Resonance scattering and singularities of the scattering function

TL;DR

This paper investigates how square root singularities in non-Hermitian Hamiltonians affect the scattering matrix, revealing mechanisms to control resonance cross sections in different channels.

Contribution

It demonstrates that singularities in the spectrum influence the pole behavior and residues of the scattering matrix, enabling control over resonance cross sections.

Findings

Singularities cause significant changes in pole behavior.

Resonance cross sections can be drastically increased or suppressed.

Mechanism explained using a two-channel model.

Abstract

Recent studies of transport phenomena with complex potentials are explained by generic square root singularities of spectrum and eigenfunctions of non-Hermitian Hamiltonians. Using a two channel problem we demonstrate that such singularities produce a significant effect upon the pole behaviour of the scattering matrix, and more significantly upon the associated residues. This mechanism explains why by proper choice of the system parameters the resonance cross section is increased drastically in one channel and suppressed in the other channel.