https://doi.org/10.1140/epjc/s10052-022-10707-0
Regular Article - Theoretical Physics
Remarks on sine-Gordon kink–fermion system: localized modes and scattering
1
Department of Mathematics, National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), 115409, Moscow, Russia
2
Kurchatov Complex for Theoretical and Experimental Physics of National Research Centre “Kurchatov Institute”, 117218, Moscow, Russia
3
Osmanağa Mahallesi Vahapbey Sokak No:8 Kadiköy, 34714, Istanbul, Turkey
4
Wargaming Vilnius, UAB, Konstitucijos pr. 21A, LT-08130, Vilnius, Lithuania
5
Department of Theoretical Physics and Astrophysics, Belarusian State University, 220004, Minsk, Belarus
6
BLTP, JINR, 141980, Dubna, Moscow Region, Russia
7
Institute of Physics, University of Oldenburg, D-26111, Oldenburg, Germany
Received:
15
May
2022
Accepted:
12
August
2022
Published online:
29
August
2022
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.
© The Author(s) 2022
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