Klein's paradox and the relativistic \(\delta\)-shell interaction in \(\mathbb{R}^3\)

DOI10.2140/apde.2018.11.705OpenAlexW2952717739MaRDI QIDQ1686234

Albert Mas, Fabio Pizzichillo

Publication date: 21 December 2017

Published in: Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.09271

zbMATH Keywords

singular integral operatorDirac operatorstrong resolvent convergenceKlein's paradox\(\delta\)-shell interactionapproximation by scaled regular potentials

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Spectrum, resolvent (47A10) PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Tunneling in quantum theory (81U26)

Related Items (21)

Spectral analysis of Dirac operators with delta interactions supported on the boundaries of rough domains ⋮ Spectral properties of the Dirac operator coupled with \(\delta\)-shell interactions ⋮ Dirac operators with Lorentz scalar shell interactions ⋮ Dirac operators with delta-interactions on smooth hypersurfaces in \(\mathbb{R}^n\) ⋮ Non-self-adjoint relativistic point interaction in one dimension ⋮ Self-adjointness of the 2D Dirac operator with singular interactions supported on star graphs ⋮ The MIT bag model as an infinite mass limit ⋮ Curvature contribution to the essential spectrum of Dirac operators with critical shell interactions ⋮ The relativistic spherical δ-shell interaction in R3: Spectrum and approximation ⋮ Self-adjoint Dirac operators on domains in \(\mathbb{R}^3\) ⋮ Method of potential operators for interaction problems on unbounded hypersurfaces in \(\mathbb{R}^n\) for Dirac operators ⋮ Limiting absorption principle and scattering matrix for Dirac operators with δ-shell interactions ⋮ Interaction problems on periodic hypersurfaces for Dirac operators on \(\mathbb{R}^n \) ⋮ General \(\delta\)-shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation ⋮ Fredholm property of interaction problems on unbounded \(C^2-\) hypersurfaces in \(\mathbb{R}^n\) for Dirac operators ⋮ Eigenvalue curves for generalized MIT bag models ⋮ Approximation of one-dimensional relativistic point interactions by regular potentials revised ⋮ Leaky quantum structures ⋮ Self-adjointness of two-dimensional Dirac operators on corner domains ⋮ On Dirac operators in \(\mathbb{R}^3\) with electrostatic and Lorentz scalar \(\delta\)-shell interactions ⋮ Two-dimensional Dirac operators with general δ-shell interactions supported on a straight line

Cites Work

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• Klein's paradox and the relativistic point interaction
• Shell interactions for Dirac operators
• Dirac operators with a spherically symmetric δ-shell interaction
• Leaky Quantum Graphs: A Review
• Self-adjoint extensions of restrictions
• Opérateurs d'intégrale singulière sur les surfaces régulières
• Quantum mechanics of electrons in crystal lattices
• Shell Interactions for Dirac Operators: On the Point Spectrum and the Confinement
• Approximation of Schrödinger operators with δ-interactions supported on hypersurfaces

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