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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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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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).
The authors declare no competing interests.
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 sections 1 and 2 and Figs. 1–5.
Animated versions of Fig. 2b,c of the main text, visualizing the symmetric (top row) and asymmetric (bottom row) oscillations of the dominant eigenmodes.
Data represented in Fig. 1e of the main text.
Data represented in Fig. 2 of the main text.
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
Nature Communications (2021)
Nature Communications (2021)