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<p>The latest research has found that spherical 2-designs or the direct sum of spherical 2-designs can give stationary points of many-body systems under certain conditions. Euclidean <i>t</i>-designs are the two-step generalization of spherical <i>t</i>-designs. Inspired by this, we consider when a Euclidean 2-design can give a stationary point for the classical mechanical system of particles in a Euclidean space interacting by a double-well potential. We characterize the necessary and sufficient conditions for a Euclidean 2-design (on two concentric spheres) to be a stationary point.</p>

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

  • 期刊论文

  • 发表日期：

    2025年9月2日

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  • Aiguo Wang

摘要

The latest research has found that spherical 2-designs or the direct sum of spherical 2-designs can give stationary points of many-body systems under certain conditions. Euclidean t-designs are the two-step generalization of spherical t-designs. Inspired by this, we consider when a Euclidean 2-design can give a stationary point for the classical mechanical system of particles in a Euclidean space interacting by a double-well potential. We characterize the necessary and sufficient conditions for a Euclidean 2-design (on two concentric spheres) to be a stationary point.