A quantum hybrid with a thin antenna at the vertex of a wedge

Abstract

We study the spectrum, resonances and scattering matrix of a quantum hamiltonian on a "hybrid surface" consisting of a half-line attached by its endpoint to the vertex of a concave planar wedge. At the boundary of the wedge, outside the vertex, Dirichlet boundary are imposed. The system is tunable by varying the measure of the angle at the vertex.