Can we trust the relationship between resonance poles and lifetimes?

TL;DR

This paper investigates how small electric fields affect shape resonances in a one-dimensional quantum system, revealing that such resonances vanish under the field, but the associated lifetimes remain continuous at zero field, challenging traditional interpretations.

Contribution

It demonstrates that shape resonances induced by delta function wells disappear with small electric fields, and introduces an analysis of the new resonances replacing them, highlighting the difference between resonance widths and experimental lifetimes.

Findings

Shape resonances vanish under small electric fields.

Experimental lifetimes remain continuous at zero field.

New resonances emerge replacing the original shape resonances.

Abstract

We show that the shape resonances induced by a one dimensional well of delta functions disappear as soon as a small constant electric field is applied. In particular, in any compact subset below the positive real axis there are no resonances if the non-zero field is small enough. In contrast to the lack of convergence of the lifetimes computed from the widths of the resonances we show that the "experimental lifetimes" are continuous at zero field. The shape resonances are replaced by an infinite set of other resonances whose location and number we analyze.