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.
We consider metamolecule consisting of bosonic mode correlated with the two-level system: it can be, for example, plasmonic mode interacting with the quantum dot. We focus on the parameter range where all the correlations are strong and of the same o
rder: interaction between bosonic mode correlated with the two-level system, external coherent drive and dissipation. Quantum Monte-Carlo simulations show a fluorescence of this system at dissipation larger than the driving amplitude and strong (by the order of magnitude) narrowing of its spectral line. This effect may be related to kind of a quantum stochastic resonance. We show that the fluorescence corresponds to finite domain over the coherent drive with sharp lower threshold and there is splitting of the Wigner function.
