Quantum manifestations of classical nonlinear resonances

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
D A Wisniacki, Peter Schlagheck

Abstract

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.

References

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Sep 21, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·D A WisniackiF Borondo
Mar 12, 2015·Scientific Reports·Hojeong KwakKyungwon An
May 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Chang-Hwan YiChil-Min Kim
May 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Yasutaka HanadaKensuke S Ikeda
Sep 19, 2015·Physical Review Letters·Stefan GehlerHans-Jürgen Stöckmann

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Citations

Apr 7, 2017·Optics Express·Chang-Hwan YiChil-Min Kim
Jan 14, 2017·Physical Review. E·Normann MertigRoland Ketzmerick
Sep 15, 2016·Physical Review. E·Julius Kullig, Jan Wiersig

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