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

E. L. Lakshtanov^a, B. R. Vainberg<sup>b

a</sup> Department of Mathematics, University of Aveiro, Aveiro, Portugal
^b Department of Mathematics and Statistics, University of North Carolina, Charlotte, USA

Abstract: Exceptional points are values of the spectral parameter for which the homogeneous Faddeev scattering problem has a nontrivial solution. We formulate a criterion for existence of exceptional points that belong to a given path. For this, we use measurements at the endpoints of the path. We also study the existence or 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.

Keywords: exceptional point, Faddeev Green's function, conductive potential.

Received: 26.09.2015

DOI: 10.4213/tmf9056

 English version: Theoretical and Mathematical Physics, 2017, 190:1, 77–90

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