  Extending a previous study of the velocity autocorrelation function (VAF) in
a simulated Lennard-Jones fluid to cover higher-density and lower-temperature
states, we show that the recently demonstrated multiexponential expansion
allows for a full account and understanding of the 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
via 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
multiexponential expansion reveals a transition marking the onset of
propagating excitations when the density is increased above a threshold value.
While this finding agrees with 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 its nonpropagating and
propagating aspects which are linked by dynamical transitions depending on both
the thermodynamic states and the excitation wavevectors.
