Planar waveguide with "twisted" boundary conditions: small width

Abstract

We consider a planar waveguide with "twisted" boundary conditions. By twisting we mean a special combination of Dirichlet and Neumann boundary conditions. Assuming that the width of the waveguide goes to zero, we identify the effective (limiting) operator as the width of the waveguide tends to zero, establish the uniform resolvent convergence in various possible operator norms, and give the estimates for the rates of convergence. We show that studying the resolvent convergence can be treated as a certain threshold effect and we present an elegant technique which justifies such point of view.

References in corpus (4)

• Coupling in the singular limit of thin quantum waveguides
• Convergence of resonances on thin branched quantum wave guides
• Planar waveguide with "twisted" boundary conditions: discrete spectrum
• On the spectrum and weakly effective operator for Dirichlet Laplacian in thin deformed tubes

Cited by in corpus (5)

• Tunneling resonances in systems without a classical trapping
• Embedded eigenvalues of the Neumann problem in a strip with a box-shaped perturbation
• Scattering through a straight quantum waveguide with combined boundary conditions
• A straight waveguide with a wire inducing resonances
• Absolute continuity of the spectrum in a twisted Dirichlet-Neumann waveguide