Local equilibria and state transfer of charged classical particles on a helix in an electric field

TL;DR

This paper investigates how a homogeneous electric field influences the static and dynamic behavior of two charged particles on a helix, revealing bifurcations and enabling controlled state transfer through external force modulation.

Contribution

It introduces a detailed analysis of bifurcations in charged particles on a helix under electric fields and demonstrates a method for controlled state transfer via time-dependent external forces.

Findings

External electric field couples center-of-mass and relative motion.

Various fixed points are created or destroyed through bifurcations.

Robust state transfer between equilibrium configurations is achievable.

Abstract

We explore the effects of a homogeneous external electric field on the static properties and dynamical behavior of two charged particles confined to a helix. In contrast to the field-free setup which provides a separation of the center-of-mass and relative motion, the existence of an external force perpendicular to the helix axis couples the center-of-mass to the relative degree of freedom leading to equilibria with a localized center of mass. By tuning the external field various fixed points are created and/or annihilated through different bifurcation scenarios. We provide a detailed analysis of these bifurcations based on which we demonstrate a robust state transfer between essentially arbitrary equilibrium configurations of the two charges that can be induced by making the external force time-dependent.