Synchronization in disordered oscillator lattices: Nonequilibrium phase transition for driven-dissipative bosons

We show that a lattice of phase oscillators with random natural frequencies, described by generalization the nearest-neighbor Kuramoto model an additional cosine coupling term, undergoes transition from desynchronized to synchronized state. This may be derived complex Ginzburg-Landau equations describing disordered driven-dissipative Bose-Einstein condensates exciton polaritons. derive diagrams classify and states exist in both one two dimensions. is achieved outlining connection oscillator quantum description localization particle potential through mapping modified Kardar-Parisi-Zhang equation. Our results indicate long-range order polariton condensates, other systems coupled oscillators, not destroyed randomness their frequencies.