Geodesic
Establishment of~statistical equilibrium in~a~quantum chain of~harmonic oscillators
Teoretičeskaâ i matematičeskaâ fizika, Tome 44 (1980) no. 2, pp. 263-270

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A quantum chain of $N$ harmonic oscillators is considered using perturbation theory methods. The author derives the density matrix dynamics of a subsystem containing $N'$ oscillators when the whole chain relaxes from some initial pure state. The Gibbs distribution is shown to be the time-average thermodynamical limit of the relevant statistical operator. The presence of a weak anharmonic interaction in the system makes the density matrix deviations from the canonical distribution extremely rare. 
@article{TMF_1980_44_2_a11,
     author = {S. B. Rutkevich},
     title = {Establishment of~statistical equilibrium in~a~quantum chain of~harmonic oscillators},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {263--270},
     publisher = {mathdoc},
     volume = {44},
     number = {2},
     year = {1980},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1980_44_2_a11/}
}
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S. B. Rutkevich. Establishment of~statistical equilibrium in~a~quantum chain of~harmonic oscillators. Teoretičeskaâ i matematičeskaâ fizika, Tome 44 (1980) no. 2, pp. 263-270. http://geodesic.mathdoc.fr/item/TMF_1980_44_2_a11/