Density fluctuations in classical monatomic liquids

Diffusion theory of molecular liquids in the energy representation and application to solvation dynamics

The generalized Langevin equation (GLE) formalism is a useful theoretical fundament for analyzing dynamical phenomena rigorously. Despite the systematic formulation of dynamics theories with practical approximations, however, the applicability of GLE-based methods is still limited to simple polyatomic liquids due to the approximate treatment of molecular orientations involved in the static molecular liquid theory. Here, we propose an exact framework of dynamics based on the GLE formalism incorporating the energy representation theory of solution, an alternative static molecular liquid theory. A fundamental idea is the projection of the relative positions and orientations of solvents around a solute onto the solute-solvent interaction, namely the energy coordinate, enabling us to describe the dynamics on a one-dimensional coordinate. Introducing systematic approximations, such as the overdamped limit, leads to the molecular diffusion equation in the energy representation that is described in terms of the distribution function of solvents on the energy coordinate and the diffusion coefficients. The present theory is applied to the solvation dynamics triggered by the photoexcitation of benzonitrile. The long-time behavior of the solvation time correlation function is in good agreement with that obtained by the molecular dynamics simulation.

Wave vector dependent damping of THz collective modes in a liquid metal

Well-defined damped collective modes have been observed in liquid metals over a wide range of wave vectors. Hydrodynamics predicts that viscosity and thermal conductivity are the cause for the damping of the collective modes. Here we present experimental data from neutron spectroscopy on the damping of collective modes of liquid rubidium over a wide range of wave vectors. We propose a phenomenological model derived from generalized hydrodynamics to describe the damping of the modes and the evolution with increasing wave vector based on the viscoelastic picture of liquid response. As necessary ingredients a wave vector dependent high frequency shear modulus and shear relaxation time appear. We obtain a remarkable good agreement on a quantitative basis between experiment and calculation over a wide range of wave vectors. The emergent picture is that the lifetime of the collective modes in the THz regime is mainly limited through the diffusion of momentum. The proposed methodology might be applicable to a wide range of liquids.

Dynamics theory for molecular liquids based on an interaction site model

Dynamics theories for molecular liquids based on an interaction site model have been developed over the past few decades and proved to be powerful tools to investigate various dynamical phenomena.

Transition from hydrodynamic to viscoelastic propagation of sound in molten RbBr

Inelastic neutron scattering was applied to measure the acoustic-type excitations in the molten alkali halide rubidium bromide. For molten RbBr neutron scattering is mainly sensitive to the number density fluctuation spectrum and is not influenced by charge fluctuations. Utilizing a dedicated Brillouin scattering spectrometer, we focused on the small-wave-vector range. From inelastic excitations in the spectra a dispersion relation was obtained, which shows a large positive dispersion effect. This frequency enhancement is related to a viscoelastic response of the liquid at high frequencies. Towards small wave vectors we identify the transition to hydrodynamic behavior. This observation is supported by a transition of the sound velocity from a viscoelastic enhanced value to the adiabatic speed of sound for the acoustic-type excitations. Furthermore, the spectrum transforms into a line shape compatible with a prediction from hydrodynamics.

Orbital free ab initio simulations of liquid alkaline earth metals: from pseudopotential construction to structural and dynamic properties

We have performed a comprehensive study of the properties of liquid Be, Ca and Ba, through the use of orbital free ab initio simulations. To this end we have developed a force-matching method to construct the necessary local pseudopotentials from standard ab initio calculations. The structural magnitudes are analyzed, including the average and local structures and the dynamic properties are studied. We find several common features, like an asymmetric second peak in the structure factor, a large amount of local structures with five-fold symmetry, a quasi-universal behaviour of the single-particle dynamic properties and a large degree of positive dispersion in the propagation of collective density fluctuations, whose damping is dictated by slow thermal relaxations and fast viscoelastic ones. Some peculiarities in the dynamic properties are however observed, like a very high sound velocity and a large violation of the Stokes-Einstein relation for Be, or an extremely high positive dispersion and a large slope in the dispersion relation of shear waves at the onset of the wavevector region where they are supported for Ba.

On the absence of a positive sound dispersion in the THz dynamics of glycerol: an inelastic x-ray scattering study

The high frequency transport properties of glycerol are derived from inelastic x-ray scattering spectra measured at different pressures and compared with ultrasound absorption data. As a result, the presence of two distinct relaxation processes is inferred: a slow one, occurring in the GHz window and having an essentially structural character, and a fast one, related instead to microscopic degrees of freedom. While the former originates a neat increase of the apparent, i.e. frequency-dependent, sound velocity, the latter induces no visible dispersive effects on the acoustic propagation. The observed behavior is likely paradigmatic of all glass formers near or below the melting and it is here discussed and explained in some detail.

Zwanzig-Mori equation for the time-dependent pair distribution function

We develop a microscopic theoretical framework for the time-dependent pair distribution function starting from the Liouville equation. An exact Zwanzig-Mori equation of motion for the time-dependent pair distribution function is derived based on the projection-operator formalism. It is demonstrated that, under the Markovian approximation, our equation reduces to the so-called telegraph equation that includes the potential of mean force acting between the pair particles. With the additional approximation neglecting the inertia term, our equation takes the form of Smoluchowski's equation, which has been previously introduced with intuitive arguments and shown to satisfactorily reproduce the simulation results of the particle-pair dynamics.

X-ray Thomson scattering in warm dense matter at low frequencies

The low-frequency portion of the x-ray Thomson scattering spectrum is determined by electrons that follow the slow ion motion. This ion motion is characterized by the ion-ion dynamic structure factor, which contains a wealth of information about the ions, including structure and collective modes. The frequency-integrated (diffraction) contribution is considered first. An effective dressed-particle description of warm dense matter is derived from the quantum Ornstein-Zernike equations, and this is used to identify a Yukawa model for warm dense matter. The efficacy of this approach is validated by comparing a predicted structure with data from the extreme case of a liquid metal; good agreement is found. A Thomas-Fermi model is then introduced to allow the separation of bound and free states at finite temperatures, and issues with the definition of the ionization state in warm dense matter are discussed. For applications, analytic structure factors are given on either side of the Kirkwood line. Finally, several models are constructed for describing the slow dynamics of warm dense matter. Two classes of models are introduced that both satisfy the basic sum rules. One class of models is the "plasmon-pole"-like class, which yields the dispersion of ion-acoustic waves. Damping is then included via generalized hydrodynamics models that incorporate viscous contributions.

Dynamical Structure of Liquid Metals: Recent Theoretical Progress

Recently, experimental studies on the dynamical structure of liquid metals have been actively carried out by the inelastic X-ray scattering (IXS) technique using the synchrotron radiation which have stimulated theoretical studies. In this paper, recent progress in theoretical studies on the dynamical structure of liquid metals are described in two approaches, i.e. the theoretical approach based on the memory function formalism and the various kinds of computer simulations.

State dependent particle dynamics in liquid alkali metals

This paper gives a survey of the particle dynamics in the liquid alkali metals observed with inelastic x-ray and neutron scattering experiments. Liquid rubidium and sodium are chosen as model fluids to represent the behaviour of this group of fluids. In the dense metallic monatomic melt the microscopic dynamics is characterized by collective excitations similar to those in the corresponding solids. The collective particle behaviour is appropriately described using a memory function formalism with two relaxation channels for the density correlation. A similar behaviour is found for the single particle motion where again two relaxation mechanisms are needed to accurately reproduce the experimental findings. Special emphasis is given to the density dependence of the particle dynamics. An interesting issue in liquid metals is the metal to non-metal transition, which is observed if the fluid is sufficiently expanded with increasing temperature and pressure. This causes distinct variations in the interparticle interactions, which feed back onto the motional behaviour. The associated variations in structure and dynamics are reflected in the shape of the scattering laws. The experimentally observed features are discussed and compared with simple models and with the results from computer simulations.

Collective acoustic modes as renormalized damped oscillators: unified description of neutron and x-ray scattering data from classical fluids

In the Q range where inelastic x-ray and neutron scattering are applied to the study of acoustic collective excitations in fluids, various models of the dynamic structure factor S(Q, omega) generalize in different ways the results obtained from linearized-hydrodynamics theory in the Q-->0 limit. Here we show that the models most commonly fitted to experimental S(Q, omega) spectra can be given a unified formulation. In this way, direct comparisons among the results obtained by fitting different models become now possible to a much larger extent than ever. We also show that a consistent determination of the dispersion curve and of the propagation Q range of the excitations is possible, whichever model is used. We derive an exact formula which describes in all cases the dispersion curve and allows for the first quantitative understanding of its shape, by assigning specific and distinct roles to the various structural, thermal, and damping effects that determine the Q dependence of the mode frequencies. The emerging picture describes the acoustic modes as Q-dependent harmonic oscillators whose characteristic frequency is explicitly renormalized in an exact way by the relaxation processes, which also determine, through the widths of both the inelastic and the elastic lines, the whole shape of collective-excitation spectra.

de Gennes slowing in a liquid metal revisited: a neutron spin-echo study

In liquids the decay of density fluctuations shows a slowing down at the structure factor maximum, which is well known as de Gennes narrowing. Molecular dynamics simulations of the liquid metal rubidium and mode coupling theory suggested that this process can be described by a two-step relaxation function. We have probed these predictions with inelastic neutron scattering using the spin-echo technique to measure the dynamics directly in the time domain. The dynamics of liquid rubidium was investigated near the melting point at times beyond the fast contribution. The resulting intermediate-scattering function is in remarkable agreement with predicted values from the mode coupling calculations.

Signatures of quantum behavior in the microscopic dynamics of liquid hydrogen and deuterium

We discuss the microscopic dynamics and structure of liquid hydrogen and deuterium, as probed by inelastic x-ray scattering measurements. Samples are kept in corresponding thermodynamic conditions, at which classical systems are expected to exhibit the same dynamic and static responses. On the contrary, we observe clear differences revealing the onset of quantum deviations, both in the broadening of inelastic excitations and in the position of the first sharp diffraction peak. These features are discussed, compared to path-integral Monte Carlo simulations, and finally associated with the different de Broglie wavelengths of the two isotopes.

Generalized Langevin theory on the dynamics of simple fluids under external fields

A theory on the time development of the density and current fields of simple fluids under an external field is formulated through the generalized Langevin formalism. The theory is applied to the linear solvation dynamics of a fixed solute regarding the solute as the external field on the solvent. The solute-solvent-solvent three-body correlation function is taken into account through the hypernetted-chain integral equation theory, and the time correlation function of the random force is approximated by that in the absence of the solute. The theoretical results are compared with those of molecular-dynamics (MD) simulation and the surrogate theory. As for the transient response of the density field, our theory is shown to be free from the artifact of the surrogate theory that the solvent can penetrate into the repulsive core of the solute during the relaxation. We have also found a large quantitative improvement of the solvation correlation function compared with the surrogate theory. In particular, the short-time part of the solvation correlation function is in almost perfect agreement with that from the MD simulation, reflecting that the short-time expansion of the theoretical solvation correlation function is exact up to t(2) with the exact three-body correlation function. A quantitative improvement is found in the long-time region, too. Our theory is also applied to the force-force time correlation function of a fixed solute, and similar improvement is obtained, which suggests that our present theory can be a basis to improve the mode-coupling theory on the solute diffusion.

Quantum effects in the dynamics of He probed by inelastic x-ray scattering

Quantum effects in the teraherz dynamics of supercritical 4He have been studied as a function of both density rho and temperature T; they have been characterized through their effects on the second and third spectral moments of the dynamic structure factor S(Q, omega), measured by the inelastic x-ray scattering (IXS) technique. The IXS spectra were collected in the low-Q region below and around the position of the first diffraction peak Q(m), i.e., in a range relatively unusual in this kind of investigation. The measured spectral moments clearly show a departure from their high-T classical expected values. We observe, moreover, that the amplitude of quantum deviations increases slightly with increasing density. This experimental method allows us to extract, even in a region where the dynamics still maintains a collective character, such typical single particle properties as the mean atomic kinetic energy.

Self-dynamic structure factor of dense liquids: theory and simulation

The self-intermediate dynamic structure factor Fs(k,t) of liquid lithium near the melting temperature is calculated by molecular dynamics. The results are compared with the predictions of several theoretical approaches, paying special attention to the Lovesey model and the Wahnström and Sjögren mode-coupling theory. To this end the results for the Fs(k,t) second memory function predicted by both models are compared with the ones calculated from the simulations.

Dynamics of a charged simple fluid with exponential memory and two relaxation times

The memory function formalism is applied to the study of charge fluctuations in a symmetric simple fluid. We assume the ions interact through the Rammanathan-Friedman potential. We calculate the distribution function using the hypernetted-chain approximation and use an exponential form, depending on two relaxation times, for the second-order memory function. Following this procedure, two algebraic equations for the relaxation times are obtained. These can be solved using the fourth- and sixth-order frequency momenta, yielding expressions for the relaxation times in terms of the characteristic parameters of the system. This approach allows the analysis of the dynamical structure factor and the dynamical behavior of the charge fluctuations. A comparison of these results with some recently reported in which the distribution function is calculated via mean spherical approximation theory, shows clearly the limitations of mean-field formalisms to describe the dynamics of charged fluids.

Collective dynamical properties of molten salts: molecular dynamics calculations on sodium chloride

We present the results of molecular dynamics calculations on a system simulating molten NaCl at a temperature of 1090 K. Attention has been focused on the study of the collective modes, as described by the auto-correlation functions of the longitudinal and transverse components of the currents of mass and charge. Explicit expressions are given for the coefficients in the small-time Taylor development of the autocorrelation functions and these, together with data on the static structure factors, are used in analysing the current fluctuations and their spectra in terms of memory functions. The memory function has the same basic structure in all cases, consisting of a short-lived initial decay and a long-lived quasi-exponential tail. Inclusion of the tail is essential in order to achieve quantitative agreement with the measured spectra, particularly at small wavenumbers. To that extent our results are consistent with calculations on simpler systems, suggesting that the dynamical events which contribute to the tail in the memory functions are a feature characteristic of liquids in general. The relation to neutron-scattering experiments is also discussed. It is shown, in particular, that a propagating charge density fluctuation of the type seen in the molecular dynamics results is likely to be undetectable in a neutron experiment, except in particularly favourable circumstances.