Planar waveguide with "twisted" boundary conditions: discrete spectrum

TL;DR

This paper investigates the spectral properties of a planar waveguide with twisted boundary conditions, revealing how discrete eigenvalues emerge from the essential spectrum and providing criteria for their existence.

Contribution

It introduces a novel analysis of the discrete spectrum in waveguides with twisted boundary conditions, including criteria for eigenvalue emergence and construction methods.

Findings

Discrete eigenvalues can emerge from the essential spectrum in twisted waveguides.

A criterion for the existence of discrete eigenvalues is established.

Eigenvalues are constructed as convergent holomorphic series.

Abstract

We consider a planar waveguide with combined Dirichlet and Neumann conditions imposed in a "twisted" way. We study the discrete spectrum and describe it dependence on the configuration of the boundary conditions. In particular, we show that in certain cases the model can have discrete eigenvalues emerging from the threshold of the essential spectrum. We give a criterium for their existence and construct them as convergent holomorphic series.