Exceptional points in Faddeev scattering problem

TL;DR

This paper investigates the conditions under which exceptional points occur in the Faddeev scattering problem, particularly focusing on small perturbations of conductive potentials and the absence of such points in absorbing potentials near the origin.

Contribution

It provides new criteria for the existence of exceptional points and analyzes their presence or absence in specific classes of potentials.

Findings

Absorbing potentials near the origin lack exceptional points.

A criterion for the existence of exceptional points is established.

Small perturbations of conductive potentials can lead to exceptional points.

Abstract

Exceptional points are values of the spectral parameter for which the homogeneous Faddeev scattering problem has a non-trivial solution. We study the existence/absence of exceptional points for small perturbations of conductive potentials of arbitrary shape and show that problems with absorbing potentials do not have exceptional points in a neighborhood of the origin. A criterion for existence of exceptional points is given.