Classical scattering of charged particles confined on an inhomogeneous helix

TL;DR

This paper investigates how inhomogeneities in a helical confinement affect the dynamics of charged particles, revealing energy transfer mechanisms, dissociation, and bound states through phase space analysis.

Contribution

It demonstrates that inhomogeneous helices cause coupling between center of mass and relative motion, leading to dissociation and resonant states, unlike homogeneous helices.

Findings

Inhomogeneity induces energy transfer between motions.

Bound states can dissociate due to inhomogeneity.

Resonant states are identified within the phase space.

Abstract

We explore the effects arising due to the coupling of the center of mass and relative motion of two charged particles confined on an inhomogeneous helix with a locally modified radius. It is first proven that a separation of the center of mass and the relative motion is provided if and only if the confining manifold represents a homogeneous helix. In this case bound states of repulsively Coulomb interacting particles occur. For an inhomogeneous helix, the coupling of the center of mass and relative motion induces an energy transfer between the collective and relative motion, leading to dissociation of initially bound states in a scattering process. Due to the time reversal symmetry, a binding of the particles out of the scattering continuum is thus equally possible. We identify the regimes of dissociation for different initial conditions and provide an analysis of the underlying phase space via Poincar\'e surfaces of section. Bound states inside the inhomogeneity as well as resonant states are identified.