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Generalized Thomson problem in arbitrary dimensions and non-euclidean geometries

Author

Listed:
  • Batle, J.
  • Bagdasaryan, Armen
  • Abdel-Aty, M.
  • Abdalla, S.

Abstract

Systems of identical particles with equal charge are studied under a special type of confinement. These classical particles are free to move inside some convex region S and on the boundary of it Ω (the Sd−1−sphere, in our case). We shall show how particles arrange themselves under the sole action of the Coulomb repulsion in many dimensions in the usual Euclidean space, therefore generalizing the so called Thomson problem to many dimensions. Also, we explore how the problem varies when non-Euclidean geometries are considered. We shall see that optimal configurations in all cases possess a high degree of symmetry, regardless of the concomitant dimension or geometry.

Suggested Citation

  • Batle, J. & Bagdasaryan, Armen & Abdel-Aty, M. & Abdalla, S., 2016. "Generalized Thomson problem in arbitrary dimensions and non-euclidean geometries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 237-250.
    • Handle: RePEc:eee:phsmap:v:451:y:2016:i:c:p:237-250
    DOI: 10.1016/j.physa.2016.01.069
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    Cited by:

    1. Amore, Paolo & Jacobo, Martin, 2019. "Thomson problem in one dimension: Minimal energy configurations of N charges on a curve," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 519(C), pages 256-266.

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