Fermions on wobbling kinks: normal versus quasinormal modes

Abstract

The system consisting of a fermion in the background of a wobbling kink is studied in this paper. To investigate the impact of the wobbling on the fermion-kink interaction, we employ the time-dependent perturbation theory formalism in quantum mechanics. To do so, we compute the transition probabilities between states given in terms of the Bogoliubov coefficients. We derive Fermi’s golden rule for the model, which allows the transition to the continuum at a constant rate if the fermion-kink coupling constant is smaller than the wobbling frequency. Moreover, we study the system replacing the shape mode with a quasinormal mode. In this case, the transition rate to continuum decays in time due to the leakage of the mode, and the final transition probability decreases sharply for large coupling constants in a way that is analogous to Fermi’s golden rule. Throughout the paper, we compare the perturbative results with numerical simulations and show that they are in good agreement.

Kink-antikink collision in the supersymmetric 𝜙4 model

“…First, we know that the scalar field internal modes are excited after the collision. Thus, the fermion interacts with an oscillating field [54]. Second, fermion internal modes are also excited after the collision.…”

“…In [51,52], the authors studied the kink-antikink collision, but without the back-reaction as well. More recently, we have studied fermions interacting with another dynamic scalar field with the same assumption [53,54]. Therefore, it is essential to study the effect created by the fermion on the scalar field evolution, which is lacking in the literature.…”

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

“…Fermions bound by kinks were considered in many papers [38,[41][42][43][44][45][46][47]. The typical assumption in most of such considerations is that the the spinor field does not backreact on the soliton.…”