A straight waveguide with a wire inducing resonances

TL;DR

This paper investigates how attaching a leaky wire to a straight waveguide affects its spectral properties, demonstrating that symmetry breaking transforms embedded eigenvalues into resonances.

Contribution

It introduces a model of a waveguide with a finite segment wire and analyzes the transition from embedded eigenvalues to resonances upon symmetry breaking.

Findings

Symmetry preservation leads to embedded eigenvalues.

Breaking symmetry converts eigenvalues into resonances.

Resonance behavior depends on wire placement and interaction strength.

Abstract

We study a straight infinite planer waveguide with, so called, leaky wire attached to the walls of the waveguide. The wire is modelled by an attractive delta interaction supported by a finite segment. If the wire is placed perpendicularly then the system preserves mirror symmetry which leads the embedded eigenvalues phenomena. We show that if we break the symmetry the corresponding resolvent poles turn to resonances.