Abstract:
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.
Citation:
G. O. Balabanyan, “Construction of a kinetic equation for a quantum dynamical system interacting with a phonon field by the method of ordered operators”, TMF, 48:1 (1981), 89–105; Theoret. and Math. Phys., 48:1 (1981), 624–635
\Bibitem{Bal81}
\by G.~O.~Balabanyan
\paper Construction of a~kinetic equation for a~quantum dynamical system interacting with a~phonon field by the method of ordered operators
\jour TMF
\yr 1981
\vol 48
\issue 1
\pages 89--105
\mathnet{http://mi.mathnet.ru/tmf4475}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=630273}
\transl
\jour Theoret. and Math. Phys.
\yr 1981
\vol 48
\issue 1
\pages 624--635
\crossref{https://doi.org/10.1007/BF01037988}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1981ND61200010}
Linking options:
https://www.mathnet.ru/eng/tmf4475
https://www.mathnet.ru/eng/tmf/v48/i1/p89
This publication is cited in the following 4 articles:
G. O. Balabanyan, “Application of the method of ordered operators in the theory of liquid metals”, Theoret. and Math. Phys., 59:2 (1984), 499–509
G. O. Balabanyan, “Use of the method of ordered operators in the theory of laser systems. II. Construction of a theory of laser radiation for Dicke models”, Theoret. and Math. Phys., 54:2 (1983), 181–188
G. O. Balabanyan, “Derivation of asymptotically exact equations for the radiation in model systems of Dicke type”, Theoret. and Math. Phys., 56:3 (1983), 912–921
G. O. Balabanyan, “Use of the method of ordered operators in the theory of laser systems. Derivation of asymptotically exact equations for radiation. I”, Theoret. and Math. Phys., 54:1 (1983), 82–92