Comptes Rendus
Mathematical questions about the computation of eigenvalues of Dirac operators with critical potentials in atomic and molecular physics
[Quelques questions mathématiques sur le calcul des valeurs propres des opérateurs de Dirac avec potentiels critiques en physique atomique et moléculaire]
Comptes Rendus. Physique, Volume 21 (2020) no. 2, pp. 177-183.

Cette Note présente divers résultats analytiques et numériques concernant le calcul des valeurs propres de l’opérateur de Dirac, ou plus généralement, des opérateurs avec des “gaps” spectraux. Un algorithme basé sur un théorème abstrait caractérisant les valeurs propres dans les écarts a été trouvé il y a des années, mais ce n’est que récemment qu’une analyse délicate pour identifier et étudier les domaines de ces opérateurs a permis de mettre cet algorithme sur une base ferme concernant le choix des approximations, et ceci aussi bien pour les atomes légers que pour les atomes lourds. Les travaux décrits ici concernent des travaux réalisés avec plusieurs collaborateurs : J. Dolbeault, M. Lewin, M. Loss, E. Séré et M. Vanbreugel.

This Note describes various analytical and computational results concerning the calculation of Dirac eigenvalues, or more generally, of operators with gaps. An algorithm based on an abstract theorem characterizing the eigenvalues in gaps was found years ago, but it is only recently that a delicate analysis to identify and study the domains of those operators has allowed to put that algorithm on a firm basis concerning the choice of approximation basis sets, and this both for light and for heavy atoms. The works described here concern joint papers with several collaborators: J. Dolbeault, M. Lewin, M. Loss, E. Séré and M. Vanbreugel.

Publié le :
DOI : 10.5802/crphys.16
Keywords: Dirac operator, Eigenvalue, Operator domain, Eigenvalue computation, Self-adjoint operator
Mot clés : Opérateur de Dirac, Valeur propre, Domaine de l’opérateur, Calcul des valeurs propres, Opérateur auto-adjoint
Maria J. Esteban 1

1 CEREMADE (CNRS UMR no 7534), PSL university, Université Paris-Dauphine, Place de Lattre de Tassigny, F-75775 Paris 16, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Maria J. Esteban. Mathematical questions about the computation of eigenvalues of Dirac operators with critical potentials in atomic and molecular physics. Comptes Rendus. Physique, Volume 21 (2020) no. 2, pp. 177-183. doi : 10.5802/crphys.16. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.16/

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