  For atoms described by a 1-dimensional Friedrichs model we present the
following result: pre-existing resonances, when subjected to a small constant
electric field (DC Stark effect), are unstable in the weak field limit. In
contrast, pre-existing resonances under the influence of a small time-periodic
electric field (AC Stark effect) are stable in this limit. This article is a
review of our results in "Instability of pre-existing resonances under a small
constant electric field", arXiv:1310.4745.
