WAVEGUIDES COUPLED THROUGH A SEMITRANSPARENT BARRIER: A BIRMAN–SCHWINGER ANALYSIS

DOI10.1142/S0129055X01000703zbMath1029.81025arXivmath-ph/0005030OpenAlexW3125487655MaRDI QIDQ4418285

Pavel Exner, David Krejčiřík

Publication date: 7 August 2003

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0005030

zbMATH Keywords

Schrödinger operatorweak-coupling expansionspectral propertiesmesoscopic systemnumber of bound statesground-state eigenvalue\(\delta\) interactionparallel planar waveguidessemitransparent boundary

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10)

Related Items (7)

Geometric coupling thresholds in a two-dimensional strip ⋮ Weakly coupled bound state of 2-D Schrödinger operator with potential-measure ⋮ Resonances for Laplacian perturbed on surface and cell membrane model ⋮ Waveguides with combined Dirichlet and Robin boundary conditions ⋮ Lieb-Thirring inequalities for geometrically induced bound states ⋮ Separation of variables in deformed cylinders ⋮ On the spectrum of curved planar waveguides

Cites Work

• Bound states in a locally deformed waveguide: The critical case
• On the bound state of Schrödinger operators in one dimension
• The bound state of weakly coupled Schrödinger operators in one and two dimensions
• Schrödinger operators with singular interactions
• Point interactions in a strip
• Bargmann's inequalities in spaces of arbitrary dimension
• Perturbation of Dirichlet forms by measures
• Asymptotics of bound state for laterally coupled waveguides.
• Weakly coupled bound states in quantum waveguides
• CURVATURE-INDUCED BOUND STATES IN QUANTUM WAVEGUIDES IN TWO AND THREE DIMENSIONS
• Bound states and scattering in quantum waveguides coupled laterally through a boundary window

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