A straight waveguide with a wire inducing resonances

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.