Complex scaling in finite volume

TL;DR

This paper combines complex scaling and finite-volume techniques to effectively compute quantum resonances, enabling the extraction of resonance energies and lifetimes from finite-volume simulations.

Contribution

It introduces a novel approach that integrates complex scaling with finite-volume methods to analyze quantum resonances.

Findings

Derived volume dependence relations for resonance states

Demonstrated method with explicit examples

Enabled inference of infinite-volume resonance properties

Abstract

Quantum resonances, i.e., metastable states with a finite lifetime, play an important role in nuclear physics and other domains. Describing this phenomenon theoretically is generally a challenging task. In this work, we combine two established techniques to address this challenge. Complex scaling makes it possible to calculate resonances with bound-state-like methods. Finite-volume simulations exploit the fact that the infinite-volume properties of quantum systems are encoded in how discrete energy levels change as one varies the size of the volume. We apply complex scaling to systems in finite periodic boxes and derive the volume dependence of states in this scenario, demonstrating with explicit examples how one can use these relations to infer infinite-volume resonance energies and lifetimes.