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In a recent paper, S. Singh and K. Tankeshwar (ST), [Phys. Rev. E textbf{67}, 012201 (2003)], proposed a new interpretation of the collective dynamics in liquid metals, and, in particular, of the relaxation mechanisms ruling the density fluctuations propagation. At variance with both the predictions of the current literature and the results of recent Inelastic X-ray Scattering (IXS) experiments, ST associate the quasielastic component of the $S(Q,omega)$ to the thermal relaxation, as it holds in an ordinary adiabatic hydrodynamics valid for non-conductive liquids and in the $Q to 0$ limit. We show here that this interpretation leads to a non-physical behaviour of different thermodynamic and transport parameters.
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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.
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 $C^L(k,omegato 0)$ contradicts the continuity equation.
The collective dynamics of liquid Gallium close to the melting point has been studied using Inelastic X-ray Scattering to probe lengthscales smaller than the size of the first coordination shell. %(momentum transfers, $Q$, $>$15 nm$^{-1}$). Although the structural properties of this partially covalent liquid strongly deviate from a simple hard-sphere model, the dynamics, as reflected in the quasi-elastic scattering, are beautifully described within the framework of the extended heat mode approximation of Enskogs kinetic theory, analytically derived for a hard spheres system. The present work demonstrates the applicability of Enskogs theory to non hard- sphere and non simple liquids.
The experimental results relevant for the understanding of the microscopic dynamics in liquid metals are reviewed, with special regards to the ones achieved in the last two decades. Inelastic Neutron Scattering played a major role since the development of neutron facilities in the sixties. The last ten years, however, saw the development of third generation radiation sources, which opened the possibility of performing Inelastic Scattering with X rays, thus disclosing previously unaccessible energy-momentum regions. The purely coherent response of X rays, moreover, combined with the mixed coherent/incoherent response typical of neutron scattering, provides enormous potentialities to disentangle aspects related to the collectivity of motion from the single particle dynamics. If the last twenty years saw major experimental developments, on the theoretical side fresh ideas came up to the side of the most traditional and established theories. Beside the raw experimental results, therefore, we review models and theoretical approaches for the description of microscopic dynamics over different length-scales, from the hydrodynamic region down to the single particle regime, walking the perilous and sometimes uncharted path of the generalized hydrodynamics extension. Approaches peculiar of conductive systems, based on the ionic plasma theory, are also considered, as well as kinetic and mode coupling theory applied to hard sphere systems, which turn out to mimic with remarkable detail the atomic dynamics of liquid metals. Finally, cutting edges issues and open problems, such as the ultimate origin of the anomalous acoustic dispersion or the relevance of transport properties of a conductive systems in ruling the ionic dynamic structure factor are discussed.
Reply to the Comment by L. Berthier and J.-P. Bouchaud, Phys. Rev. Lett. 90, 059701 (2003), also cond-mat/0209165, on our paper Phys. Rev. Lett. 89, 097201 (2002), also cond-mat/0203444
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