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

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arxiv 2011.00039 v1 pith:DKCHVDHS submitted 2020-10-30 math.AP math-phmath.MPmath.SP

Jean Dolbeault , Maria J. Esteban , Michael Loss This is my paper · ORCID
classification math.APmath-phmath.MPmath.SP
keywords magneticfieldcriticaldirac-coulombhardyoperatortwo-dimensionaladmits
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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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Cited by 1 Pith paper

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