On the spectrum of magnetic Dirac operators with Coulomb-type perturbations |
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Authors: | Serge Richard Rafael Tiedra de Aldecoa |
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Institution: | aUniversité de Lyon, Lyon, F-69003, France;bUniversité Lyon 1, Institut Camille Jordan, Villeurbanne Cedex, F-69622, France;cCNRS, UMR 5208, Villeurbanne Cedex, F-69622, France;dDépartement de mathématiques, Université de Paris XI, 91405 Orsay Cedex, France |
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Abstract: | We carry out the spectral analysis of singular matrix valued perturbations of 3-dimensional Dirac operators with variable magnetic field of constant direction. Under suitable assumptions on the magnetic field and on the perturbations, we obtain a limiting absorption principle, we prove the absence of singular continuous spectrum in certain intervals and state properties of the point spectrum. Constant, periodic as well as diverging magnetic fields are covered, and Coulomb potentials up to the physical nuclear charge Z<137 are allowed. The importance of an internal-type operator (a 2-dimensional Dirac operator) is also revealed in our study. The proofs rely on commutator methods. |
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Keywords: | Dirac operator Magnetic field Coulomb potentials Absolutely continuous spectrum Limiting absorption principle Commutators methods |
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