  We study the reduced dynamics of a pair of non-degenerate oscillators coupled
collectively to a thermal bath. The model is related to the trilinear boson
model where the idler mode is promoted to a field. Due to nonlinear coupling,
the Markovian master equation for the pair of oscillators admits non-Gaussian
equilibrium states, where the modes distribute according to the Bose-Einstein
statistics. These states are metastable before the nonlinear coupling is taken
over by linear coupling between the individual oscillators and the field. The
Gibbs state for the individual modes lies in the subspace with infinite
occupation quantum number. We present the time evolution of a few states to
illustrate the behaviors of the system.
