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arXiv · 1511.07104

Weakly bound states in heterogeneous waveguides

Paolo Amore·Francisco M. Fernandez·Christoph P. Hofmann
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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.

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Paolo Amore, Francisco M. Fernandez, Christoph P. Hofmann. 2015-11-23. Weakly bound states in heterogeneous waveguides. https://doi.org/10.1140/epjb%2Fe2016-70197-0

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