Universal wave function structure of mixed systems

D. A. WISNIACKI

EUROPHYSICS LETTERS

EPL ASSOCIATION

Lugar: Bologna; Año: 2014 vol. 106 p. 600061 - 600066

0295-5075

When a regular classical system is perturbed, nonlinear resonances appear as pre- scribed by the KAM and Poincar`e-Birkhoff theorems. Manifestations of this classical phenomena to the morphologies of quantum wave functions are studied in this letter. We reveal a system- atic 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 reso- nance. 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.