Universal wave functions structure in mixed systems
When a regular classical system is perturbed, nonlinear 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 a universal stru...
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| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_02955075_v106_n6_p_Wisniacki |
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| Sumario: | When a regular classical system is perturbed, nonlinear 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 a 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 of 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 revealed using the zeros of the Husimi distribution. © CopyrightEPLA, 2014. |
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