Identification of Resonant States via the Generalized Virial Theorem

TL;DR

This paper introduces a new operator-based method to identify resonant states in open quantum systems, simplifying the process and reducing reliance on complex regularization techniques.

Contribution

The authors propose an operator that measures invariance of resonant states, enabling straightforward identification without complex coordinate mappings or absorbing potentials.

Findings

Method effectively identifies resonant states in 1D systems.

Works well even with challenging numerical potentials.

Eliminates need for ad hoc regularization techniques.

Abstract

The numerical extraction of resonant states of open quantum systems is usually a difficult problem. Regularization techniques, such as the mapping to complex coordinates or the addition of Complex Absorbing Potentials are typically employed, as they render resonant wavefunctions localized and therefore normalizable. Physically relevant metastable states have energies that do not depend on the chosen regularization method. Their identification therefore involves cumbersome comparisons between multiple regularised calculations, often performed graphically, which require fine-tuning and specific intuition to avoid approximated, if not wrong, results. In this Letter, we define an operator that explicitly measures such invariance, valid for any arbitrary mapping of spatial coordinates. Resonant states of the system can eventually simply be identified evaluating the expectation value of this operator. Our method eases the extraction of resonant states even for numerical potentials that are difficult to scale to complex coordinates, and avoids the need for ad hoc complex absorbing potentials. We provide explicit evidence of our findings discussing one-dimensional case-studies,also in the presence of external electric fields.