Geodesic
Multilevel Landau–Zener formulae: adiabatic reduction on a complex path
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 4 (1997) no. 3, pp. 360-390 
Gabriel Firica. Multilevel Landau–Zener formulae: adiabatic reduction on a complex path. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 4 (1997) no. 3, pp. 360-390. http://geodesic.mathdoc.fr/item/JMAG_1997_4_3_a7/
@article{JMAG_1997_4_3_a7,
     author = {Gabriel Firica},
     title = {Multilevel {Landau{\textendash}Zener} formulae: adiabatic reduction on a complex path},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {360--390},
     year = {1997},
     volume = {4},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_1997_4_3_a7/}
}
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We consider, in the semi-classical (adiabatic) limit, evolution equations whose generators extend into a strip around real axis as a holomorphic family of operators (with respect to the time-variable). The asymptotic expansion of the $\mathbb S$-matrix associated to this evolution can be expressed in terms of simple quantities attached to the singularities for the spectrum of Hamiltonians from complex-time plane. We extend to many-level case the result from [26] which contains as limit cases both the Landau–Zener formula and Friedrichs–Hagedorn results for this problem.