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Critical magnetic field for 2d magnetic Dirac-Coulomb operators and Hardy inequalities

Dolbeault, Jean; Esteban, Maria J.; Loss, Michael (2021), Critical magnetic field for 2d magnetic Dirac-Coulomb operators and Hardy inequalities, in Pavel Exner, Rupert L. Frank, Fritz Gesztesy, Helge Holden, Timo Weidl, Partial Differential Equations, Spectral Theory, and Mathematical Physics .The Ari Laptev Anniversary Volume, European Mathematical Society : Zürich, p. 41-63. 10.4171/ECR/18-1/4

Type
Chapitre d'ouvrage
Date
2021
Book title
Partial Differential Equations, Spectral Theory, and Mathematical Physics .The Ari Laptev Anniversary Volume
Book author
Pavel Exner, Rupert L. Frank, Fritz Gesztesy, Helge Holden, Timo Weidl
Publisher
European Mathematical Society
Published in
Zürich
ISBN
978-3-98547-007-5
Number of pages
494
Pages
41-63
Publication identifier
Metadata
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Author(s)
Dolbeault, Jean cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Esteban, Maria J. cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Loss, Michael
School of Mathematics - Georgia Institute of Technology
Abstract (EN)
This paper is devoted to the study of the two-dimensional Dirac–Coulomb operator in presence of an Aharonov–Bohm external magnetic potential. We characterize the highest intensity of the magnetic field for which a two-dimensional magnetic Hardy inequality holds. Up to this critical magnetic field, the operator admits a distinguished self-adjoint extension and there is a notion of ground state energy, defined as the lowest eigenvalue in the gap of the continuous spectrum.
Subjects / Keywords
Aharonov-Bohm magnetic potential; magnetic Dirac operator; Coulomb potential; critical magnetic field; self-adjoint operators; eigenvalues; ground state energy; Hardy inequality; Wirtinger derivatives; Pauli operator Mathematics Subject Classification 2020 Primary 81Q10; Secondary 46N50; 81Q05; 47A75