Analyticity of the time dependence of resonance poles: Solving the Friedrichs model with a time-dependent interaction

Abstract

We extend the standard Friedrichs model with an extra term that includes time-dependent interactions. The time dependence of the poles of the reduced resolvent of the model is explicitly calculated. It is found that these poles behave as analytical functions of the added time-dependent interaction. The present results are compared with the ones reported by Kälbermann, concerning the assisted tunnelling of α particles. © 2012 American Physical Society.