Curvature-induced bound states in Robin waveguides and their asymptotical properties

DOI10.1063/1.4903184zbMath1315.81045arXiv1406.7624OpenAlexW2035312650MaRDI QIDQ2939204

Pavel Exner, Alexander A. Minakov

Publication date: 19 January 2015

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

Full work available at URL: https://arxiv.org/abs/1406.7624

zbMATH Keywords

eigenvalue problemSchrödinger operatoredge statesquantum particleslarge parameterstrong delta-interaction

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Estimates of eigenvalues in context of PDEs (35P15) Operations with distributions and generalized functions (46F10) PDEs in connection with quantum mechanics (35Q40) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Quantum dots, waveguides, ratchets, etc. (81Q37)

Related Items (14)

An effective Hamiltonian for the eigenvalue asymptotics of the Robin Laplacian with a large parameter ⋮ On the discrete spectrum of Schrödinger operators with Ahlfors regular potentials in a strip ⋮ Singular Schrödinger operators and Robin billiards. Spectral properties and asymptotic expansions ⋮ Robin eigenvalues on domains with peaks ⋮ Asymptotics of Robin eigenvalues on sharp infinite cones ⋮ Quantum Information Measures of the One‐Dimensional Robin Quantum Well ⋮ Thermodynamic Properties of the 1D Robin Quantum Well ⋮ On the Discrete Spectrum of Robin Laplacians in Conical Domains ⋮ Spectral asymptotics for Robin Laplacians on polygonal domains ⋮ Localization effects for Dirichlet problems in domains surrounded by thin stiff and heavy bands ⋮ On the \(p\)-Laplacian with Robin boundary conditions and boundary trace theorems ⋮ Effective operators for Robin eigenvalues in domains with corners ⋮ On the existence of bound states in asymmetric leaky wires ⋮ Asymptotics of the bound state induced by δ-interaction supported on a weakly deformed plane

Cites Work

• Unnamed Item
• Unnamed Item
• Asymptotic eigenvalue estimates for a Robin problem with a large parameter
• Resonant alteration of propagation in guiding structures with complex Robin parameter and its magnetic-field-induced restoration
• On the extended nature of edge states of quantum Hall Hamiltonians
• Asymptotics of eigenvalues of the Schrödinger operator with a strong \(\delta\)-interaction on a loop
• Waveguides with combined Dirichlet and Robin boundary conditions
• Thin waveguides with Robin boundary conditions
• Bound states in curved quantum waveguides
• Leaky Quantum Graphs: A Review
• On edge states in semi-infinite quantum Hall systems
• On the principal eigenvalue of a Robin problem with a large parameter
• On the asymptotics of the principal eigenvalue for a Robin problem with a large parameter in planar domains
• Band gap of the Schrödinger operator with a strong \(\delta\)-interaction on a periodic curve

This page was built for publication: Curvature-induced bound states in Robin waveguides and their asymptotical properties