An Adiabatic Theorem for Resonances

TL;DR

This paper extends the quantum adiabatic theorem to systems with resonances, allowing for applications where only approximate bound states are known, demonstrated through shape resonances.

Contribution

It provides a robust extension of the adiabatic theorem applicable to resonance systems and approximate bound states, broadening its practical utility.

Findings

The theorem applies to systems with resonances instead of bound states.

It is useful when only approximate bound states are known.

Demonstrated application to shape resonances.

Abstract

We prove a robust extension of the quantum adiabatic theorem. The theorem applies to systems that have resonances instead of bound states, and to systems for which just an approximation to a bound state is known. To demonstrate the theorem's usefulness in a concrete situation, we apply it to shape resonances.