Nonstationary perturbation theory for a degenerate discrete level

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.