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The nonlinear Schrödinger equation for orthonormal functions: II. Application to Lieb-Thirring inequalities

hal.structure.identifierDepartment of Mathematics (Caltech)
dc.contributor.authorFrank, Rupert L.
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorGontier, David
HAL ID: 11393
ORCID: 0000-0001-8648-7910
hal.structure.identifier
dc.contributor.authorLewin, Mathieu
HAL ID: 1466
ORCID: 0000-0002-1755-0207
dc.date.accessioned2020-10-26T10:37:48Z
dc.date.available2020-10-26T10:37:48Z
dc.date.issued2020
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/21165
dc.language.isoenen
dc.subjectLieb-Thirringen
dc.subjectSchrödinger equationen
dc.subject.ddc520en
dc.titleThe nonlinear Schrödinger equation for orthonormal functions: II. Application to Lieb-Thirring inequalitiesen
dc.typeDocument de travail / Working paper
dc.description.abstractenWe prove that the best Lieb-Thirring constant when the eigenvalues of a Schrödinger operator −Δ+V(x) are raised to the power κ≥1 (κ≥3/2 in 1D and κ>1 in 2D) can never be attained for a potential having finitely many eigenvalues. We thereby disprove a conjecture of Lieb and Thirring in 2D that the best constant is given by the one-bound state case for 1<κ≲1.165. In a different but related direction, we also show that the cubic nonlinear Schrödinger equation admits no orthonormal ground state in 1D, for more than one function.en
dc.identifier.citationpages43en
dc.relation.ispartofseriestitleCahier de recherche CEREMADEen
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-02477148en
dc.subject.ddclabelSciences connexes (physique, astrophysique)en
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2020-10-26T10:33:25Z
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