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

TL;DR

This paper investigates the spectral properties and scattering behavior of a quantum system composed of a half-line attached to a wedge, analyzing how the system's characteristics change with the wedge's angle.

Contribution

It introduces a model of a quantum hybrid surface with a thin antenna at the wedge vertex and studies its spectral and scattering properties as a function of the wedge angle.

Findings

Spectrum depends on the wedge angle.

Resonances are characterized for the hybrid system.

Scattering matrix behavior varies with geometry.

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.