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.
Highlights
In cosmology, where domain walls can describe branes that live in higher-dimensional universes leading to fermions localization in the extra dimensions [23,24,25]
An interesting modification of the usual scalar field models occurs when the potential is constructed to turn the vibrational mode into a quasinormal mode
This mode can be turned into a quasinormal mode if one modifies the scalar potential, which was shown to suppress the resonance windows, as the decay rate of the quasinormal mode is increased [52, 53]
Summary
We repeat the same procedure for a toy model, which allows kinks with either a normal mode or a quasinormal mode [53]. For eq (4.2), the continuity relations imply that there are three free parameters, which we fix at γ = 3.0, γ = 1.0 and = 0.05 Choosing these values, we guarantee that the only shape mode in the square-well stability potential turns into a quasinormal mode. The fermion spectra for both kinks, resulting from eq (2.5), are shown in figure 3 They are very similar, except that the bound states appear earlier in the quasinormal mode case. The oscillations of the fermion field decrease slowly due to a decrease in the amplitude of quasinormal mode perturbation This occurs because the quasinormal mode can tunnel the potential barrier created by the kink and radiate to infinity. We will discuss the perturbed system for both normal and quasinormal mode cases in detail and compare both numerical and perturbative solutions in the following subsections
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
