Synchronization and Stability for Quantum Kuramoto

TL;DR

This paper introduces a quantum version of the Kuramoto model, analyzing its stability, attractors, and effects of modifications, providing insights into synchronization phenomena in nonabelian systems.

Contribution

It develops a nonabelian quantum Kuramoto model, analyzing stability, attractors, and heterogeneity effects, extending classical synchronization theory to quantum systems.

Findings

Multiple attractors exist for certain topologies

Stability conditions depend on connection structure

Heterogeneity limits for sustained synchronization

Abstract

We present and analyze a nonabelian version of the Kuramoto system, which we call the quantum Kuramoto system. We study the stability of several classes of special solutions to this system, and show that for certain connection topologies the system supports multiple attractors. We also present estimates on the maximal possible heterogeneity in this system that can support an attractor, and study the effect of modifications analogous to phase-lag.