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Spherical 2-Designs as Stationary Points of Many-Body Systems

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Abstract

We show that spherical 2-designs give stationary points of the classical mechanical system of particles in a Euclidean space interacting by a double-well potential.

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Notes

  1. A JavaScript program which visualizes a numerical evidence for this expectation for \(m=3\) is available at https://github.com/miurror/mds-visualization.

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Acknowledgements

M. M. was supported by Korea Institute for Advanced Study. K. U. was partially supported by JSPS Grant-in-Aid for Scientific Research (15KT0105, 16H03930, 16K13743). The authors thank the anonymous referees for providing a number of valuable comments. In particular, Remark 3.3 came from one of them.

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Authors and Affiliations

  1. Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul, 130-722, Republic of Korea

    Makoto Miura

  2. Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan

    Kazushi Ueda

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  1. Makoto Miura
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  2. Kazushi Ueda
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Correspondence to Makoto Miura.

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Miura, M., Ueda, K. Spherical 2-Designs as Stationary Points of Many-Body Systems. Graphs and Combinatorics 37, 485–492 (2021). https://doi.org/10.1007/s00373-020-02259-5

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  • DOI: https://doi.org/10.1007/s00373-020-02259-5

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