Density of states and dynamical crossover in a dense fluid revealed by exponential mode analysis of the velocity autocorrelation function

Abstract

Extending a preceding study of the velocity autocorrelation function (VAF) in a simulated Lennard-Jones fluid [Phys. Rev. E 92, 042166 (2015)] to cover higher-density and lower-temperature states, we show that the recently demonstrated multi-exponential expansion method allows for a full account and understanding of the basic dynamical processes encompassed by a fundamental quantity as the VAF. In particular, besides obtaining evidence of a persisting long-time tail, we assign specific and unambiguous physical meanings to groups of exponential modes related to the longitudinal and transverse collective dynamics, respectively. We have made this possible by consistently introducing the interpretation of the VAF frequency spectrum as a global density of states in fluids, generalizing a solid-state concept, and by giving to specific spectral components, obtained through the VAF exponential expansion, the corresponding meaning of partial densities of states relative to specific dynamical processes. The clear identification of a high-frequency oscillation of the VAF with the near-top excitation frequency in the dispersion curve of acoustic waves is a neat example of the power of the method. As for the transverse mode contribution, its analysis turns out to be particularly important, because the multi-exponential expansion reveals a transition marking the onset of propagating excitations when the density is increased beyond a threshold value. While this finding agrees with the recent literature debating the issue of dynamical crossover boundaries, such as the one identified with the Frenkel line, we can add detailed information on the modes involved in this specific process in the domains of both time and frequency. This will help obtain a still missing full account of transverse dynamics, in both its nonpropagating and propagating aspects which are linked through dynamical transitions depending on both the thermodynamic states and the excitation wavevectors.

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“…Analysis of the VAF spectrum Z ( ω ) can further support the preceding deductions, keeping in mind that such a function has peaks or shoulders where vibrational state frequencies occur more often with varying Q , i.e., as already stated, it represents the DoS of the liquid 17 , 34 . The DoS behaviour can help not only in confirming the presence of propagating modes of both longitudinal and transverse nature, but also in establishing which excitations give rise to flat branches in the dispersion curve.…”

“…In particular, from the particle configurations we calculated the VAF as: where v (t) is the velocity of one particle at time t and the brackets 〈...〉 define an ensemble average over all particles. We recall that its spectrum Z ( ω ) can be accessed either by simulations 34 or by incoherent neutron scattering determinations of the self dynamic structure factor S self ( Q , ω ) 17 .…”

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“…At certain densities and length scales, shear modes are unambiguously present also in simple monatomic dense fluids, as confirmed by innumerable simulation results for the density of states of liquids (i.e., the spectrum of the velocity autocorrelation function) or for the transverse current-current correlation, since the late 1970s [18][19][20] up to more recent [21,22] and present times [7,23,24]. Nonetheless, there are contrasting indications about what can effectively be extracted from measurements of S(Q, ω), if one takes into account that a more or less elaborate data correction involving some approximations, and a sensible choice of the model fit functions are required.…”

“…We will show, as in the case of other important functions for the dynamics of the liquid state, that a multiexponential analysis [41][42][43] of the intermediate scattering function F (Q, t ) [or, equivalently, a multi-Lorentzian analysis of the dynamic structure factor S(Q, ω)] is once again extremely accurate, ensuring the fulfillment of the first few sum rules along with excellent descriptions of the addressed function, and leading to a clear characterization of the main dynamical properties of the system. Thus the multimode representation is demonstrated here to account very well not only for single-particle (self-) quantities like the VAF, Z (t ), [23,[44][45][46], or the self-intermediate scattering function, F self (Q, t ) [24], but also for a collective function as F (Q, t ). Of course, the same holds for their respective spectra, Z (ω), S self (Q, ω), and S(Q, ω).…”

“…In recent years we have shown the effectiveness of the exponential series representation [41][42][43] in accounting for the behavior of time correlation functions of classical [23,24,44] and quantum [45,46] fluids. The power of the method lies not only in its providing excellent descriptions of the most relevant functions in liquid state physics, but also in its merit to facilitate the imposition of, at least a few, physical constraints, thus largely increasing the reliability of the results.…”