Statistics of resonance width shifts as a signature of eigenfunction non-orthogonality

TL;DR

This paper investigates how resonance width shifts in open quantum systems reveal eigenfunction non-orthogonality, using random matrix theory to analyze the statistical distribution of these shifts in chaotic systems under weak coupling.

Contribution

It introduces a novel statistical approach to quantify eigenfunction non-orthogonality through resonance width shifts in open quantum systems, especially in chaotic regimes.

Findings

Resonance width shifts are sensitive indicators of eigenfunction non-orthogonality.

Derived the distribution of width shifts for weakly coupled chaotic systems.

Established a new parametric statistical framework for open quantum systems.

Abstract

We consider an open (scattering) quantum system under the action of a perturbation of its closed counterpart. It is demonstrated that the resulting shift of resonance widths is a sensitive indicator of the non-orthogonality of resonance wavefunctions, being zero only if those were orthogonal. Focusing further on chaotic systems, we employ random matrix theory to introduce a new type of parametric statistics in open systems, and derive the distribution of the resonance width shifts in the regime of weak coupling to the continuum.