Wisniacki Diego A, Schlagheck Peter
Departamento de Física and IFIBA, FCEyN, UBA Ciudad Universitaria, Pabellón 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina.
Departement de Physique, University of Liege, 4000 Liège, Belgium.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Dec;92(6):062923. doi: 10.1103/PhysRevE.92.062923. Epub 2015 Dec 28.
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.
