Universal wave functions structure in mixed systems
Departamento de Física and IFIBA, FCEyN, UBA Ciudad Universitaria - Pabellón 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Received: 10 March 2014
Accepted: 7 June 2014
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.
PACS: 05.45.Mt – Quantum chaos; semiclassical methods / 03.65.Sq – Semiclassical theories and applications
© EPLA, 2014