Geodesic
Superoperator method in the theory of an oscillator which interacts weakly with a medium. I. General results
Teoretičeskaâ i matematičeskaâ fizika, Tome 35 (1978) no. 1, pp. 113-126 
V. F. Los'. Superoperator method in the theory of an oscillator which interacts weakly with a medium. I. General results. Teoretičeskaâ i matematičeskaâ fizika, Tome 35 (1978) no. 1, pp. 113-126. http://geodesic.mathdoc.fr/item/TMF_1978_35_1_a11/
@article{TMF_1978_35_1_a11,
     author = {V. F. Los'},
     title = {Superoperator method in the theory of an~oscillator which interacts weakly with a~medium. {I.~General} results},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {113--126},
     year = {1978},
     volume = {35},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1978_35_1_a11/}
}
TY  - JOUR
AU  - V. F. Los'
TI  - Superoperator method in the theory of an oscillator which interacts weakly with a medium. I. General results
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1978
SP  - 113
EP  - 126
VL  - 35
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1978_35_1_a11/
LA  - ru
ID  - TMF_1978_35_1_a11
ER  - 
%0 Journal Article
%A V. F. Los'
%T Superoperator method in the theory of an oscillator which interacts weakly with a medium. I. General results
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1978
%P 113-126
%V 35
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1978_35_1_a11/
%G ru
%F TMF_1978_35_1_a11

Voir la notice de l'article provenant de la source Math-Net.Ru

The superoperator method is used to construct the quantum theory of an oscillator which interacts weakly with a medium. General expressions are obtained for the spectral representations of the correlations functions of the displacements and the population numbers of the oscillator, and also kinetic equations for the time correlation functions. These results make it possible to investigate the dynamics of an oscillator when allowance is made for any power of the oscillator displacement operator in the Hamiltonian describing the nonlinearity of the oscillator and in the Hamiltonian describing the interaction between the oscillator and the fluctuations of the medium. The influence of fluctuations of the medium on the dynamics of the oscillator is described by the correlation functions for the potential energy of the medium. This yields, in particular, the fine structure in the spectral distribution of a nonlinear oscillator, the line widths of the structure being expressed in terms of the correlation function of the medium. In the theory developed here, the medium with which the oscillator interacts is not particularized.

[1] N. N. Bogolyubov, O nekotorykh statisticheskikh metodakh v matematicheskoi fizike, Izd-vo AN USSR, Kiev, 1945 | MR

[2] J. Schwinger, J. Math. Phys., 2 (1961), 407 | DOI | MR | Zbl

[3] B. Ya. Zeldovich, A. M. Perelomov, V. S. Popov, ZhETF, 55 (1968), 589; 57 (1969), 196

[4] M. O. Scully, W. E. Lamb, Phys. Rev., 159 (1967), 208 | DOI

[5] L. Mandel, E. Wolf, Rev. Mod. Phys., 37 (1965), 231 | DOI | MR

[6] M. I. Dykman, M. A. Krivoglaz, Phys. Stat. Sol. (b), 48 (1971), 497 ; УФЖ, 17 (1972), 1971 | DOI

[7] M. I. Dykman, M. A. Krivoglaz, ZhETF, 64 (1973), 993

[8] M. I. Dykman, M. A. Krivoglaz, Phys. Stat. Sol. (b), 68 (1975), 111 | DOI

[9] R. Zwanzig, Physica, 30 (1964), 1109 | DOI | MR

[10] L. Mower, Phys. Rev., 142 (1966), 799 | DOI