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A very recent simulation study of the transverse current autocorrelation of the Lennard-Jones fluid revealed, as expected, that this function can be perfectly described within the exponential expansion theory. However, above a certain wavevector $Q$, not only transverse collective excitations are found to propagate in the fluid, but a second oscillatory component of unclear origin (thereby called X) must be considered to properly account for the time behavior of the correlation. Here we present an extended investigation of the transverse current autocorrelation of liquid Au as obtained by ab initio molecular dynamics in the very wide range 5.7 nm$^{-1}$ $\le Q \le$ 32.8 nm$^{-1}$ in order to follow the behavior of the X component, if present, also at large $Q$ values. By combining the study of the transverse current autocorrelation with the analogous analysis of its self part, we show that the second oscillatory component originates from the longitudinal dynamics and appears in the same form as a collective excitation is represented in the single-particle behavior. Therefore, the signature of the longitudinal processes (sound waves) in the transverse current autocorrelation is not due to often conjectured couplings of longitudinal and trasverse modes, but descends from the self part of the function, which contains the traces of all processes acting in the fluid as the density of states, that is the spectrum of the velocity autocorrelation function, does.

Understanding how molecules engage in collective motions in a liquid where a network of bonds exists has both fundamental and applied relevance. On the one hand, it can elucidate the ``ordering" role of long-range correlations in an otherwise strongly dissipative system; on the other hand, it can inspire new avenues to control such order to implement sound manipulation. Water represents an ideal investigation case to unfold these general aspects and, across the decades, it has been the focus of thorough scrutiny. Despite this investigative effort, the spectrum of terahertz density fluctuations of water largely remains a puzzle for Condensed Matter physicists. To unravel it, we compare previous scattering measurements of water spectra with new ones on ice. Thanks to the unique asset of Bayesian inference, we draw a more detailed portrayal of the phonon response of ice. The comparison with the one of liquid water challenges the current understanding of density fluctuations in water, or more in general, of any networked liquid., Comment: 30 pages, 9 figures

A thorough analysis of the transverse current autocorrelation function obtained by molecular dynamics simulations of a dense Lennard-Jones fluid reveals that even such a simple system is characterized by a varied dynamical behavior with changing length scale. By using the exponential expansion theory, we provide a full account of the time correlation at wavevectors $Q$ between the upper boundary of the hydrodynamic region and $Q_p/2$, with $Q_p$ the position of the main peak of the static structure factor. In the $Q$ range studied we identify and accurately locate the wavevector at which shear wave propagation starts to take place, and show clearly how this phenomenon may be represented by a damped harmonic oscillator changing, in a continuous way, from an overdamped to an underdamped condition. The decomposition into exponential modes allows one to convincingly establish not only the crossover related to the onset of transverse waves but, surprisingly, also the existence of a second pair of modes equivalent to another oscillator that undergoes, at higher $Q$ values, a similarly smooth over- to underdamped transition., Comment: 6 pages and 4 figures in main text, 6 pages and 3 figures in supplementary material

The present work deals with the formal description of the response to neutrons of heteronuclear diatomic liquids, with special interest in the case of hydrogen deuteride as a possible candidate for the moderation process required in the production of cold neutrons. Preliminary evaluations of the model giving the neutron double differential cross section of a heteronuclear vibrating rotor are performed by using, as a first approximation, the ideal gas law for the centre-of-mass translational dynamics, which is expected to be appropriate at incident neutron energies above the thermal region. The unavailability of double differential cross section experimental data on liquid HD compels to test the model calculations only at an integral level, i.e. against the only measurement carried out on liquid HD for the determination of its neutron total cross section. The present findings indicate the evident need of more accurate measurements of the total cross section, as well as of future work devoted to double differential cross section determinations and appropriate simulations of the translational dynamics of this weakly quantum fluid., Comment: 24 pages, 6 figures

We review exact formalisms for describing the dynamics of liquids in terms of static parameters. We discuss how these formalisms are prone to suffer from imposing restrictions that appear to adhere to common sense but which are overly restrictive, resulting in a flawed description of the dynamics of liquids. We detail a fail-safe way for modeling the scattering data of liquids that is free from any unwarranted restriction and that models the scattering using the fewest possible number of free parameters. We also list some common habits in analyzing data and how these habits do not do justice to the accuracy of the results obtained in scattering experiments, and how these habits may stand in the way of rejecting some models used in describing the dynamics of liquids., Comment: 20 pages, 9 figures, intended for Phys. Rev. E

The design of moderators and cold sources of neutrons is a key point in research-reactor physics, requiring extensive knowledge of the scattering properties of very important light molecular liquids such as methane, hydrogen and their deuterated counterparts. Inelastic scattering measurements constitute the basic source of such information but are difficult to perform, the more so when high accuracy is required, and additional experimental information is scarce. The need of data covering as large as possible portions of the kinematic Q-E plane thus pushes towards the use of computable models, validated by testing them, mainly, against integral quantities (either known from theory or measured) such as spectral moments and total cross section data. A few recent experiments demonstrated that, at least for the self contribution, which dominates in the incoherent scattering case of hydrogen, accurate calculations can be performed by means of quantum simulations of the velocity autocorrelation function. This method is shown here to be by far superior to the use of standard analytical models devised, although rather cleverly, for generic classical samples. The neutron dynamic structure factor (and consequently the well-known S({\alpha},{\beta}) of parahydrogen and deuterium, suitable for use in packages like NJOY, are given and shown to agree very well with total cross section measurements and expected quantum properties.

We present a neutron spin echo study (NSE) of the nanosecond dynamics of polyethylene glycol (PEG) functionalised nanosized gold particles dissolved in D$_2$O at two temperatures and two different PEG molecular weights. The analysis of the NSE data was performed by applying a Bayesian approach to the description of time correlation function decays in terms of exponential terms, recently proved to be theoretically rigorous. This approach, which addresses in a direct way the fundamental issue of model choice in any dynamical analysis, provides here a guide to the most statistically supported way to follow the decay of the Intermediate Scattering Functions I(Q, t) by basing on statistical grounds the choice of the number of terms required for the description of the nanosecond dynamics of the studied systems. Then, the presented analysis avoids from the start resorting to a pre-selected framework and can be considered as model free. By comparing the results of PEG coated nanoparticles with those obtained in PEG2000 solutions, we were able to disentangle the translational diffusion of the nanoparticles from the internal dynamics of the polymer grafted to them, and to show that the polymer corona relaxation follows a pure exponential decay in agreement with the behavior predicted by coarse grained molecular dynamics simulations and theoretical models. This methodology has one further advantage: in the presence of a complex dynamical scenario I(Q,t) is often described in terms of the Kohlrausch-Williams-Watts function that can implicitly represent a distribution of relaxation times. By choosing to describe the I(Q,t) as a sum of exponential functions and with the support of the Bayesian approach, we can explicitly determine when a finer-structure analysis of the dynamical complexity of the system exists according to the available data without the risk of overparametrisation.

Molecular dynamics results for the dynamic structure of a He0.77Ne0.23 gas mixture at two densities (15.8 nm-3 and 36.1 nm-3) are presented. A clear description of the crossover from hydrodynamic modes to distinct excitations for the two species is obtained. The higher density data neatly show high- and low-frequency branches setting on in the dispersion curve, with a rather localized transition. The lower density results remarkably agree with existing neutron scattering data and, differently from previous simulation studies, display hydrodynamic behavior up to k = 2 nm-1. A smooth transition to fast sound is shown to take place for 2 < k / nm-1 < 5, where the present MD data fill the existing gap in the experimental results., Comment: 6 pages, 4 figures