Geodesic
Derivation of quantum kinetic equation from the Liouville-von Neumann equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 1, pp. 33-43

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A quantum Markov kinetic equation is derived from the Liouville–von Neumann equation in the framework of second-order kinetic perturbation theory. The proposed method can be used to obtain an equation that describes the quantum diffusion of a particle in a crystal. 
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     author = {B. V. Bondarev},
     title = {Derivation of quantum kinetic equation from the {Liouville-von} {Neumann} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {100},
     number = {1},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_100_1_a3/}
}
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B. V. Bondarev. Derivation of quantum kinetic equation from the Liouville-von Neumann equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 1, pp. 33-43. http://geodesic.mathdoc.fr/item/TMF_1994_100_1_a3/