Distant perturbation asymptotics in window-coupled waveguides. I. The nonthreshold case

DOI10.1063/1.2364179zbMath1112.81043arXivmath-ph/0606022OpenAlexW3101658418MaRDI QIDQ3442102

Pavel Exner, Denis I. Borisov

Publication date: 16 May 2007

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

Full work available at URL: https://arxiv.org/abs/math-ph/0606022

Mathematics Subject Classification ID

General mathematical topics and methods in quantum theory (81Q99)

Related Items (10)

Transmission of waves through a small aperture in the cross-wall in an acoustic waveguide ⋮ Perturbation of threshold of essential spectrum for waveguides with windows. II: Asymptotics ⋮ Asymptotics of an eigenvalue on the continuous spectrum of two quantum waveguides coupled through narrow windows ⋮ On occurrence of resonances from multiple eigenvalues of the Schrödinger operator in a cylinder with distant perturbations ⋮ Tunneling resonances in systems without a classical trapping ⋮ Asymptotic behaviour of the spectrum of a waveguide with distant perturbations ⋮ On finitely many resonances emerging under distant perturbations in multi-dimensional cylinders ⋮ On infinite system of resonance and eigenvalues with exponential asymptotics generated by distant perturbations ⋮ Planar waveguide with “twisted” boundary conditions: Discrete spectrum ⋮ Perturbation of threshold of essential spectrum for waveguides with windows. I: Decreasing resonance solutions

Cites Work

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• The twisting trick for double well Hamiltonians
• Universal lower bounds on eigenvalue splittings for one dimensional Schrödinger operators
• Double wells
• Local perturbations of the Schrödinger operator on the axis
• Bound-state asymptotic estimates for window-coupled Dirichlet strips and layers
• Exponential splitting of bound states in a waveguide with a pair of distant windows
• Bound states in straight quantum waveguides with combined boundary conditions
• Bound states and scattering in quantum waveguides coupled laterally through a boundary window
• Discrete spectrum of an asymmetric pair of waveguides coupled through a window

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