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TMF, 2017, Volume 190, Number 1, Pages 87–103 (Mi tmf9056)  

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

E. L. Lakshtanova, B. R. Vainbergb

a 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

Funding Agency Grant Number
Center for Research and Development in Mathematics and Applications
Fundação para a Ciência e a Tecnologia PEst-OE/MAT/UI4106/2014
National Science Foundation DMS-1410547
The research of E. L. Lakshtanov was supported by Portuguese funds through the CIDMA, Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (FCT–Fundção para a Ciência e a Tecnologia) in the framework of project PEst-OE/MAT/UI4106/2014.
The research of B. R. Vainberg was supported in part by the National Science Foundation (Grant No. DMS-1410547).


DOI: https://doi.org/10.4213/tmf9056

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

Bibliographic databases:

Received: 26.09.2015

Citation: E. L. Lakshtanov, B. R. Vainberg, “A test for the existence of exceptional points in the Faddeev scattering problem”, TMF, 190:1 (2017), 87–103; Theoret. and Math. Phys., 190:1 (2017), 77–90

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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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