Quasiadiabatic time evolution, avoided level crossings, and Berry’s phase

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A nonperturbative theory for quasiadiabatic time evolution in quantum systems is presented. The dynamics of the passage through an avoided level crossing is given by a nonperturbative alternative to the Landau-Zener theory used for diatomic predissociation. The theory provides the theoretical framework for a quantitative understanding of the quantum steps in the hyteresis loops observed very recently in manganese acetate crystals. These steps correspond to avoided level crossings for the associated, fully adiabatic problem. A natural extention of the theory yields quasiadiabatic corrections to Berry's phase.