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Chapitre D'ouvrage Année : 2021

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

Résumé

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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Dates et versions

hal-02984354 , version 1 (30-10-2020)

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Jean Dolbeault, Maria J. Esteban, Michael Loss. Critical magnetic field for 2d magnetic Dirac-Coulomb operators and Hardy inequalities. Partial Differential Equations, Spectral Theory, and Mathematical Physics. The Ari Laptev Anniversary Volume, 18, EMS Press, pp.41-63, 2021, Partial Differential Equations, Spectral Theory, and Mathematical Physics. The Ari Laptev Anniversary Volume. EMS Series of Congress Reports. ⟨hal-02984354⟩
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