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arXiv · 2208.14993

Stable motions of high energy particles interacting via a repelling potential

V. Rom-Kedar·D. Turaev
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Abstract

The motion of N particles interacting by a smooth repelling potential and confined to a compact d-dimensional region is proved to be, under mild conditions, non-ergodic for all sufficiently large energies. Specifically, choreographic solutions, for which all particles follow approximately the same path close to an elliptic periodic orbit of the single-particle system, are proved to be KAM stable in the high energy limit. Finally, it is proved that the motion of N repelling particles in a rectangular box is non-ergodic at high energies for a generic choice of interacting potential: there exists a KAM-stable periodic motion by which the particles move fast only in one direction, each on its own path, yet in synchrony with all the other parallel moving particles.

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V. Rom-Kedar, D. Turaev. 2022-08-31. Stable motions of high energy particles interacting via a repelling potential. https://doi.org/10.1007/s00220-024-04946-3

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