  It is well known from the quantum theory of strongly correlated systems that
poles (or more subtle singularities) of dynamic correlation functions in
complex plane usually correspond to the collective or localized modes. Here we
address singularities of velocity autocorrelation function $Z$ in complex
$\omega$-plain for the one-component particle system with isotropic pair
potential. We have found that naive few poles picture fails to describe
analytical structure of $Z(\omega)$ of Lennard-Jones particle system in complex
plain. Instead of few isolated poles we see the singularity manifold of
$Z(\omega)$ forming branch cuts that suggests Lennard-Jones velocity
autocorrelation function is a multiple-valued function of complex frequency.
The brunch cuts are separated from the real axis by the well-defined "gap". The
gap edges extend approximately parallel to the real frequency axis. The
singularity structure is very stable under increase of the temperature; we have
found its trace at temperatures even several orders of magnitude higher than
the melting point. Our working hypothesis that the branch cut origin is related
to the "interference" in $Z$ of one-particle kinetics and collective
hydrodynamic motion.
