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PreprintarXiv licencearXiv

Synchronization Mpemba Effect

  • Yan Li
  • Wenlin Li
  • Xingli Li
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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.

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Cite

BibTeXRIS
BibTeX
@misc{li2026synchronization,
  title = {{Synchronization Mpemba Effect}},
  author = {Yan Li and Wenlin Li and Xingli Li},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04994},
  eprint = {2611.04994},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04994},
}
RIS
TY  - UNPB
TI  - Synchronization Mpemba Effect
AU  - Yan Li
AU  - Wenlin Li
AU  - Xingli Li
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04994
UR  - https://arxiv.org/abs/2611.04994
AB  - 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.
ER  -