Landau–Zener transition with energy-dependent decay rate of the excited state

A remarkable feature of the Landau–Zener transition is insensitivity survival probability to decay rate, τ−1, excited state. Namely, for a particle which initially (at t→−∞) in ground state remain at t→∞ same insensitive τ−1 due e.g. coupling continuum (Akulin and Schleich, 1992). This was demonstrated case when density states energy-independent. We study opposite limit step-like function energy. As result this behavior states, rate driven level experiences jump as time certain moment t0. take advantage fact that analytical solution tt0 known. show enters t0 comparable time.