Nonadiabatic transitions induced by a time-dependent Hamiltonian in the semiclassical/adiabatic limit: The two-state case

We show rigorously, within the two-state approximation, that in the semiclassical limit h/→0 a nonadiabatic transition induced by an analytic time-dependent Hamiltonian is localized to the vicinity of a complex crossing of the two adiabatic potential curves, with transition amplitude independent of the nonadiabatic coupling and given by a simple formula of A. M.Dykhne.