Dynamics of nonlinear excitations of helically confined charges

TL;DR

This paper investigates how the geometry of a helix influences the long-term nonlinear dynamics of charged particles, revealing regimes of dispersion and localization controlled by the helix radius.

Contribution

It demonstrates the impact of helix radius on nonlinear excitations and introduces an effective discrete nonlinear Schrödinger model to analyze these effects.

Findings

Small radii lead to excitation dispersion across the crystal.

Larger radii induce self-focusing and localized breather-like excitations.

Beyond certain radii, excitation defocuses and dispersion increases again.

Abstract

We explore the long-time dynamics of a system of identical charged particles trapped on a closed helix. This system has recently been found to exhibit an unconventional deformation of the linear spectrum when tuning the helix radius. Here we show that the same geometrical parameter can affect significantly also the dynamical behaviour of an initially broad excitation for long times. In particular, for small values of the radius, the excitation disperses into the whole crystal whereas within a specific narrow regime of larger radii the excitation self-focuses, assuming finally a localized form. Beyond this regime, the excitation defocuses and the dispersion gradually increases again. We analyze this geometrically controlled nonlinear behaviour using an effective discrete nonlinear Schr\"{o}dinger model, which allows us among others to identify a number of breather-like excitations.