Geodesic
Fokker--Planck equation and allowance for quantum fluctuations in the theory of excitons and biexcitons of high density
Teoretičeskaâ i matematičeskaâ fizika, Tome 75 (1988) no. 2, pp. 295-305

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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. 
@article{TMF_1988_75_2_a13,
     author = {S. A. Moskalenko and A. Kh. Rotaru and Yu. M. Shvera},
     title = {Fokker--Planck equation and allowance for quantum fluctuations in the theory of excitons and biexcitons of high density},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {295--305},
     publisher = {mathdoc},
     volume = {75},
     number = {2},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1988_75_2_a13/}
}
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S. A. Moskalenko; A. Kh. Rotaru; Yu. M. Shvera. Fokker--Planck equation and allowance for quantum fluctuations in the theory of excitons and biexcitons of high density. Teoretičeskaâ i matematičeskaâ fizika, Tome 75 (1988) no. 2, pp. 295-305. http://geodesic.mathdoc.fr/item/TMF_1988_75_2_a13/