Fixed points for one-dimensional particle system with strong interaction

TL;DR

This paper investigates the fixed points of a one-dimensional Hamiltonian particle system with strong Coulomb interactions, revealing that neighbor distances become asymptotically uniform regardless of external force as the system size grows.

Contribution

It provides a new analysis of fixed points in a particle system with Coulomb interactions, showing asymptotic uniformity of neighbor distances independent of external force.

Findings

Neighbor distances become asymptotically uniform for large N.

The asymptotic behavior is independent of the external force F.

The study advances understanding of equilibrium configurations in strongly interacting particle systems.

Abstract

We consider hamiltonian $N$ particle system on the finite segment with nearest-neighbor Coulomb interaction and external force $F$. We study the fixed points of such system and show that the distances between neighbors are asymptotically, for large $N$, the same for any $F$.