Abstract
An approximate analytical solution is developed for the Floquet states of a quantum-mechanical rigid rotor subject to an arbitrary periodically-time-dependent driving force. The rotor Hamiltonian is expanded in powers of the rotational ``anharmonicity'' about the angular-momentum state \ensuremath{\Vert}${\mathit{j}}_{0}$〉 and a perturbative Lie algebraic form of the evolution operator is derived. Except in special cases, the resulting Floquet states are localized. The localization length shows a sharp transition from narrow to broad for those Floquet states in the vicinity of a resonance with one of the Fourier components of the driving field. The special case of the periodically kicked rotor is also discussed, which, because of its unbounded frequency spectrum, can lead to delocalized Floquet states.
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