Nonadiabatic Transition Probabilities in the Presence of Strong Dissipation at an Avoided Level Crossing Point

Dissipative effects on the nonadiabatic transition for the two and three level systems are studied. When the system is affected by a strong dissipation through the diabatic states, the exact transition probability is enumerated making use of the effective master equation. In the two-level system, we consider the case where the external field is swept from not only a negative large value but also from the resonant field, and the exact transition probabilities in these cases are derived. The transition probabilities are derived for the three-level system where the three diabatic states form only one avoided level crossing point. These probabilities are compared with the one in the pure quantum case obtained by Carroll and Hioe.