Geodesic
Quantum resonance for a~rotator in~a~nonlinear periodic field
Teoretičeskaâ i matematičeskaâ fizika, Tome 43 (1980) no. 3, pp. 417-428

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Behaviour of a plane quantum ratator under a timeperiodic perturbation given as delta-like “kicks” nonlinearly dependent on a phase is studied. The case of so-called quantum resonance is investigated both analytically and numerically. It is shown that for large times the rotator energy is proportional to $t^2$. The structure of quasi-energy spectrum is analysed and its continuity is proved. 
@article{TMF_1980_43_3_a11,
     author = {F. M. Izrailev and D. L. Shepelyanskii},
     title = {Quantum resonance for a~rotator in~a~nonlinear periodic field},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {417--428},
     publisher = {mathdoc},
     volume = {43},
     number = {3},
     year = {1980},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1980_43_3_a11/}
}
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F. M. Izrailev; D. L. Shepelyanskii. Quantum resonance for a~rotator in~a~nonlinear periodic field. Teoretičeskaâ i matematičeskaâ fizika, Tome 43 (1980) no. 3, pp. 417-428. http://geodesic.mathdoc.fr/item/TMF_1980_43_3_a11/