Fermions on wobbling kinks: normal versus quasinormal modes

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