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Extending a previous study of the velocity autocorrelation function (VAF) ina simulated Lennard-Jones fluid to cover higher-density and lower-temperaturestates, we show that the recently demonstrated multiexponential expansionallows for a full account and understanding of the dynamical processesencompassed by a fundamental quantity as the VAF. In particular, besidesobtaining evidence of a persisting long-time tail, we assign specific andunambiguous physical meanings to groups of exponential modes related to thelongitudinal and transverse collective dynamics, respectively. We have madethis possible by consistently introducing the interpretation of the VAFfrequency spectrum as a global density of states in fluids, generalizing asolid-state concept, and by giving to specific spectral components, obtainedvia the VAF exponential expansion, the corresponding meaning of partialdensities of states relative to specific dynamical processes. The clearidentification of a high-frequency oscillation of the VAF with the near-topexcitation frequency in the dispersion curve of acoustic waves is a neatexample of the power of the method. As for the transverse mode contribution,its analysis turns out to be particularly important, because themultiexponential expansion reveals a transition marking the onset ofpropagating excitations when the density is increased above a threshold value.While this finding agrees with recent literature debating the issue ofdynamical crossover boundaries, such as the one identified with the Frenkelline, we can add detailed information on the modes involved in this specificprocess in the domains of both time and frequency. This will help obtain astill missing full account of transverse dynamics, in its nonpropagating andpropagating aspects which are linked by dynamical transitions depending on boththe thermodynamic states and the excitation wavevectors.

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