  We implement externally excited ZnO Mie resonators in a framework of a
generalized Hubbard Hamiltonian to investigate the lifetimes of excitons and
exciton-polaritons out of thermodynamical equilibrium. Our results are derived
by a Floquet-Keldysh-Green's formalism with Dynamical Mean Field Theory (DMFT)
and a second order iterative perturbation theory solver (IPT). We find that the
Fano resonance which originates from coupling of the continuum of electronic
density of states to the semiconductor Mie resonator yields polaritons with
lifetimes between 0.6 ps and 1.45 ps. These results are compared to ZnO
polariton lasers and to ZnO random lasers. We interpret the peaks of the
exciton-polariton lifetimes in our results as a sign of gain narrowing which
may lead to stable polariton lasing modes in the single excited ZnO Mie
resonator. This form of gain may lead to polariton random lasing in an ensemble
of ZnO Mie resonators in the non-equilibrium.
