Time dependence of the velocity autocorrelation function of a fluid: An eigenmode analysis of dynamical processes

Abstract

The velocity autocorrelation function (VAF), a key quantity in the atomic-scale dynamics of fluids, has been the first paradigmatic example of a long-time tail phenomenon, and much work has been devoted to detecting such long-lasting correlations and understanding their nature. There is, however, much more to the VAF than simply the evidence of this long-time dynamics. A unified description of the VAF from very short to long times, and of the way it changes with varying density, is still missing. Here we show that an approach based on very general principles makes such a study possible and opens the way to a detailed quantitative characterization of the dynamical processes involved at all time scales. From the analysis of molecular dynamics simulations for a slightly supercritical Lennard-Jones fluid at various densities, we are able to evidence the presence of distinct fast and slow decay channels for the velocity correlation on the time scale set by the collision rate. The density evolution of these decay processes is also highlighted. The method presented here is very general, and its application to the VAF can be considered as an important example.

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

“…In summary, it was found [20] that, for all the considered thermodynamical states considered and in the whole time range accessed by MD, the VAF is described perfectly by fitting the sum of a small number of exponential terms. Four of them are real exponentials having decay times ranging from the order of one collision time ("fast modes") up to the order of several tens of collision times ("slow modes").…”

“…MD simulations of the VAF for the LJ (12-6) fluid along the slightly supercritical T * = 1.35 isotherm were already reported for particle number densities up to ρ * = 0.60 [20]. [20].…”

“…3 and 4 where the log-log scale is used for an easy comparison with a power-law time dependence. As already recalled [20], the calculated VAF beyond a certain time is affected by spurious effects due to the use of periodic boundary conditions [1,31,32]. This occurs for time lags greater than the so-called recurrence time t R = (N/ρ) 1/3 /c s required by a density fluctuation to propagate over the box length at the adiabatic sound speed c s .…”

“…[20], these constraints both reduce the number of free fit parameters and allow for a very accurate description of the VAF short-time dependence by ensuring finiteness of its time derivatives at t = 0 up to the sixth order. Computational details of the fitting analysis are also reported in Ref.…”

“…Computational details of the fitting analysis are also reported in Ref. [20]. Table refers to the T * = 1.35 isotherm, the lower part to the ρ * = 0.80 isochore.…”