Synchronization and Stability for Quantum Kuramoto

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.

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• A Geometric Obstruction to Almost Global Synchronization on Riemannian Manifolds
• Stability of twisted states on lattices of Kuramoto oscillators
• On the Schrödinger-Lohe hierarchy for aggregation and its emergent dynamics
• Synchronization in the complexified Kuramoto model
• A dynamical systems approach for the shape matching of polytopes along rigid-body motions
• A gradient flow formulation of the Lohe matrix model with a high-order polynomial coupling
• The Kuramoto model on a sphere: Explaining its low-dimensional dynamics with group theory and hyperbolic geometry
• On the Equivalence of Synchronization Definitions in the Kuramoto Flow: A Unified Approach
• Asymptotic formation and orbital stability of phase-locked states in Kuramoto--Lohe type synchronization models on Lie groups