Stable motions of high energy particles interacting via a repelling potential

TL;DR

This paper demonstrates that high-energy particles interacting via a repelling potential exhibit non-ergodic behavior, with stable choreographic solutions and specific periodic motions, under mild conditions and in rectangular confinement.

Contribution

It proves the existence of KAM-stable choreographic and periodic solutions for high-energy repelling particles, revealing non-ergodic dynamics in such systems.

Findings

Choreographic solutions are KAM stable at high energies.

Motion in a rectangular box is non-ergodic at high energies.

Particles can move in parallel, synchronized paths with high velocity.

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.