Eigenvalues collision for PT-symmetric waveguide

TL;DR

This paper provides an analytical explanation for the eigenvalues collision phenomenon observed in PT-symmetric waveguides when boundary conditions are perturbed, complementing previous numerical findings.

Contribution

It offers the first rigorous analytical analysis of eigenvalues collision in PT-symmetric waveguides under boundary condition perturbations.

Findings

Eigenvalues collision occurs under boundary perturbations.

Analytic methods explain the collision phenomenon.

Results confirm previous numerical observations.

Abstract

We consider a model of planar PT-symmetric waveguide and study the phenomenon of the eigenvalues collision under the perturbation of boundary conditions. This phenomenon was discovered numerically in previous works. The main result of this work is an analytic explanation of this phenomenon.