High-Q cavity-induced synchronization in oscillator arrays

A model for a large number of Josephson junctions coupled to a cavity is presented. The system displays synchronization behavior very similar to that reported in recent experiments [P. Barbara ct al., Phys. Rev. Lett. 82, 1963 (1999)]. The essential dynamical mechanism responsible for coherence should be generic in nonlinear oscillator systems where the interactions are mediated by a highly resonant cavity, in analogy with gas lasers.