2022/08/31 by V. Rom-Kedar, Rom-Kedar, V., D. Turaev +1 · 1 citation
Physics and Astronomy · #Quantum chaos and dynamical systems #Nuclear physics research studies #Cold Atom Physics and Bose-Einstein Condensates
paper · pdf · doi:10.48550/arxiv.2208.14993
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.