Spectral properties of relativistic quantum waveguides

DOI10.1007/s00023-022-01179-9zbMath1505.35277arXiv2101.04009OpenAlexW3120445677MaRDI QIDQ2085725

David Krejčiřík, Thomas Ourmières-Bonafos, William Borrelli, Philippe Briet

Publication date: 18 October 2022

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.04009

zbMATH Keywords

bound statesmassive Dirac operatorlocation of the essential spectrumtubular neighbourhood of an unbounded planar curve

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Perturbation theories for operators and differential equations in quantum theory (81Q15) Quantum dots, waveguides, ratchets, etc. (81Q37) Quantum waveguides, quantum wires (82D77)

Related Items (4)

Spectral optimization of Dirac rectangles ⋮ Spectral inequality for Dirac right triangles ⋮ Dirichlet fractional Laplacian in multi-tubes ⋮ Dirac operator spectrum in tubes and layers with a zigzag-type boundary

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The adiabatic limit of Schrödinger operators on fibre bundles
• Self-adjointness of two-dimensional Dirac operators on domains
• Boundary problems for three-dimensional Dirac operators and generalized MIT bag models for unbounded domains
• Generalised quantum waveguides
• Self-adjointness of Dirac operators with infinite mass boundary conditions in sectors
• On the nonlinear Dirac equation on noncompact metric graphs
• Quantum waveguides
• On the MIT bag model in the non-relativistic limit
• A sharp upper bound on the spectral gap for graphene quantum dots
• Resolvent convergence to Dirac operators on planar domains
• On the spectrum of curved planar waveguides
• THE EFFECTIVE HAMILTONIAN IN CURVED QUANTUM WAVEGUIDES UNDER MILD REGULARITY ASSUMPTIONS
• REDUCTION OF DIMENSION AS A CONSEQUENCE OF NORM‐RESOLVENT CONVERGENCE AND APPLICATIONS
• Quantum strips in higher dimensions
• Bound states in curved quantum waveguides
• The free Dirac operator on compact and noncompact graphs
• The Stability of Matter in Quantum Mechanics
• Spectral statistics for the Dirac operator on graphs
• Nonlinear Dirac Equation on Graphs with Localized Nonlinearities: Bound States and Nonrelativistic Limit
• CURVATURE-INDUCED BOUND STATES IN QUANTUM WAVEGUIDES IN TWO AND THREE DIMENSIONS

This page was built for publication: Spectral properties of relativistic quantum waveguides