  We present an analytical and numerical analysis of the particle creation in
an optomechanical cavity in parametric resonance. We treat both the
electromagnetic field and the mirror as quantum degrees of freedom and study
the dynamical evolution as a closed quantum system. We consider different
initial states and investigate the spontaneous emission of photons from phonons
in the mirror. We find that for initial phononic product states the evolution
of the photon number can be described as a non-harmonic quantum oscillator,
providing an useful tool so as to estimate the maximum and mean number of
photons produced for arbitrary high energies. The efficiency of this mechanism
is further analyzed for a detuned cavity as well as the possibility of
stimulating the photon production by adding some initial ones to the cavity. We
also find relationships for the maximum and mean entanglement between the
mirror and the wall in these states. Additionally we study coherent states for
the motion of the mirror to connect this model with previous results from
quantum field theory with a classical mirror. Finally we study thermal states
of phonons in the wall and the equilibration process that leads to a stationary
distribution.
