dc.contributor.author Hainzl, Christian dc.contributor.author Lewin, Mathieu dc.contributor.author Séré, Eric dc.date.accessioned 2009-07-01T12:23:04Z dc.date.available 2009-07-01T12:23:04Z dc.date.issued 2009 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/603 dc.language.iso en en dc.subject Mathematical Physics en dc.subject.ddc 519 en dc.title Existence of Atoms and Molecules in the Mean-Field Approximation of No-Photon Quantum Electrodynamics en dc.type Article accepté pour publication ou publié dc.contributor.editoruniversityother Université de Cergy Pontoise;France dc.contributor.editoruniversityother University of Alabama at Birmingham;États-Unis dc.description.abstracten The 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.isversionofjnlname Archive for Rational Mechanics and Analysis dc.relation.isversionofjnlvol 192 en dc.relation.isversionofjnlissue 3 en dc.relation.isversionofjnldate 2009-06 dc.relation.isversionofjnlpages 453-499 en dc.relation.isversionofdoi http://dx.doi.org/10.1007/s00205-008-0144-2 en dc.identifier.urlsite http://fr.arXiv.org/abs/math-ph/0606001 en dc.description.sponsorshipprivate oui en dc.relation.isversionofjnlpublisher Springer Berlin / Heidelberg en dc.subject.ddclabel Probabilités et mathématiques appliquées en
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