Universal wave functions structure in mixed systems

Abstract

When a regular classical system is perturbed, non-linear resonances appear as prescribed by the KAM and Poincarè-Birkhoff theorems. Manifestations of this classical phenomena to the morphologies of quantum wave functions are studied in this letter. We reveal a systematic formation of an universal structure of localized wave functions in systems with mixed classical dynamics. Unperturbed states that live around invariant tori are mixed when they collide in an avoided crossing if their quantum numbers differ in a multiple to the order of the classical resonance. At the avoided crossing eigenstates are localized in the island chain or in the vicinity of the unstable periodic orbit corresponding to the resonance. The difference of the quantum numbers determines the excitation of the localized states which is reveled using the zeros of the Husimi distribution.

6 pages, 4 figures

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Cited by in corpus (2)

• Effective versus Floquet theory for the Kerr parametric oscillator
• Perturbation-Free Prediction of Resonance-Assisted Tunneling in Mixed Regular--Chaotic Systems