Synchronization Mpemba Effect

Abstract:We introduce the synchronization Mpemba effect, in which a less synchronized initial state overtakes a more synchronized one, and demonstrate it in dissipatively coupled quantum van der Pol oscillators. Within a graph-Laplacian framework, we show that for two oscillators, the mechanism is a competition between a slowly decaying collective background and a fast transverse transient, equivalently an exchange between relative-mode displacement and phase-fluctuation errors. The same decomposition extends to networks: the synchronization error splits into transverse Laplacian modes, yielding closed-form crossing times from eigenvalue separations and initial mode weights, and a sufficient screening criterion. With only these eigenvalues entering, the rule is topology independent: crossing times of different networks collapse onto a single spectral-gap line. Thus, quantum many-body dynamics can be designed and controlled at low dimension without constructing the exponentially large Liouvillian, opening a route to quantum synchronization as a resource.

arXiv:2611.04994 [quant-ph]

(or arXiv:2611.04994v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2611.04994 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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