Geodesic
Generalized Fokker--Planck equation for quantum systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 48 (1981) no. 3, pp. 373-384

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A dynamical equation (of Fokker–Planck type) is obtained for the quantum distribution function of an arbitrary set of coarse-grain variables used to describe the evolution of a strongly fluctuating nonequilibrium system. In the general case, this equation is an integrodifferential equation, and its “nonlocality” is due not only to the contribution of small-scale fluctuations but also to the noncommutativity of the basis operators corresponding to the coarse-grain variables. The conditions under which a transition to a local approximation is possible are considered. If the basis operators form a complete set, the obtained generalized Fokker–Planck equation goes over into a “continuity equation” for the Weyl distribution function, and in this case it is equivalent to an exact Liouville equation. 
@article{TMF_1981_48_3_a8,
     author = {V. G. Morozov},
     title = {Generalized {Fokker--Planck} equation for quantum systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {373--384},
     publisher = {mathdoc},
     volume = {48},
     number = {3},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1981_48_3_a8/}
}
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V. G. Morozov. Generalized Fokker--Planck equation for quantum systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 48 (1981) no. 3, pp. 373-384. http://geodesic.mathdoc.fr/item/TMF_1981_48_3_a8/