Multilevel Landau-Zener formulae: adiabatic reduction on a complex path

Анотація

We consider, in the semi-classical (adiabatic) limit, evolution equations whose generation extend into a strip around real axis as a holomorphic family of operators (with respect to the time-variable). The asymptotic expansion of the 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-Zenner formula and Friedrichs-Hagedorn results for this problem.