Geodesic
Construction of a kinetic equation for a quantum dynamical system interacting with a phonon field by the method of ordered operators
Teoretičeskaâ i matematičeskaâ fizika, Tome 48 (1981) no. 1, pp. 89-105 Cet article a éte moissonné depuis la source Math-Net.Ru

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The derivation of a general kinetic equation for a quantum dynamical system interacting with a phonon field is considered. The theory is constructed by the method of ordered operators without the use of any approximations. The general theory is illustrated by the example of a quantum harmonic oscillator under the influence of a variable external classical force that is linearly coupled to a thermal bath, i.e., a system of noninteraeting quantum oscillators. A generalized kinetic equation of Hloeh type is derived on the basis of the obtained exact relations after an appropriate approximation procedure for the quantum oscillator. 
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     title = {Construction of a~kinetic equation for a~quantum dynamical system interacting with a~phonon field by the method of ordered operators},
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G. O. Balabanyan. Construction of a kinetic equation for a quantum dynamical system interacting with a phonon field by the method of ordered operators. Teoretičeskaâ i matematičeskaâ fizika, Tome 48 (1981) no. 1, pp. 89-105. http://geodesic.mathdoc.fr/item/TMF_1981_48_1_a9/

[1] Feynman R. P., “An operators calculus having application in quantum electrodynamics”, Phys. Rev., 84:2 (1951), 108–128 | DOI | MR | Zbl

[2] Maslov V. P., “Primenenie metoda uporyadochennykh operatorov dlya polucheniya tochnykh reshenii”, TMF, 33:2 (1977), 185–209 | MR | Zbl

[3] Maslov V. P., Operatornye metody, Nauka, M., 1973 | MR

[4] Bogolyubov N. N. (ml.), “Kineticheskoe uravnenie dlya dinamicheskoi sistemy, vzaimodeistvuyuschei s fononnym polem”, TMF, 40:1 (1979), 77–94 | MR

[5] Bogolubov N. N., Kinetic equations for the electron-phonon system, Preprint E17-11822, JINR, Dubna, 1978 | MR

[6] Glauber R. J., “The quantum theory of optical coherence”, Phys. Rev., 130:6 (1963), 2529–2539 | DOI | MR

[7] Glauber R., “Kogerentnost i detektirovanie kvantov”, Kogerentnye sostoyaniya v kvantovoi teorii, Sb., Mir, M., 1972 | MR

[8] Goldberger M., Vatson K., Teoriya stolknovenii, Mir, M., 1967

[9] Magnus M., “On the exponential solution of differential equations for a linear operator”, Commun. Pure and Appl. Math., 7:4 (1954), 649–673 | DOI | MR | Zbl

[10] Wilcox R. M., “Exponential operators and parameter differentiation in quantum physics”, J. Math. Phys., 8:4 (1964), 962–982 | DOI | MR

[11] Zubarev D. N., “Dvukhvremennye funktsii Grina v statisticheskoi fizike”, UFN, 71:1 (1960), 71–116 | DOI

[12] Tyablikov S. V., Metody kvantovoi teorii magnetizma, 2-e izd. ispr. i dop., Nauka, M., 1975 | MR

[13] Bogolyubov N. N., Shirkov D. V., Vvedenie v teoriyu kvantovannykh polei, 3-e izd. pererab., Nauka, M., 1976 | MR

[14] Bogolyubov N. N., Problemy dinamicheskoi teorii v statisticheskoi fizike, Gostekhizdat, M.–L., 1946 | MR

[15] Zubarev D. N., “Sovremennye metody statisticheskoi teorii neravnovesnykh protsessov”, Itogi nauki i tekhn. Sovr. probl. matematiki, 15, VINITI, M., 1980, 131–226

[16] Zubarev D. N., Kalashnikov V. P., “Ekvivalentnost nekotorykh metodov v statisticheskoi mekhanike neobratimykh protsessov”, TMF, 7:3 (1971), 372–394 | Zbl

[17] Vladimirov V. S., Uravneniya matematicheskoi fiziki, 2-e izd. pererab. i dop., Nauka, M., 1971 | MR | Zbl

[18] Gakhov F. D., Kraevye zadachi, 3-e izd. pererab. i dop., Nauka, M., 1977 | MR

[19] Balesku R., Statisticheskaya mekhanika zaryazhennykh chastits, Mir, M., 1967 | MR

[20] Evgrafov M. A., Analiticheskie funktsii, 2-e izd. ispr. i dop., Nauka, M., 1968 | MR | Zbl