Geodesic
Quantum theory of channeling: Generalized transport equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 29 (1976) no. 3, pp. 376-387

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The theory of channeling is formulated in the framework of nonequilibrium statistical mechanics. A statistical operator is constructed for a nonequilibrium system consisting of a thermal bath and fast charged particles (below-barrier and above-barrier levels) with allowance for the transport of energy and particles. Generalized transport equations are obtained by averaging the equations of motion for the operators with respect to this nonequilibrium distribution. The formalism is applied to the analysis of dechanneling, the energy losses of particles, and the electron diffusion coefficient. 
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     author = {D. N. Zubarev and Yu. A. Kashlev},
     title = {Quantum theory of channeling: {Generalized} transport equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {29},
     number = {3},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1976_29_3_a8/}
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D. N. Zubarev; Yu. A. Kashlev. Quantum theory of channeling: Generalized transport equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 29 (1976) no. 3, pp. 376-387. http://geodesic.mathdoc.fr/item/TMF_1976_29_3_a8/