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Journal of Statistical Physics

, Volume 174, Issue 1, pp 160–187 | Cite as

Synchronization and Stability for Quantum Kuramoto

  • Lee DeVilleEmail author
Article

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.

Keywords

Kuramoto model Kuramoto–Sakaguchi model Lohe model Synchronization Quantum synchronization 

Mathematics Subject Classification

82C10 34D06 58C40 15A18 

Notes

Acknowledgements

The author thanks Jared Bronski, Thomas Carty, and Eddie Nijholt for illuminating discussions in the course of writing this manuscript. The author would also like to thank an anonymous referee for suggesting a line of investigation that culminated in the entirely new Theorem 2.21 and in enhancements to the conclusions of Theorem 2.18.

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Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA

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