Synchronization in disordered oscillatory media: a nonequilibrium phase transition for driven-dissipative bosons [article]

John P. Moroney, Paul R. Eastham
2021 arXiv   pre-print
We show that a lattice of phase oscillators with random natural frequencies, described by a generalization of the nearest-neighbor Kuramoto model with an additional cosine coupling term, undergoes a phase transition from a desynchronized to a synchronized state. This model may be derived from the complex Ginzburg-Landau equations describing a disordered lattice of driven-dissipative Bose-Einstein condensates of exciton polaritons. We derive phase diagrams that classify the desynchronized and
more » ... chronized states that exist in both one and two dimensions. This is achieved by outlining the connection of the oscillator model to the quantum description of localization of a particle in a random potential through a mapping to a modified Kardar-Parisi-Zhang equation. Our results indicate that long-range order in polariton condensates, and other systems of coupled oscillators, is not destroyed by randomness in their natural frequencies.
arXiv:2101.05776v2 fatcat:4d5hw224wfhqheo2erbji25p7q