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

The text is based on the presentation at the 9th Workshop on Quantum Chaos and Localization Phenomena, May 25--26, 2019, Warsaw, Poland

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• Generalization of Wigner Time Delay to Sub-Unitary Scattering Systems
• Statistics of Complex Wigner Time Delays as a counter of S-matrix poles: Theory and Experiment
• Use of Transmission and Reflection Complex Time Delays to Reveal Scattering Matrix Poles and Zeros: Example of the Ring Graph
• Chaotic Scattering with Localized Losses: S-Matrix Zeros and Reflection Time Difference for Systems with Broken Time Reversal Invariance
• Eigenfunction non-orthogonality factors and the shape of CPA-like dips in a single-channel reflection from lossy chaotic cavities
• A Physical Interpretation of Imaginary Time Delay
• Superuniversal Statistics of Complex Time-Delays in Non-Hermitian Scattering Systems
• Superuniversal Statistics with Topological Origins for non-Hermitian Scattering Singularities