Weakly bound states in heterogeneous waveguides

FRANCISCO MARCELO FERNÁNDEZ; PABLO R. DUCHOWICZ; PAOLO AMORE

EUROPEAN PHYSICAL JOURNAL B - CONDENSED MATTER

SPRINGER

Lugar: Berlin; Año: 2016 vol. 89 p. 163 - 180

1434-6028

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 use the variational theorem to derive the condition for which 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.