We discuss the validity of recent results in [Phys. Rev. Lett. 125, 125501 (2020)] on an universal relation between the heat capacity and dispersions of collective excitations in liquids.
We show, that the theoretical expression for the dispersion of collective excitations reported in [Phys. Rev. B {bf 103}, 099901 (2021)], at variance with what was claimed in the paper, does not account for the energy fluctuations and does not tend i
n the long-wavelegth limit to the correct hydrodynamic dispersion law.
We report an {it ab initio} simulation study of changes in structural and dynamic properties of liquid Si at 7 pressures ranging from 10.2 GPa to 24.3 GPa along the isothermal line 1150~K, which is above the minimum of the melting line. The increase
of pressure from 10.2 GPa to 16 GPa causes strong reduction in the tetrahedral ordering of the most close neighbors. The diffusion coefficient shows a linear decay vs drop in atomic volume, that agrees with theoretical prediction for simple liquid metals, thus not showing any feature at the pressures corresponding to the different crystal phase boundaries. The Fourier-spectra of velocity autocorrelation function shows two-peak structure at pressures 20 GPa and higher. These characteristic frequencies correspond well to the peak frequencies of the transverse current spectral function in the second pseudo-Brillouin zone. Two almost flat branches of short-wavelength transverse modes were observed for all the studied pressures. We discuss the pressure evolution of characteristic frequencies in the longitudinal and transverse branches of collective modes.
We show that the presented in Phys.Rev.B, v.101, 214312 (2020) theoretical expressions for longitudinal current spectral function $C^L(k,omega)$ and dispersion of collective excitations are not correct. Indeed, they are not compatible with the contin
uum limit and $C^L(k,omegato 0)$ contradicts the continuity equation.
Non-monotonous changes in velocity autocorrelations across the transformation from molecular to atomic fluid in hydrogen under pressure are studied by ab initio molecular dynamics simulations at the temperature 2500 K. We report diffusion coefficient
s in a wide range of densities from purely molecular fluid up to metallic atomic fluid phase. An analysis of contributions to the velocity autocorrelation functions from the motion of molecular centers-of-mass, rotational and intramolecular vibrational modes is performed, and a crossover in the vibrational density of intramolecular modes across the transition is discussed.
Velocity autocorrelation functions (VAF) of the fluids are studied on short- and long-time scales within a unified approach. This approach is based on an effective summation of the infinite continued fraction at a reasonable assumption about converge
nce of relaxation times of the high order memory functions, which have purely kinetic origin. The VAFs obtained within our method are compared with computer simulation data for the liquid Ne at different densities and the results, which follow from the Markovian approximation for the highest order kinetic kernels. It is shown that in all the thermodynamic points and at the chosen level of the hierarchy, our results agree much better with the MD data than those of the Markovian approximation. The density dependence of the transition time, needed for the fluid to attain the hydrodynamic stage of evolution, is evaluated. The common and distinctive features of our method are discussed in their relations to the generalized collective mode (GCM) theory, the mode coupling theory (MCT), and some other theoretical approaches.
High-resolution inelastic x-ray scattering measurements were carried out on molten NaI near the melting point at 680$^circ$C at SPring-8. Small and damped indications of longitudinal optic excitation modes were observed on the tails of the longitudin
al acoustic modes at small momentum transfers, $Qsim5$ nm$^{-1}$. The measured spectra are in good agreement, in both frequency and linewidth, with {it ab initio} molecular dynamics (MD) simulations but not classical MD simulations. The observation of these modes at small $Q$ and a good agreement with the simulation permits clear identification of these as collective optic modes with well defined phasing between different ionic motions.
A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales is proposed. The ansatz is based on an effective summation of the infinite continued fraction at a reasonable assumption about convergence of relaxa
tion times of the higher order memory functions, which have a purely kinetic origin. The VAFs obtained within our approach are compared with the results of the Markovian approximation for memory kernels. It is shown that although in the overdamped regime both approaches agree to a large extent at the initial and intermediate times of the system evolution, our formalism yields power law relaxation of the VAFs which is not observed at the description with a finite number of the collective modes. Explicit expressions for the transition times from kinetic to hydrodynamic regimes are obtained from the analysis of the singularities of spectral functions in the complex frequency plane.
We comment on an expression for positive sound dispersion (PSD) in fluids and analysis of PSD from molecular dynamics simulations reported in the Letter by Fomin et al (J.Phys.:Condens.Matt. v.28, 43LT01, 2016)
The collective dynamics in liquid water is an active research topic experimentally, theoretically and via simulations. Here, ab initio molecular dynamics simulations are reported in heavy and ordinary water at temperature 323.15 K, or 50$^circ$C. The
simulations in heavy water were performed both with and without dispersion corrections. We found that the dispersion correction (DFT-D3) changes the relaxation of density-density time correlation functions from a slow, typical of a supercooled state, to exponential decay behaviour of regular liquids. This implies an essential reduction of the melting point of ice in simulations with DFT-D3. Analysis of longitudinal (L) and transverse (T) current spectral functions allowed us to estimate the dispersions of acoustic and optic collective excitations and to observe the L-T mixing effect. The dispersion correction shifts the L and T optic (O) modes to lower frequencies and provides by almost thirty per cent smaller gap between the longest-wavelength LO and TO excitations, which can be a consequence of a larger effective high-frequency dielectric permittivity in simulations with dispersion corrections. Simulation in ordinary water with the dispersion correction results in frequencies of optic excitations higher than in D$_2$O, and in a long-wavelength LO-TO gap of 24 ps$^{-1}$ (127 cm$^{-1}$).
