Dykhne-Davis-Pechukas formula

Nonresonant Deviations from Adiabaticity Perturbation Theory, Superadiabatic Schemes, and Dykhne—Davis—Pechukas Formula... 

This result is due to Dykhne [48] and Davis and Pechukas [49] and has been extended to A-level systems [50]. The conditions of validity of the so-called Dykhne-Davis-Pechukas (DDP) formula has been established in [51,52], This formula allows us to calculate in the adiabatic asymptotic limit the probability of the nonadiabatic transitions. This formula captures, for example, the result of the Landau-Zener formula, which we study below. 

---