Reference : Quantum manifestations of classical nonlinear resonances
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Physics
http://hdl.handle.net/2268/191274
Quantum manifestations of classical nonlinear resonances
English
Wisniacki, Diego A. []
Schlagheck, Peter mailto [Université de Liège > Département de physique > Physique quantique statistique >]
Dec-2015
Physical Review. E ,Statistical, Nonlinear, and Soft Matter Physics
American Physical Society
92
062923
Yes (verified by ORBi)
International
1539-3755
1550-2376
College Park
MD
[en] When an integrable classical system is perturbed, nonlinear resonances are born, grow, and eventually disappear due to chaos. In this paper the quantum manifestations of such a transition are studied in the standard map. We show that nonlinear resonances act as a perturbation that break eigenphase degeneracies for unperturbed states with quantum numbers that differ in a multiple of the order of the resonance. We show that the eigenphase splittings are well described by a semiclassical expression based on an integrable approximation of the Hamiltonian in the vicinity of the resonance. The morphology in phase space of these states is also studied. We show that the nonlinear resonance imprints a systematic influence in their localization properties
Researchers
http://hdl.handle.net/2268/191274
10.1103/PhysRevE.92.062923

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