[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
Disciplines :
Physics
Author, co-author :
Wisniacki, Diego A.
Schlagheck, Peter ; Université de Liège > Département de physique > Physique quantique statistique
Language :
English
Title :
Quantum manifestations of classical nonlinear resonances
Publication date :
December 2015
Journal title :
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
ISSN :
1539-3755
eISSN :
1550-2376
Publisher :
American Physical Society, College Park, United States - Maryland
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