Exponential splitting of bound states in a waveguide with a pair of distant windows

DOI10.1088/0305-4470/37/10/007zbMath1050.81008arXivmath-ph/0312013OpenAlexW2031570685MaRDI QIDQ4466234

Pavel Exner, Denis I. Borisov

Publication date: 9 June 2004

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

Full work available at URL: https://arxiv.org/abs/math-ph/0312013

zbMATH Keywords

bound statesexponential splittingNewmann windows

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Antennas, waveguides in optics and electromagnetic theory (78A50)

Related Items (20)

Distant perturbation asymptotics in window-coupled waveguides. I. The nonthreshold case ⋮ Transmission of waves through a small aperture in the cross-wall in an acoustic waveguide ⋮ Spectral gap of segments of periodic waveguides ⋮ Spectrum of periodic elliptic operators with distant perturbations in space ⋮ Counting zeros of holomorphic functions of exponential growth ⋮ 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 the resolvent of elliptic operators with distant perturbations in the space ⋮ Lifshitz tails for acoustic waves in random quantum waveguide ⋮ 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 ⋮ Resolvents of self-adjoint extensions with mixed boundary conditions ⋮ Asymptotic behaviour of the spectrum of a waveguide with distant perturbations ⋮ On finitely many resonances emerging under distant perturbations in multi-dimensional cylinders ⋮ On the discrete spectrum of a spatial quantum waveguide with a disc window ⋮ Tunneling between corners for Robin Laplacians ⋮ On infinite system of resonance and eigenvalues with exponential asymptotics generated by distant perturbations ⋮ Lifshitz tails for quantum waveguides with random boundary conditions ⋮ Planar waveguide with “twisted” boundary conditions: Discrete spectrum ⋮ On the spectrum of curved planar waveguides

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