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

TL;DR

This paper studies how fermions interact with oscillating domain walls modeled after sine-Gordon breathers, revealing that such backgrounds induce fermion particle production and cause bound states to decay over time.

Contribution

It demonstrates the non-stability of fermionic bound states in oscillating sine-Gordon-like backgrounds and explores the dynamics of particle production in these nonlinear systems.

Findings

Fermions initially form bound states around oscillating domain walls.

Oscillations induce fermion and antifermion fluxes leading to particle emission.

Fermion density exhibits quasiperiodic behavior with partial recurrences.

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.