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dc.contributor.authorLewin, Mathieu
HAL ID: 1466
ORCID: 0000-0002-1755-0207
dc.date.accessioned2009-07-08T15:17:14Z
dc.date.available2009-07-08T15:17:14Z
dc.date.issued2004
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/1008
dc.language.isoenen
dc.subjectPhysicsen
dc.subjectMathematical Physicsen
dc.subjectMathematicsen
dc.subjectAnalysis of PDEsen
dc.subject.ddc519en
dc.titleA mountain pass for reacting moleculesen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn this paper, we consider a neutral molecule that possesses two distinct stable positions for its nuclei, and look for a mountain pass point between the two minima in the non-relativistic Schrödinger framework. We first prove some properties concerning the spectrum and the eigenstates of a molecule that splits into pieces, a behavior which is observed when the Palais-Smale sequences obtained by the mountain pass method are not compact. This enables us to identify precisely the possible values of the mountain pass energy and the associated ldquocritical points at infinityrdquo (a concept introduced by Bahri [2]) in this non-compact case. We then restrict our study to a simplified (but still relevant) model: a molecule made of two interacting parts, the geometry of each part being frozen. We show that this lack of compactness is impossible under some natural assumptions about the configurations ldquoat infinityrdquo, proving the existence of the mountain pass in these cases. More precisely, we suppose either that the molecules at infinity are charged, or that they are neutral but with dipoles at their ground state.en
dc.relation.isversionofjnlnameAnnales Henri Poincaré
dc.relation.isversionofjnlvol5en
dc.relation.isversionofjnldate2004
dc.relation.isversionofjnlpages477-521en
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s00023-004-0176-6
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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