Abstract
The quantum dynamics of a charged particle gyrating in a uniform magnetic field and interacting with a monochromatic wave is investigated here under the condition of cyclotron resonance. The classical counterpart of this system is intrinsically degenerate. The structure of the Floquet spectrum and quasienergy functions for the exact and near resonance cases is obtained and related to the classical phase space structure. The evolution of various representative initial states is investigated and the close connection between classical and quantum dynamics at nonlinear cyclotron resonance is demonstrated. The condition for the experimental realization of the acoustic quantum nonlinear cyclotron resonance in conductors is given, and the influence of sound waves on some oscillatory phenomena in quantizing magnetic fields is predicted.
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