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arXiv · 2011.00039

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

Jean Dolbeault·Maria J. Esteban·Michael Loss
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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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Jean Dolbeault, Maria J. Esteban, Michael Loss. 2020-10-30. Critical magnetic field for 2d magnetic Dirac-Coulomb operators and Hardy inequalities. https://arxiv.org/abs/2011.00039

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