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The canonical $\,NLT\,$ partition function of a quasi-one dimensional (q1D) one-file system of equal hard disks [J. Chem Phys. \textbf{153}, 144111 (2020)] provides an analytical description of the thermodynamics and ordering in this system (a pore) as a function of linear density $\,Nd/L\,$ where $\,d\,$ is the disk diameter. We derive the analytical formulae for the distance dependence of the translational pair distribution function and the distribution function of distances between next neighbor disks, and then demonstrate their use by calculating the translational order in the pore. In all cases, the order is found to be of a short range and to exponentially decay with the disks' separation. The correlation length presented for different pore widths and densities shows a non-monotonic dependence with a maximum at $\,Nd/L = 1\,$ and tends to the 1D value for a vanishing pore width. The results indicate a special role of this density when the pore length $\,L\,$ is equal exactly to $N$ disk diameters. A comparison between the theoretical results for an infinite system and the results of a molecular dynamics simulation for a finite system with periodic boundary conditions is presented and discussed., Comment: published in Journal of Molecular Liquids. arXiv admin note: substantial text overlap with arXiv:2206.05980

The analytical canonical NLT partition function of a quasi-one dimensional (q1D) system of hard disks [J. Chem Phys. v.153, 144111 (2020)] provides a direct analytical description of the thermodynamics and ordering in this system (a pore) as a function of the linear density N/L both for finite and infinite systems. It is alternative to the well-developed transfer matrix method based on the isobaric NPT ensemble. We derive the analytical formulae for the actual distance dependence of the translational pair distribution function (PDF) and the DF of distances between next neighbor disks, and then demonstrate their use by calculating the translational order in the pore. In all cases, the order is found to be of a short range and to exponentially decay with the disks' separation. The correlation length presented for the whole range of the q1D pore widths and different densities shows a non-monotonic dependence with a maximum at the density N/L=1 and tends to the 1D value for a vanishing pore width. The results indicate a special role of this density when the pore length L is equal exactly to N disk diameters. We introduce an orientational order parameter that accounts for the local quality of the crystalline zigzag formed by disks and is related to its structural element. This parameter is maximum in the densely packed state and vanishes for a very low density. Due to specific quasi-one dimensional geometry, this macroscopic order parameter is constant along the pore so that the macroscopic orientational order is of a liquid crystalline type., Comment: 29 pages, 4 figures

In a recent article M. Baggioli and A. Zaccone (Phys. Rev. Lett. {\bf 112}, 145501 (2019)) claimed that an anharmonic damping, leading to a sound attenuation proportional to $\omega^2$ (Akhiezer-type damping) would imply a boson peak, i.e.\ a maximum in the vibrational density of states, divided by the frequency squared (reduced density of states). This would apply both to glasses and crystals.Here we show that this is not the case. In a mathematically correct treatment of the model the reduced density of states monotonously decreases, i.e.\ there is no boson peak. We further show that the formula for the would-be boson peak, presented by the authors, corresponds to a very short one-dimensional damped oscillator system. The peaks they show correspond to resonances, which vanish in the thermodynamic limit., Comment: 3 pages, 2 figures

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., Comment: 7 pages, 4 figures

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 in the long-wavelegth limit to the correct hydrodynamic dispersion law., Comment: 6 pages, no figures

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., Comment: 12 pages, 8 figures

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 continuum limit and $C^L(k,\omega\to 0)$ contradicts the continuity equation., Comment: Submitted to Phys.Rev.B

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 coefficients 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., Comment: 7 pages, 5 figures

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 convergence 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., Comment: 26 pages, 4 figures

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 longitudinal acoustic modes at small momentum transfers, $Q\sim5$ 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., Comment: 7 pages, 4 figures

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 relaxation 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., Comment: 14 pages, 2 figures

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$^{-1}$)., Comment: 14 pages, 9 figures

Ice-water, water-vapor interfaces and ice surface are studied by molecular dynamics simulations with the SPC/E model of water molecules having the purpose to estimate the profiles of electrostatic potential across the interfaces. We have proposed a methodology for calculating the profiles of electrostatic potential based on a trial particle, which showed good agreement for the case of electrostatic potential profile of the water-vapor interface of TIP4P model calculated in another way. The measured profile of electrostatic potential for the pure ice-water interface decreases towards the liquid bulk region, which is in agreement with simulations of preferential direction of motion of Li$^{+}$ and F$^{-}$ solute ions at the liquid side of the ice-water interface. These results are discussed in connection with the Workman-Reynolds effect., Comment: 7 pages, 5 figures

We comment on three incorrect claims in the paper by Fomin et al (arXiv:1507.06094) concerning the generalized hydrodynamic methodology and positive sound dispersion in fluids.

We study autocorrelation functions of energy, heat and entropy densities obtained by molecular dynamics simulations of supercritical Ar and compare them with the predictions of the hydrodynamic theory. It is shown that the predicted by the hydrodynamic theory single-exponential shape of the entropy density autocorrelation functions is perfectly reproduced for small wave numbers by the molecular dynamics simulations and permits the calculation of the wavenumber-dependent specific heat at constant pressure. The estimated wavenumber-dependent specific heats at constant volume and pressure, $C_{v}(k)$ and $C_{p}(k)$, are shown to be in the long-wavelength limit in good agreement with the macroscopic experimental values of $C_{v}$ and $C_{p}$ for the studied thermodynamic points of supercritical Ar., Comment: 8 pages, 5 figures