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Network experiment demonstrates converse symmetry breaking

Nature Physics volume 16, pages 351–356 (2020)Cite this article

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Abstract

Symmetry breaking—the phenomenon in which the symmetry of a system is not inherited by its stable states—underlies pattern formation, superconductivity and numerous other effects. Recent theoretical work has established the possibility of converse symmetry breaking, a phenomenon in which the stable states are symmetric only when the system itself is not. This includes scenarios in which interacting entities are required to be non-identical in order to exhibit identical behaviour, such as in reaching consensus. Here we present an experimental demonstration of this phenomenon. Using a network of alternating-current electromechanical oscillators, we show that their ability to achieve identical frequency synchronization is enhanced when the oscillators are tuned to be suitably non-identical and that converse symmetry breaking persists for a range of noise levels. These results have implications for the optimization and control of network dynamics in a broad class of systems whose function benefits from harnessing uniform behaviour.

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Fig. 1: Experiment involving a network of coupled electromechanical oscillators.
Fig. 2: Oscillator heterogeneity breaks the symmetry of the dominant eigenmodes.
Fig. 3: Experimental confirmation of converse symmetry breaking.

Data availability

The data represented in Figs. 1–3 are provided with the paper as source data. All other data that support results in this Article are available from the corresponding author upon reasonable request.

Code availability

The custom code used for the analysis of the data from the experiment is available from the corresponding author upon reasonable request.

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Acknowledgements

We thank J.B. Ketterson for insightful discussions about this research. This research was funded by ARO Grant No. W911NF-15-1-0272 and by Northwestern University’s Finite Earth Initiative (supported by L. McQuown and M. McQuown).

Author information

Author notes

  1. Ferenc Molnar

    Present address: Department of Physics and Center for Network and Data Science, University of Notre Dame, Notre Dame, IN, USA

Authors and Affiliations

  1. Department of Physics and Astronomy, Northwestern University, Evanston, IL, USA

    Ferenc Molnar, Takashi Nishikawa & Adilson E. Motter

  2. Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL, USA

    Takashi Nishikawa & Adilson E. Motter

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  1. Ferenc Molnar
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Contributions

F.M., T.N. and A.E.M. designed the research and contributed to the modelling. F.M. performed the experiments and simulations. F.M., T.N. and A.E.M. analysed the results and wrote the paper. All authors approved the final manuscript.

Corresponding authors

Correspondence to Takashi Nishikawa or Adilson E. Motter.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Eckehard Schöll and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary sections 1 and 2 and Figs. 1–5.

Supplementary Video 1

Animated versions of Fig. 2b,c of the main text, visualizing the symmetric (top row) and asymmetric (bottom row) oscillations of the dominant eigenmodes.

Source Data Fig. 1

Data represented in Fig. 1e of the main text.

Source Data Fig. 2

Data represented in Fig. 2 of the main text.

Source Data Fig. 3

Data represented in Fig. 3 of the main text.

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Molnar, F., Nishikawa, T. & Motter, A.E. Network experiment demonstrates converse symmetry breaking. Nat. Phys. 16, 351–356 (2020). https://doi.org/10.1038/s41567-019-0742-y

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