On the spectral properties of Dirac operators with electrostatic \(\delta\)-shell interactions

DOI10.1016/j.matpur.2017.07.018zbMath1382.81095arXiv1609.00608OpenAlexW3105617276MaRDI QIDQ1696018

Markus Holzmann, Vladimir Lotoreichik, Jussi Behrndt, Pavel Exner

Publication date: 14 February 2018

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.00608

zbMATH Keywords

Dirac operatorspectral propertiesself-adjoint extensionshell interaction

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Spectrum, resolvent (47A10) Linear symmetric and selfadjoint operators (unbounded) (47B25) General theory of partial differential operators (47F05) PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

Related Items (33)

Dirac–Coulomb operators with infinite mass boundary conditions in sectors ⋮ Two-dimensional Dirac operators with interactions on unbounded smooth curves ⋮ Interior-boundary conditions for many-body Dirac operators and codimension-1 boundaries ⋮ 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 ⋮ Fredholm property and essential spectrum of 3-D Dirac operators with regular and singular potentials ⋮ Dirac operators with Lorentz scalar shell interactions ⋮ Dirac operators with singular potentials supported on unbounded surfaces in \(\mathbb{R}^3 \) ⋮ Dirac operators with delta-interactions on smooth hypersurfaces in \(\mathbb{R}^n\) ⋮ Spectral transition for Dirac operators with electrostatic \(\delta\)-shell potentials supported on the straight line ⋮ On the single layer boundary integral operator for the Dirac equation ⋮ Self-adjointness of the 2D Dirac operator with singular interactions supported on star graphs ⋮ Two-dimensional Dirac operators with singular interactions supported on closed curves ⋮ Schrödinger operators with oblique transmission conditions in \(\mathbb{R}^2\) ⋮ The relativistic spherical δ-shell interaction in R3: Spectrum and approximation ⋮ On the calculation of the discrete spectra of one‐dimensional Dirac operators ⋮ 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 \(\mathbb{R}^n \) ⋮ The physical interpretation of point interactions in one-dimensional relativistic quantum mechanics ⋮ Self‐adjointness for the MIT bag model on an unbounded cone ⋮ General \(\delta\)-shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation ⋮ Non-relativistic limit for matrix 1D-Dirac operators with point interactions ⋮ Fredholm property of interaction problems on unbounded \(C^2-\) hypersurfaces in \(\mathbb{R}^n\) for Dirac operators ⋮ Dirac Operators on $$ \mathbb {R}$$ with General Point Interactions ⋮ Eigenvalue curves for generalized MIT bag models ⋮ Leaky quantum structures ⋮ Deficiency indices and discreteness property of block Jacobi matrices and Dirac operators with point interactions ⋮ Unnamed Item ⋮ Self-adjoint extensions of the two-valley Dirac operator with discontinuous infinite mass boundary conditions ⋮ 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

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An isoperimetric-type inequality for electrostatic shell interactions for Dirac operators
• Spectral estimates for resolvent differences of self-adjoint elliptic operators
• Shell interactions for Dirac operators
• Boundary value problems for elliptic partial differential operators on bounded domains
• New analytically solvable models of relativistic point interactions
• Generalized resolvents and the boundary value problems for Hermitian operators with gaps
• Extensions of symmetric operators and symmetric binary relations
• Schrödinger operators with singular interactions
• Perturbation theory for linear operators.
• A trace formula for multidimensional Schrödinger operators
• The extension theory of Hermitian operators and the moment problem
• Schrödinger operators with \(\delta\) and \(\delta^{\prime}\)-potentials supported on hypersurfaces
• On the spectral theory of Gesztesy-Šeba realizations of 1-D Dirac operators with point interactions on a discrete set
• Quantum waveguides
• Variations on a theme of Jost and Pais
• Trace formulae and singular values of resolvent power differences of self-adjoint elliptic operators
• Boundary relations and their Weyl families
• Dirac operators with a spherically symmetric δ-shell interaction
• SPECTRA OF SELF-ADJOINT EXTENSIONS AND APPLICATIONS TO SOLVABLE SCHRÖDINGER OPERATORS
• Leaky Quantum Graphs: A Review
• Shell Interactions for Dirac Operators: On the Point Spectrum and the Confinement
• Approximation of Schrödinger operators with δ-interactions supported on hypersurfaces
• Interpolation zwischen den Klassen 𝔖_p von Operatoren in Hilberträumen

This page was built for publication: On the spectral properties of Dirac operators with electrostatic \(\delta\)-shell interactions