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dc.contributor.authorHainzl, Christian
dc.contributor.authorLewin, Mathieu
dc.contributor.authorSéré, Eric
dc.subjectMathematical Physicsen
dc.titleExistence of Atoms and Molecules in the Mean-Field Approximation of No-Photon Quantum Electrodynamicsen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherUniversité de Cergy Pontoise;France
dc.contributor.editoruniversityotherUniversity of Alabama at Birmingham;États-Unis
dc.description.abstractenThe Bogoliubov-Dirac-Fock (BDF) model is the mean-field approximation of no-photon Quantum Electrodynamics. The present paper is devoted to the study of the minimization of the BDF energy functional \emph{under a charge constraint}. An associated minimizer, if it exists, will usually represent the ground state of a system of $N$ electrons interacting with the Dirac sea, in an external electrostatic field generated by one or several fixed nuclei. We prove that such a minimizer exists when a binding (HVZ-type) condition holds. We also derive, study and interpret the equation satisfied by such a minimizer. Finally, we provide two regimes in which the binding condition is fulfilled, obtaining the existence of a minimizer in these cases. The first is the weak coupling regime for which the coupling constant $\alpha$ is small whereas $\alpha Z$ and the particle number $N$ are fixed. The second is the non-relativistic regime in which the speed of light tends to infinity (or equivalently $\alpha$ tends to zero) and $Z$, $N$ are fixed. We also prove that the electronic solution converges in the non-relativistic limit towards a Hartree-Fock ground state.en
dc.relation.isversionofjnlnameArchive for Rational Mechanics and Analysis
dc.relation.isversionofjnlpublisherSpringer Berlin / Heidelbergen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen

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