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

TL;DR

This paper demonstrates a phase transition from desynchronized to synchronized states in a disordered lattice of oscillators, with implications for driven-dissipative Bose-Einstein condensates and other coupled systems.

Contribution

It introduces a generalized Kuramoto model with cosine coupling, connecting oscillator synchronization to quantum localization and phase transitions in disordered media.

Findings

Identifies a phase transition in oscillator synchronization due to disorder.

Derives phase diagrams for 1D and 2D systems.

Shows long-range order persists despite randomness.

Abstract

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 synchronized 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.