Complex singularities of fluid velocity autocorrelation function^{1)}

N. M. Chtchelkatchev^{+ 2)}, R. E. Ryltsev^{+*×}

^{+}Landau Institute for Theoretical Physics of the RAS, 142432 Chernogolovka, Russia

^{*}Institute of Metallurgy UB of the RAS, 620016 Ekaterinburg, Russia

^{×}Ural Federal University, 620002 Ekaterinburg, Russia

**Abstract**

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(ω) 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.