Reflection Time Difference as a probe of S-matrix Zeroes in Chaotic Resonance Scattering

TL;DR

This paper introduces Reflection Time Difference, a new concept that helps identify the zeroes of the S-matrix in chaotic resonance scattering, analogous to how Wigner time delay relates to poles.

Contribution

It proposes the Reflection Time Difference as a novel tool for probing S-matrix zeroes in chaotic resonance scattering, extending the understanding of resonance phenomena.

Findings

Reflection Time Difference correlates with S-matrix zeroes

The method provides a new way to analyze resonance scattering

It enhances the theoretical framework for chaotic scattering

Abstract

Motivated by recent interest in the zeroes of S-matrix entries in the complex energy plane, I use the Heidelberg model of resonance scattering to introduce the notion of Reflection Time Difference which is shown to play the same role for the {\it zeroes} as the Wigner time delay plays for the S- matrix {\it poles}.