Effective Long-Range Interactions in Confined Curved Dimensions

TL;DR

This paper investigates how confinement to a curved helical geometry alters long-range interactions between charged particles, leading to oscillating forces, stable configurations, and tunable bound states, with implications for many-body systems.

Contribution

It reveals that confinement on a helical manifold causes oscillating effective interactions and introduces stable equilibrium states, a novel insight into curved low-dimensional systems.

Findings

Charged particles experience oscillating forces due to confinement.

Stable equilibrium configurations are possible in helical geometries.

Number of bound states is tunable via helix parameters.

Abstract

We explore the effective long-range interaction of charged particles confined to a curved low-dimensional manifold using the example of a helical geometry. Opposite to the Coulomb interaction in free space the confined particles experience a force which is oscillating with the distance between the particles. This leads to stable equilibrium configurations and correspondingly induced bound states whose number is tunable with the parameters of the helix. We demonstrate the existence of a plethora of equilibria of few-body chains with different symmetry character that are allowed to freely move. An outline concerning the implications on many-body helical chains is provided.