Bound States and Particle Production by Breather-Type Background Field Configurations

Abstract

We investigate the interaction of fermion fields with oscillating domain walls, inspired by breather-type solutions of the sine-Gordon equation, a nonlinear system of fundamental importance. Our study focuses on the fermionic bound states and particle production induced by a time-dependent scalar background field. The fermions couple to two domain walls undergoing harmonic motion, and we explore the resulting dynamics of the fermionic wave functions. We demonstrate that while fermions initially form bound states around the domain walls, the energy provided by the oscillatory motion of the scalar field induces an outward flux of fermions and antifermions, leading to particle production and eventual flux propagation toward spatial infinity. Through numerical simulations, we observe that the fermion density exhibits quasiperiodic behavior, with partial recurrences of the bound state configurations after each oscillation period. However, the fermion wave functions do not remain localized, and over time, the density decreases as more particles escape the vicinity of the domain walls. Our results highlight that the sine-Gordon-like breather background, when coupled non-supersymmetrically to fermions, does not preserve integrability or stability, with the oscillations driving a continuous energy transfer into the fermionic modes. This study sheds light on the challenges of maintaining steady-state fermion solutions in time-dependent topological backgrounds and offers insights into particle production mechanisms in nonlinear dynamical systems with oscillating solitons.

arXiv comment17 pages

References in corpus (19)

• Anomaly and quantum corrections to solitons in two-dimensional theories with minimal supersymmetry
• Kink-kink and kink-antikink interactions with long-range tails
• Long-range interactions of kinks
• Scattering of the ${\phi }^8$ kinks with power-law asymptotics
• Successive phase transitions and kink solutions in ${\varphi }^8$, ${\varphi }^{10}$, and ${\varphi }^{12}$ field theories
• Scattering between wobbling kinks
• Remarks on bell-shaped lumps: stability and fermionic modes
• Fermionic One-Loop Corrections to Soliton Energies in 1+1 Dimensions
• Analytical study of kinklike structures with polynomial tails
• SUSY sine-Gordon theory as a perturbed conformal field theory and finite size effects
• Mode regularization of the susy sphaleron and kink: zero modes and discrete gauge symmetry
• Fermions on one or fewer Kinks
• Kinks bounded by fermions
• Kink solutions in logarithmic scalar field theory: Excitation spectra, scattering, and decay of bions
• Soliton Decay in Coupled System of Scalar Fields
• Coupled fermion-kink system in Jackiw-Rebbi model
• Inclusion of radiation in the CCM approach of the ${\varphi }^4$ model
• Fermion bound states in geometrically deformed backgrounds
• Creation of Bound Half-Fermion Pairs by Solitons