The discrete spectrum of cross-shaped waveguides

DOI10.1090/spmj/1444zbMath1356.81137OpenAlexW2587898308MaRDI QIDQ2963046

Fedor L. Bakharev, Sergey Matveenko, Sergueï A. Nazarov

Publication date: 17 February 2017

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/spmj/1444

zbMATH Keywords

cross-shaped quantum waveguidediscrete spectrum multiplicitystabilizing solution at the threshold of the continuous spectrum

Mathematics Subject Classification ID

Quantum dots, waveguides, ratchets, etc. (81Q37)

Related Items (11)

Existence of the discrete spectrum in the Fichera layers and crosses of arbitrary dimension ⋮ Dirichlet fractional Laplacian in multi-tubes ⋮ Spectral gaps in a thin-walled infinite rectangular Dirichlet box with a periodic family of cross walls ⋮ Spectrum of the Dirichlet Laplacian in a thin cubic lattice ⋮ On Brownian exit times from perturbed multi-strips ⋮ Rectangular lattices of cylindrical quantum waveguides. I. Spectral problems on a finite cross ⋮ Eigenvalue inequalities and absence of threshold resonances for waveguide junctions ⋮ Effective operators for Robin eigenvalues in domains with corners ⋮ Eigenvalue asymptotics of long Kirchhoff plates with clamped edges ⋮ Model of a saccular aneurysm of the bifurcation node of an artery ⋮ Criteria for the absence and existence of bounded solutions at the threshold frequency in a junction of quantum waveguides

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Discrete spectrum of cross-shaped quantum waveguides
• Convergence of spectra of graph-like thin manifolds
• Exponentially decreasing solutions of diffraction problems on a rigid periodic boundary
• Structure of the spectrum of a net of quantum waveguides and bounded solutions of a model problem at the threshold
• The Y-junction of quantum waveguides
• Asymptotics of eigenvalues of the Dirichlet problem in a skewed ℐ-shaped waveguide
• Bounded solutions in a T-shaped waveguide and the spectral properties of the Dirichlet ladder
• Spectra of graph neighborhoods and scattering
• Graph models for waves in thin structures
• On the validity of the inclusion of geometrical shadowing functions in the multiple-scatter Kirchhoff approximation
• Isoperimetric Inequalities in Mathematical Physics. (AM-27)

This page was built for publication: The discrete spectrum of cross-shaped waveguides