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Weakly bound states in heterogeneous waveguides

Author

Listed:
  • Paolo Amore

    (Facultad de Ciencias, CUICBAS, Universidad de Colima)

  • Francisco M. Fernández

    (INIFTA (UNLP, CCT La Plata-CONICET), Division Quimica Teorica)

  • Christoph P. Hofmann

    (Facultad de Ciencias, CUICBAS, Universidad de Colima)

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 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.

Suggested Citation

  • Paolo Amore & Francisco M. Fernández & Christoph P. Hofmann, 2016. "Weakly bound states in heterogeneous waveguides," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(7), pages 1-7, July.
    • Handle: RePEc:spr:eurphb:v:89:y:2016:i:7:d:10.1140_epjb_e2016-70197-0
    DOI: 10.1140/epjb/e2016-70197-0
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    Keywords

    Mesoscopic and Nanoscale Systems;

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