Density and time scaling effects on the velocity autocorrelation function of quantum and classical dense fluid para-hydrogen

We report the results of a ring polymer molecular dynamics study of the Kubo velocity autocorrelation function of a quantum fluid as para-hydrogen aimed at the comparison with its classical counterpart. Quite different density conditions were considered for both the classical and quantum cases, in order to compare the two systems before and after the dynamical crossover typically undergone by the velocity autocorrelation function (VAF) of fluids at densities around the triple point, where the shape of the function changes from a monotonic to an oscillatory behavior with a negative minimum. A detailed study of the phase diagram of classical para-hydrogen was necessary for a reasonable choice of the classical states to be taken into consideration, in the spirit of the classical principle of corresponding states. The shape of the quantum and classical VAF was thoroughly analyzed, exhibiting at all studied densities clear differences that might be taken as evidence of quantum effects. We show that these differences are substantially reduced by applying a state-dependent time scaling with respect to a reference time identified with the inverse of the collision rate. An even better coincidence in shape is found by comparing the two systems at slightly non-corresponding reduced densities, suggesting that the quantum system behaves almost like the classical one, but at systematically less dense reduced states of the latter. We also find an unexpected and quite interesting density trend of the collision rate of both classical and quantum para-hydrogen, which accounts for the effectiveness of the scaling throughout the explored density range. The mean kinetic energy and the diffusion coefficients are also discussed in some detail.