Instability of pre-existing resonances in the DC Stark effect vs. stability in the AC Stark effect

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.
Comment: review article, 10 pages, 4 figures