Fokker–Planck equation and allowance for quantum fluctuations in the theory of excitons and biexcitons of high density

The methods of the quantum theory of fluctuations and damping are used to obtain a master equation for the density matrix of Bogolyubov–coherent excitons, photons, and biexcitons in solids. Glauber's $P$ representation is used to derive a Fokker–Planck equation for the system of coherent quasiparticles. Conditions are found for two-photon lasing biexcitons in the case of exciton-biexciton conversion. It is shown that transition from the disordered to the ordered phase is equivalent to a phase transition of the first kind.