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The anomalous dynamical evolution and the crossing of nonadiabatic energylevels are investigated for exactly solvable time-dependent quantum systemsthrough a reverse-engineering scheme. By exploiting a typical driven model, weelucidate the peculiarities of its dynamics with anomalous behavior: theevolution of the adiabatic states and of the nonadiabatic ones exhibitsopposite behavior with their representative vectors evolving from a parallelstate to an antiparallel state: the nonadiabatic level crossing is identifiedas a necessary consequence since the crossing point corresponds exactly to theperpendicular point of the two vectors in the parametric space. In the light ofthese results, we show that various driven models with anomalous dynamicalevolution can be designed and they offer alternative protocols for the quantumstate control.

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

Anomalous dynamical evolution and nonadiabatic level crossing in exactly solvable time-dependent quantum systems