Remarks on sine-Gordon kink--fermion system: localized modes and scattering

TL;DR

This paper investigates the interaction between sine-Gordon kinks and massless Dirac fermions in a 1+1D model, revealing how coupling strength affects localized modes and how fermion scattering influences kink dynamics.

Contribution

It provides a numerical analysis of kink-fermion interactions, highlighting the dependence of localized modes on coupling and the phase-dependent scattering effects.

Findings

No localized modes for minimal Yukawa coupling

Fermion scattering causes phase-dependent kink acceleration

Fermionic spectrum varies with coupling strength

Abstract

We study numerically the kink-fermion interactions in a 1+1 dimensional toy model, which describes sine-Gordon kinks coupled to the massless Dirac fermions with backreaction. We show that the spectrum of fermionic modes strongly depends on the choice of the coupling, in particular, there are no localized modes for a minimal Yukawa coupling. We analyze the scattering of the fermionic packet by the kink. We demonstrate that the outcome of the collision dynamically depends on the phase of the incoming fermion packet, it results in alternating regimes of positive and negative acceleration of the kink.