Discrete spectrum of cross-shaped quantum waveguides

DOI10.1007/s10958-014-1662-0zbMath1301.81069OpenAlexW2013682740MaRDI QIDQ467575

Sergueï A. Nazarov

Publication date: 3 November 2014

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-014-1662-0

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Quantum dots, waveguides, ratchets, etc. (81Q37) Quantum waveguides, quantum wires (82D77)

Related Items (5)

Open waveguides in a thin Dirichlet lattice. II: Localized waves and radiation conditions ⋮ The discrete spectrum of cross-shaped waveguides ⋮ Spectrum of the Dirichlet Laplacian in a thin cubic lattice ⋮ Transmission conditions in one-dimensional model of a rectangular lattice of thin quantum waveguides ⋮ Bound states of waveguides with two right-angled bends

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic expansions of eigenvalues in the continuous spectrum of a regularly perturbed quantum waveguide
• Scattering theory for diffraction gratings
• Junctions of singularly degenerating domains with different limit dimensions. II
• A criterion for the existence of decaying solutions in the problem on a resonator with a cylindrical waveguide
• Plane waveguides with corners in the small angle limit
• The Y-junction of quantum waveguides
• Calculation of characteristics of trapped modes in T-shaped waveguides
• Bound states in curved quantum waveguides
• Properties of Spectra of Boundary Value Problems in Cylindrical and Quasicylindrical Domains
• [Russian Text Ignored]
• Wood's anomalies and surface waves in the problem of scattering by a periodic boundary. II
• Existence theorems for trapped modes
• The polynomial property of self-adjoint elliptic boundary-value problems and an algebraic description of their attributes
• CURVATURE-INDUCED BOUND STATES IN QUANTUM WAVEGUIDES IN TWO AND THREE DIMENSIONS
• Trapped modes in angular joints of 2D waveguides

This page was built for publication: Discrete spectrum of cross-shaped quantum waveguides