A test for the existence of exceptional points in the Faddeev scattering problem

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.

On reconstruction of complex-valued once differentiable conductivities

“…vanishes when A → ∞. From (12) it follows that h a (·, ·) depends on a only because µ = µ a (z, k) depends on a. The choice of A guarantees that the solutions of (59), (60) are analytic in a ∈ (0, 1].…”

“…We define µ a for complex a via this Lippmann-Schwinger equation. Let h a (ς, k), ς ∈ C, k ∈ C\D, be defined by (12) with µ a in the integrand instead of µ.…”

The D-Bar Method for Diffuse Optical Tomography: A Computational Study

“…In our paper we again conduct the same test at E < 0: the results of section 3 are the first (numerical) results on exceptional points at negative energy, when the potential is not small. Also see [15] for similar results for non-radial potentials.…”