Geodesic
Damping of a~highly excited harmonic oscillator in a~crystal
Teoretičeskaâ i matematičeskaâ fizika, Tome 35 (1978) no. 2, pp. 224-232

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The diagonal elements of the density matrix of a dynamical subsystem consisting of a highly excited harmonic oscillator that interacts with crystal vibrations are found. The result obtained is asymptotically exact. Various limiting cases are considered and, in particular, a rigorous criterion for applicability of the balance equations for the considered problem is established. 
@article{TMF_1978_35_2_a7,
     author = {B. I. Makshantsev and V. M. Finkel'berg},
     title = {Damping of a~highly excited harmonic oscillator in a~crystal},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {224--232},
     publisher = {mathdoc},
     volume = {35},
     number = {2},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1978_35_2_a7/}
}
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B. I. Makshantsev; V. M. Finkel'berg. Damping of a~highly excited harmonic oscillator in a~crystal. Teoretičeskaâ i matematičeskaâ fizika, Tome 35 (1978) no. 2, pp. 224-232. http://geodesic.mathdoc.fr/item/TMF_1978_35_2_a7/