Stable motions of high energy particles interacting via a repelling potential
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.
Keywords
Cite
@article{arxiv.2208.14993,
title = {Stable motions of high energy particles interacting via a repelling potential},
author = {V. Rom-Kedar and D. Turaev},
journal= {arXiv preprint arXiv:2208.14993},
year = {2026}
}