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Aharonov-Anandan phase and the quasistationarity of driven quantum systems

We derive necessary and sufficient conditions for the quasistationarity of time-dependent quantum systems and point out the relationship between the degree of quasistationarity, the Fubini-Study metric, and the Aharonov-Anandan phase. As an illustration, we analyze the dynamical localization of an electron in a double quantum well and the sustainability of field-induced orientation of polar molecules.