Discrete spectrum of a pair of nonsymmetric waveguides coupled by a window

Abstract

In the paper we study the discrete spectrum of a pair of quantum two-dimensional waveguides having common boundary in which a window of finite length is cut out. We study the phenomenon of new eigenvalues emerging from the threshold of the essential spectrum when the length of window passes through critical values. We construct the asymptotics expansions for the emerging eigenvalues with respect to small parameter which is the difference between current length of the window and the nearest critical value. We also study the behaviour of the spectrum when the length of the window increases unboundedly and construct asymptotics expansions with respect to great parameter which is a length of the window.

arXiv commentThe original text was written in Russian. This is a translation made by the author. In the revised version just some minor changes were made

References in corpus (5)

• Geometric coupling thresholds in a two-dimensional strip
• Exponential splitting of bound states in a waveguide with a pair of distant windows
• Spectrum of the Magnetic Schrodinger Operator in a Waveguide with Combined Boundary Conditions
• On regular and singular perturbations of acoustic and quantum waveguides
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Cited by in corpus (4)

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• On finitely many resonances emerging under distant perturbations in multi-dimensional cylinders