Long-Range Interacting Particles on a Helix: A Statistical and Correlation Analysis of Equilibrium Configurations

TL;DR

This paper analyzes the equilibrium configurations of a few charged particles confined on a helix, revealing oscillatory potentials, increasing complexity with more particles, and a transition from regular to disordered arrangements.

Contribution

It provides a detailed statistical and correlation analysis of equilibrium states for particles on a helix, highlighting new insights into their spatial and energetic properties.

Findings

Oscillatory effective potential enables stable equilibria despite repulsion.

Number of equilibria grows approximately as a power-law with system size.

Interparticle distances cluster around odd multiples of half a helical winding.

Abstract

We provide a statistical and correlational analysis of the spatial and energetic properties of equilibrium configurations of a few-body system of two to eight equally charged classical particles that are confined on a one-dimensional helical manifold. The two-body system has been demonstrated to yield an oscillatory effective potential, thus providing stable equilibrium configurations despite the repulsive Coulomb interactions. As the system size grows, the number of equilibria increases, approximately following a power-law. This can be attributed to the increasing complexity in the highly non-linear oscillatory behavior of the potential energy surface. This property is reflected in a crossover from a spatially regular distribution of equilibria for the two-body system to a heightened degree of disorder upon the addition of particles. However, in accordance with the repulsion within a helical winding, the observed interparticle distances in equilibrium configurations cluster around values of odd multiples of half a helical winding, thus maintaining an underlying regularity. Furthermore, an energetic hierarchy exists based on the spatial location of the local equilibria, which is subject to increasing fluctuations as the system size grows.