The Exciton Boser. R. J. Ram and A. İmamoğlu in Coherence and Quantum Optics VII (1996).  What the paper says!?

This text is the most likely candidate as the ... Ironically, they also refer here to their Ref.  (with the slightly different title "Quantum dynamics of nonequilibrium excitons") for the statement that «the ordered state of the boser excitons is shown to be a coherent state», so there is a circular argument here.

There is little, if anything, conceptually different from the other text.

They even suggest a way to cancel interactions:

The exciton-exciton interactions can be suppressed by application of a quantizing magnetic field perpendicular to

the quantum well.

They provide rate equations for the two-level system:

The loss terms $\Gamma_\mathrm{something}$ are included phenomenologically (why not derived everything phenomenologically then?) This rewrites as:

with condition $n_k>\bar n_\mathrm{ph}$ for final-state stimulation.

This brings them to this master equation:

which they claim «describes the complete quantum dynamics of an exciton gas in the Born-Markov approximation, provided that the exciton occupancy in the excited states is kept constant (i.e. no pump depletion)», which is somewhat surprising given that this is for a single harmonic oscillator (not an exciton gas) and the pump depletion is given such an important role to define a phase transition.

The following is very interesting but not clearly substantiated:

This inversion condition arises from the need for the entropy to increase as energy is stored in the form of coherent excitons. From the above analysis, we see that the exciton boser, like the laser oscillator, is essentially a heat engine that does work by virtue of heat exchange between the optical pump and the phonon

reservoirs.

Pump depletion is the

dominant saturation mechanism for the ideal boser.

They say that previous models «have neglected either quantum fluctuations or finite phonon occupancies».