Resonance phenomena in vortex-antivortex collisions

TL;DR

The paper investigates whether resonance energy transfer, well known from 1D soliton collisions, governs vortex-antivortex scattering in the 2+1D Abelian-Higgs (Nielsen-Olesen) model. By numerically simulating head-on collisions across a range of the coupling $\\lambda$ and initial velocities $v_{\\rm in}$ and analyzing vortex perturbations, it identifies a chaotic pattern of multi-bounce windows in the deep type II regime and attributes this structure to a Feshbach resonance that excites a vortex-bound mode. The study shows that for $\\lambda<1.5$ genuine bound modes control dynamics, while for $\\lambda>1.5$ Feshbach resonances drive energy transfer leading to re-emergence after multiple collisions, with observed vibration frequencies matching the predicted resonance. This work suggests a universal mechanism for resonant energy exchange in soliton collisions across dimensions and opens avenues for collective-coordinate models and extensions to monopoles or non-Abelian vortices.

Abstract

In this work, we provide a full map of scattering scenarios between a Nielsen-Olesen vortex and antivortex. Importantly, in the deep type II regime, such a collision reveals a chaotic pattern in the final state formation with bounce windows immersed into annihilation regions. This structure is due to the energy transfer mechanism triggered by a quasinormal mode, specifically the Feshbach resonant mode, hosted by the vortex.

Figures (7)

• Figure 1: A summary of the different outcomes in vortex-antivortex collisions. On the $x$-axis, the values for $\lambda$ are given. On the $y$-axis, the initial velocity is given.
• Figure 2: Time evolution of the real part of the scalar field at the origin, $\mathop{\rm Re}\nolimits \phi(\vec{x}=0, t)$, during a vortex-antivortex scattering for $\lambda = 4.4$, shown for different initial velocities $v_{\rm in}$.
• Figure 3: Several examples of vortex-antivortex scatterings are shown. The density plot represents the scalar field $\mathop{\rm Re}\nolimits{\phi}$ along the $x$-axis, while the solid (dashed) lines indicate the zeros of the vortex (antivortex).
• Figure 4: Measured frequency of the vibrating vortex recreated in one-bounce collisions (black dots) vs. the approximated frequency of the Feshbach resonance (orange curve) and the bound mode (red curve). Blue and green curves are the mass thresholds of the Higgs and gauge fields respectively.
• Figure 5: VAV scattering for $\lambda=4.4$. Final velocity of recreated vortex as a function of $v_{in}$.