Fermions on wobbling kinks: normal versus quasinormal modes

TL;DR

This paper investigates how wobbling kinks affect fermion interactions, deriving transition rates and comparing normal and quasinormal modes, with results validated through numerical simulations.

Contribution

It introduces a perturbative framework for analyzing fermion-wobbling kink interactions, including the impact of quasinormal modes and transition rate decay over time.

Findings

Transition probabilities follow Fermi's golden rule for small coupling.

Quasinormal modes cause decay in transition rates over time.

Numerical simulations agree well with analytical predictions.

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.