Two-dimensional Dirac operators with singular interactions supported on closed curves

DOI10.1016/j.jfa.2020.108700zbMath1446.35155arXiv1907.05436OpenAlexW2960834159MaRDI QIDQ2192357

Jussi Behrndt, Markus Holzmann, Thomas Ourmières-Bonafos, Konstantin Pankrashkin

Publication date: 17 August 2020

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.05436

zbMATH Keywords

self-adjoint extensionboundary tripleperiodic pseudodifferential operatorsDirac operator with singular interaction

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Motion of charged particles (78A35) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (20)

Two-dimensional Dirac operators with interactions on unbounded smooth curves ⋮ 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 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 ⋮ Schrödinger operators with oblique transmission conditions in \(\mathbb{R}^2\) ⋮ Curvature contribution to the essential spectrum of Dirac operators with critical shell interactions ⋮ On the calculation of the discrete spectra of one‐dimensional Dirac operators ⋮ Method of potential operators for interaction problems on unbounded hypersurfaces in \(\mathbb{R}^n\) for Dirac operators ⋮ 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 ⋮ Leaky quantum structures ⋮ Deficiency indices and discreteness property of block Jacobi matrices and Dirac operators with point interactions ⋮ A variational formulation for Dirac operators in bounded domains. Applications to spectral geometric inequalities ⋮ Self-adjoint extensions of the two-valley Dirac operator with discontinuous infinite mass boundary conditions ⋮ Two-dimensional Dirac operators with general δ-shell interactions supported on a straight line

Uses Software

• DLMF

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