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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
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorLewin, Mathieu
HAL ID: 1466
ORCID: 0000-0002-1755-0207		*
dc.date.accessioned2020-04-27T12:10:44Z
dc.date.available2020-04-27T12:10:44Z
dc.date.issued2020
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/20662
dc.language.isoenen
dc.subjectnonlinear Schrödinger equation
dc.subjectLieb-Thirring
dc.subject.ddc520en
dc.titleThe nonlinear Schrödinger equation for orthonormal functions: II. Application to Lieb-Thirring inequalities
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.
dc.publisher.cityParisen
dc.identifier.citationpages39
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphine
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-02477148
dc.subject.ddclabelSciences connexes (physique, astrophysique)en
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.date.updated2020-06-09T10:43:19Z
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