Strange attractors in periodically-kicked degenerate Hopf bifurcations

We prove that spiral sinks (stable foci of vector fields) can be transformed into strange attractors exhibiting sustained, observable chaos if subjected to periodic pulsatile forcing. We show that this phenomenon occurs in the context of periodically-kicked degenerate supercritical Hopf bifurcations. The results and their proofs make use of a new multi-parameter version of the theory of rank one maps developed by Wang and Young.Comment: 16 page

Exotic quantum phase transitions in a Bose-Einstein condensate coupled to an optical cavity

A new extended Dicke model, which includes atom-atom interactions and a driving classical laser field, is established for a Bose-Einstein condensate inside an ultrahigh-finesse optical cavity. A feasible experimental setup with a strong atom-field coupling is proposed, where most parameters are easily controllable and thus the predicted second-order superradiant-normal phase transition may be detected by measuring the ground-state atomic population. More intriguingly, a novel second-order phase transition from the superradiant phase to the \textquotedblleft Mott" phase is also revealed. In addition, a rich and exotic phase diagram is presented.Comment: 4 pages; figures 1 and 3 are modified; topos are correcte