Complex singularities of fluid velocity autocorrelation function

There are intensive debates regarding the nature of supercritical fluids: if their evolution from liquid-like to gas-like behavior is a continuous multistage process or there is a sharp well defined crossover. Velocity autocorrelation function $Z$ is the established detector of evolution of fluid particles dynamics. Usually, complex singularities of correlation functions give more information. So we investigate $Z$ in complex plane of frequencies using numerical analytical continuation. We have found that naive picture with few isolated poles fails describing $Z(\omega)$ of one-component Lennard–Jones (LJ) fluid. Instead we see the singularity manifold forming branch cuts extending approximately parallel to the real frequency axis. That suggests LJ velocity autocorrelation function is a multiple-valued function of complex frequency. The branch cuts are separated from the real axis by the well-defined “gap” whose width corresponds to an important time scale of a fluid characterizing crossover of system dynamics from kinetic to hydrodynamic regime. Our working hypothesis is that the branch cut origin is related to competition between one-particle dynamics and hydrodynamics. The observed analytical structure of $Z$ is very stable under changes of temperature; it survives at temperatures which are by the two orders of magnitude higher than the critical one.