Geodesic
Nonstationary perturbation theory for a degenerate discrete level
Teoretičeskaâ i matematičeskaâ fizika, Tome 25 (1975) no. 3, pp. 414-418 Cet article a éte moissonné depuis la source Math-Net.Ru

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Asymptotical representations is constructed for evolution operator $S(0,-T)P$ at $T\to\infty$ regularized by means of the substitution $H_0\to H_0-i\varepsilon P'$ [1] (non-adiabatic regularisation which does not depend: on time). It is shown that $S(0,-T)P=\Omega\exp (-iQT)R_0+O(e^{-\varepsilon T})$, $Q$ and $\Omega$ being finite operators not depending of $T$ and regular in the neighbourhood $\varepsilon=0$. $Q$ can be interpreted as secular operator and $Q$ as wave operator. 
@article{TMF_1975_25_3_a12,
     author = {A. L. Kitanin},
     title = {Nonstationary perturbation theory for a degenerate discrete level},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {414--418},
     year = {1975},
     volume = {25},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1975_25_3_a12/}
}
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A. L. Kitanin. Nonstationary perturbation theory for a degenerate discrete level. Teoretičeskaâ i matematičeskaâ fizika, Tome 25 (1975) no. 3, pp. 414-418. http://geodesic.mathdoc.fr/item/TMF_1975_25_3_a12/

[1] A. N. Vasilev, A. L. Kitanin, TMF, 24 (1975), 219 | MR | Zbl

[2] V. V. Tolmachev, Teoriya fermi-gaza, Izd. MGU, 1973