Weakly bound states in heterogeneous waveguides
Mathematical Physics
2016-07-20 v1 math.MP
Abstract
We study the spectrum of the Helmholtz equation in a two-dimensional infinite waveguide, containing a weak heterogeneity localized at an internal point, and obeying Dirichlet boundary conditions at its border. We prove that, when the heterogeneity corresponds to a locally denser material, the lowest eigenvalue of the spectrum falls below the continuum threshold and a bound state appears, localized at the heterogeneity. We devise a rigorous perturbation scheme and derive the exact expression for the energy to third order in the heterogeneity.
Cite
@article{arxiv.1511.07104,
title = {Weakly bound states in heterogeneous waveguides},
author = {Paolo Amore and Francisco M. Fernandez and Christoph P. Hofmann},
journal= {arXiv preprint arXiv:1511.07104},
year = {2016}
}
Comments
14 pages