Rf. Sinclair et al., QUANTUM FOKKER-PLANCK EQUATION FOR INTERACTING WAVES, Philosophical transactions-Royal Society of London. Physical sciences and engineering, 354(1709), 1996, pp. 951-978
The quantum Fokker-Planck equation for the irreversible evolution of a
bath of interacting oscillators is derived with sufficient generality
that both the action and angle dependence of the distribution functio
n are maintained in the classical limit. This approach unifies Landau-
Rumer processes, spontaneous phonon decay, quantum renormalization of
the speed of sound, and quantum wave turbulence.