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Dissipative effects on the nonadiabatic transition for the two and threelevel systems are studied. When the system is affected by a strong dissipationthrough the diabatic states, the exact transition probability is enumeratedmaking use of the effective master equation. In the two-level system, weconsider the case where the external field is swept from not only a negativelarge value but also from the resonant field, and the exact transitionprobabilities in these cases are derived. The transition probabilities arederived for the three-level system where the three diabatic states form onlyone avoided level crossing point. These probabilities are compared with the onein the pure quantum case obtained by Carroll and Hioe.Comment: 14 pages including 2 figures and 1 table. in press PR

Nonadiabatic transition probabilities in the presence of strong dissipation at an avoided-level crossing point