Dynamics of Phase Coherence Onset in Bose Condensates of Photons by   Incoherent Phonon Emission
  Recent experiments with photons equilibrating inside a dye medium in a cavity have raised the question of whether Bose condensation can occur in a system with only incoherent interaction with phonons in a bath but without particle-particle interaction. Analytical calculations analogous to those done for a system with particle-particle interactions indicate that a system of bosons interacting only with incoherent phonons can indeed undergo Bose condensation and furthermore can exhibit spontaneous amplification of quantum coherence. We review the basic theory for these calculations. 
D. W. Snoke and S. M. Girvin
cond-mat.quant-gas