plot showing a collapse of the data representing the dependence of specific heat on key dynamical parameters in the system for many different paths on the phase diagram. As a result, the observed transition is path independent. We call it a "c" transition due to the c-shaped curve parametrizing the dependence of the specific heat on key dynamical parameters. The c transition has a fixed inversion point and provides a new structure to the phase diagram, operating deep in the supercritical state (up to, at least, 2000 times the critical pressure and 50 times the critical temperature). The data collapse and path independence as well as the existence of a special inversion point on the phase diagram are indicative of either of a sharp crossover or a new phase transition in the deeply supercritical state.

Transverse acoustic phonon excitations in liquid metals

In this article, transverse acoustic (TA) phonon excitations in various liquid metals are reviewed. Low-frequency TA phonon excitations were investigated on liquid Ga, Sn, Fe, Cu, Zn, and Bi, by using high energy resolution inelastic X-ray scattering (IXS). The current correlation functions obtained from the IXS spectra were analyzed by using two Gaussians to evaluate the excitation energies and widths of the longitudinal acoustic and TA excitation modes, which are consistent with ab initio molecular dynamics simulations. The lifetimes and propagating lengths of the TA modes were determined, and may respectively correspond to the lifetimes and sizes of cages instantaneously formed in each liquid metal. The microscopic elastic constants were estimated and characteristic differences from macroscopic polycrystalline values were found in Poisson’s ratios. Future experimental and analytical problems to be solved in the near future are addressed.

Transverse acoustic phonon excitations in liquid metals

In this article, transverse acoustic (TA) phonon excitations in various liquid metals are reviewed. Low-frequency TA phonon excitations were investigated on liquid Ga, Sn, Fe, Cu, Zn, and Bi, by using high energy resolution inelastic X-ray scattering (IXS). The current correlation functions obtained from the IXS spectra were analyzed by using two Gaussians to evaluate the excitation energies and widths of the longitudinal acoustic and TA excitation modes, which are consistent with ab initio molecular dynamics simulations. The lifetimes and propagating lengths of the TA modes were determined, and may respectively correspond to the lifetimes and sizes of cages instantaneously formed in each liquid metal. The microscopic elastic constants were estimated and characteristic differences from macroscopic polycrystalline values were found in Poisson’s ratios. Future experimental and analytical problems to be solved in the near future are addressed.

First principles study of liquid uranium at temperatures up to 2050 K

Uranium compounds are used as fissile materials in nuclear reactors. In present day reactors the most used nuclear fuel is uranium dioxide, but in generation-IV reactors other compounds are also being considered, such as uranium carbide and uranium mononitride. Upon possible accidents where the coolant would not circulate or be lost the core of the reactor would reach very high temperatures, and therefore it is essential to understand the behaviour of the nuclear fuel under such conditions for proper risk assessment. We consider here molten metallic uranium at several temperatures ranging from 1455 to 2050 K. Even though metallic uranium is not a candidate for nuclear fuel it could nevertheless be produced due to the thermochemical instability of uranium nitride at high temperatures. We use first principles techniques to analyse the behaviour of this system and obtain basic structural and dynamic properties, as well as some thermodynamic and transport properties, including atomic diffusion and viscosity.

Anticrossing of Longitudinal and Transverse Modes in Simple Fluids

If interacting modes of the same symmetry cross, they repel from each other and become hybridized. This phenomenon is called anticrossing and is well-known for mechanical oscillations, electromagnetic circuits, waveguides, metamaterials, polaritons, and phonons in crystals, but it still remains poorly understood in simple fluids. Here, we show that structural disorder and anharmonicity, governing properties of fluids, lead to the anticrossing of longitudinal and transverse modes, which is accompanied by their hybridization and strong redistribution of excitation spectra. We combined theory and simulations for noble gases to prove the reliability of mode anticrossing in simple fluids, studied here for the first time. Our results open novel prospects in understanding collective dynamics, thermodynamics, and transport phenomena in various fluids, spanning from noble gas fluids and metallic melts to strongly coupled plasmas and molecular and complex fluids.

Excitation spectra in fluids: How to analyze them properly

Although the understanding of excitation spectra in fluids is of great importance, it is still unclear how different methods of spectral analysis agree with each other and which of them is suitable in a wide range of parameters. Here, we show that the problem can be solved using a two-oscillator model to analyze total velocity current spectra, while other considered methods, including analysis of the spectral maxima and single mode analysis, yield rough results and become unsuitable at high temperatures and wavenumbers. To prove this, we perform molecular dynamics (MD) simulations and calculate excitation spectra in Lennard-Jones and inverse-power-law fluids at different temperatures, both in 3D and 2D cases. Then, we analyze relations between thermodynamic and dynamic features of fluids at (Frenkel) crossover from a liquid- to gas-like state and find that they agree with each other in the 3D case and strongly disagree in 2D systems due to enhanced anharmonicity effects. The results provide a significant advance in methods for detail analysis of collective fluid dynamics spanning fields from soft condensed matter to strongly coupled plasmas.

Onset of transverse (shear) waves in strongly-coupled Yukawa fluids

A simple practical approach to describe transverse (shear) waves in strongly-coupled Yukawa fluids is presented. Theoretical dispersion curves, based on hydrodynamic consideration, are shown to compare favorably with existing numerical results for plasma-related systems in the long-wavelength regime. The existence of a minimum wave number below which shear waves cannot propagate and its magnitude are properly accounted in the approach. The relevance of the approach beyond plasma-related Yukawa fluids is demonstrated by using experimental data on transverse excitations in liquid metals Fe, Cu, and Zn, obtained from inelastic x-ray scattering. Some potentially important relations, scalings, and quasi-universalities are discussed. The results should be interesting for a broad community in chemical physics, materials physics, physics of fluids and glassy state, complex (dusty) plasmas, and soft matter.

The nature of collective excitations and their crossover at extreme supercritical conditions

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.

Static and dynamic structures of liquid Ba8Ga16Sn30: a melt of the thermoelectric clathrate compounds

X-ray diffraction and inelastic x-ray scattering measurements of liquid Ba₈Ga₁₆Sn₃₀ have been carried out to investigate local structure and atomic dynamics in the liquid. The pair distribution function shows shorter and longer interatomic distances in the first coordination shell. The dynamic structure factor exhibits the inelastic excitations on both sides of the quasielastic central peak. The inelastic excitations disperse with increasing the momentum transfer, suggesting the longitudinal acoustic mode. We found a low energy excitation in addition to the longitudinal acoustic excitation in the dynamic structure factor and it reminds us a strong relationship with a rattling motion of a guest (Ba) atom in the solid state. The temperature dependence of the pair distribution function and the longitudinal acoustic excitation energy is very weak in a range from 600 to 900 °C. The result suggests that Ba and other atoms in the melt are located around minimum positions of the effective pair potential approximated as a harmonic one.

Dynamics, thermodynamics and structure of liquids and supercritical fluids: crossover at the Frenkel line

We review recent work aimed at understanding dynamical and thermodynamic properties of liquids and supercritical fluids. The focus of our discussion is on solid-like transverse collective modes, whose evolution in the supercritical fluids enables one to discuss the main properties of the Frenkel line separating rigid liquid-like and non-rigid gas-like supercritical states. We subsequently present recent experimental evidence of the Frenkel line showing that structural and dynamical crossovers are seen at a pressure and temperature corresponding to the line as predicted by theory and modelling. Finally, we link dynamical and thermodynamic properties of liquids and supercritical fluids by the new calculation of liquid energy governed by the evolution of solid-like transverse modes. The disappearance of those modes at high temperature results in the observed decrease of heat capacity.

Self-consistent description of local density dynamics in simple liquids. The case of molten lithium

The dynamic structure factor is the quantity, which can be measured by means of Brillouin light-scattering as well as by means of inelastic scattering of neutrons and x-rays. The spectral (or frequency) moments of the dynamic structure factor define directly the sum rules of the scattering law. The theoretical scheme formulated in this study allows one to describe the dynamics of local density fluctuations in simple liquids and to obtain the expression of the dynamic structure factor in terms of the spectral moments. The theory satisfies all the sum rules, and the obtained expression for the dynamic structure factor yields correct extrapolations into the hydrodynamic limit as well as into the free-particle dynamics limit. We discuss correspondence of this theory with the generalized hydrodynamics and with the viscoelastic models, which are commonly used to analyze the data of inelastic neutron and x-ray scattering in liquids. In particular, we reveal that the postulated condition of the viscoelastic model for the memory function can be directly obtained within the presented theory. The dynamic structure factor of liquid lithium is computed on the basis of the presented theory, and various features of the scattering spectra are evaluated. It is found that the theoretical results are in agreement with inelastic x-ray scattering data.

Lagrangian formulation and symmetrical description of liquid dynamics

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.

Excitation spectra of liquid iron up to superhigh temperatures

Investigation of excitation spectra of liquids is one of the hot test topics nowadays. In particular, recent experimental works showed that liquid metals can demonstrate transverse excitations and positive sound dispersion. However, the theoretical description of these experimental observations is still missing. Here we report a molecular dynamics study of excitation spectra of liquid iron. We compare the results with available experimental data to justify the method. After that we perform calculations for high temperatures to find the location of the Frenkel line introduced in our previous works.

Switching off hydrogen-bond-driven excitation modes in liquid methanol

Hydrogen bonding plays an essential role on intermolecular forces, and consequently on the thermodynamics of materials defined by this elusive bonding character. It determines the property of a vital liquid as water as well as many processes crucial for life. The longstanding controversy on the nature of the hydrogen bond (HB) can be settled by looking at the effect of a vanishing HB interaction on the microscopic properties of a given hydrogen-bonded fluid. This task suits the capabilities of computer simulations techniques, which allow to easily switch off HB interactions. We then use molecular dynamics to study the microscopic properties of methanol, a prototypical HB liquid. Fundamental aspects of the dynamics of methanol at room temperature were contextualised only very recently and its rich dynamics was found to have striking analogies with that of water. The lower temperature (200 K) considered in the present study led us to observe that the molecular centre-of-mass dynamics is dominated by four modes. Most importantly, the computational ability to switch on and off hydrogen bonds permitted us to identify which, among these modes, have a pure HB-origin. This clarifies the role of hydrogen bonds in liquid dynamics, disclosing new research opportunities and unexplored interpretation schemes.

Emergence and Evolution of the k Gap in Spectra of Liquid and Supercritical States

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 a solidlike 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.

Direct links between dynamical, thermodynamic, and structural properties of liquids: Modeling results

We develop an approach to liquid thermodynamics based on collective modes. We perform extensive molecular-dynamics simulations of noble, molecular, and metallic liquids, and we provide 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 interrelationships between the structure, dynamics, and thermodynamics of liquids and supercritical fluids.

A search for manifestation of two types of collective excitations in dynamic structure of a liquid metal: Ab initio study of collective excitations in liquid Na

Using a combination of ab initio molecular dynamics and several fit models for dynamic structure of liquid metals, we explore an issue of possible manifestation of non-acoustic collective excitations in longitudinal dynamics having liquid Na as a case study. A model with two damped harmonic oscillators (DHOs) in time domain is used for analysis of the density-density time correlation functions. Another similar model with two propagating contributions and three lowest exact sum rules is considered, as well as an extended hydrodynamic model known as thermo-viscoelastic one which permits two types of propagating modes outside the hydrodynamic region to be used for comparison with ab initio obtained time correlation functions and calculations of dispersions of collective excitations. Our results do not support recent suggestions that, even in simple liquid metals, non-hydrodynamics transverse excitations contribute to the longitudinal collective dynamics and can be detected as a DHO-like spectral shape at their transverse frequency. We found that the thermo-viscoelastic dynamic model permits perfect description of the density-density and current-current time correlation functions of the liquid Na in a wide range of wave numbers, which implies that the origin of the non-hydrodynamic collective excitations contributing to longitudinal dynamics can be short-wavelength heat waves.

Density of states from mode expansion of the self-dynamic structure factor of a liquid metal

We show that by exploiting multi-Lorentzian fits of the self-dynamic structure factor at various wave vectors it is possible to carefully perform the Q→0 extrapolation required to determine the spectrum Z(ω) of the velocity autocorrelation function of a liquid. The smooth Q dependence of the fit parameters makes their extrapolation to Q=0 a simple procedure from which Z(ω) becomes computable, with the great advantage of solving the problems related to resolution broadening of either experimental or simulated self-spectra. Determination of a single-particle property like the spectrum of the velocity autocorrelation function turns out to be crucial to understanding the whole dynamics of the liquid. In fact, we demonstrate a clear link between the collective mode frequencies and the shape of the frequency distribution Z(ω). In the specific case considered in this work, i.e., liquid Au, analysis of Z(ω) revealed the presence, along with propagating sound waves, of lower frequency modes that were not observed before by means of dynamic structure factor measurements. By exploiting ab initio simulations for this liquid metal we could also calculate the transverse current-current correlation spectra and clearly identify the transverse nature of the above mentioned less energetic modes. Evidence of propagating transverse excitations has actually been reported in various works in the recent literature. However, in some cases, like the present one, these modes are difficult to detect in density fluctuation spectra. We show here that the analysis of the single-particle dynamics is able to unveil their presence in a very effective way. The properties here shown to characterize Z(ω), and the information in it contained therefore allow us to identify it with the density of states (DoS) of the liquid. We demonstrate that only nonhydrodynamic modes contribute to the DoS, thus establishing its purely microscopic origin. Finally, as a by-product of this work, we provide our estimate of the self-diffusion coefficient of liquid gold just above melting.

Crossover of collective modes and positive sound dispersion in supercritical state

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 in molecular dynamics simulations and find that the supercritical system sustains propagating solid-like transverse modes below the Frenkel line but not above where there is one longitudinal mode 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 and 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.

Anomalous vacuum energy and stability of a quantum liquid

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 a negative contribution to a 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.

Pressure-induced changes in structural and dynamic properties of liquid Fe close to the melting line. An ab initio study

The static and dynamic properties of liquid Fe at high pressure and temperature have been studied using an ab initio molecular dynamics method. We have focused on four thermodynamic states at pressures of 27, 42, 50 and 58 GPa for which x-ray scattering data are available. The calculated static structure shows very good agreement with the available experimental data, including an asymmetric second peak which becomes more marked with increasing pressure. The dynamical structure reveals the existence of propagating density fluctuations and the associated dispersion relation has also been determined. The relaxation mechanisms for the density fluctuations have been analyzed in terms of a model with two decay channels (fast and slow, respectively). We found that the thermal relaxation proceeds along the slow decaying channel whereas the fast one is that of the viscoelastic relaxation. The possible coupling between longitudinal and transverse excitation modes has been investigated by looking at specific signatures in two wavevector regions: the first one is located around the position of the main peak of the structure factor, qp, as suggested by the recently reported appearance of high frequency transverse waves in liquid Li under high pressures; the second region is around qp/2, as suggested by the recent finding of transverse acoustic modes in inelastic x-ray scattering intensities of liquid Fe at ambient pressure. Finally, results are also reported for several transport coefficients.

Collective modes and thermodynamics of the liquid state

Strongly interacting, dynamically disordered and with no small parameter, liquids took a theoretical status between gases and solids with the historical tradition of hydrodynamic description as the starting point. We review different approaches to liquids as well as recent experimental and theoretical work, and propose that liquids do not need classifying in terms of their proximity to gases and solids or any categorizing for that matter. 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 τ representing non-perturbative treatment of strong interactions. On the basis of τ, solid-like high-frequency modes are predicted and we review related recent experiments. We demonstrate how the propagation of 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 evolution affects liquid energy and heat capacity as well as other properties such as fast sound. Here, our emphasis is on understanding experimental data in real, rather than model, liquids. Highlighting the dominant role of solid-like high-frequency modes for liquid energy and heat capacity, 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 in the glass transformation range and liquid-glass transition. We subsequently discuss the fairly recent area of liquid-liquid phase transitions, the area where the solid-like properties of liquids have become further apparent. We then discuss gas-like and solid-like approaches to quantum liquids and theoretical issues that are similar to the classical case. Finally, we summarize the emergent view of liquids as a unique system with a mixed dynamical state, and list several areas where interesting insights may appear and continue the extraordinary liquid story.