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

2020/10/30 by Jean Dolbeault, Maria J. Esteban, Dolbeault, Jean +3
Mathematics · Physics and Astronomy · #Differential Equations and Boundary Problems #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #math-ph #math.AP #math.MP #math.SP #msc:46N50 #msc:47A75 #msc:81Q05 #msc:81Q10

paper · pdf · doi:10.48550/arxiv.2011.00039

arxiv created 2020/10/30 · arxiv updated 2020/11/03

Abstract

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.

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