Abstract

We study a straight infinite planar waveguide with a 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 to an embedded eigenvalue phenomenon. We show that if we break the symmetry, the corresponding resolvent poles turn into resonances. The widths of the resonances are calculated explicitly in the lowest order perturbation term.

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