| dc.contributor.author | Frank, Rupert L. | * |
| dc.contributor.author | Gontier, David | * |
| dc.contributor.author | Lewin, Mathieu | * |
| dc.date.accessioned | 2020-04-27T12:10:44Z | |
| dc.date.available | 2020-04-27T12:10:44Z | |
| dc.date.issued | 2020 | |
| dc.identifier.uri | https://basepub.dauphine.fr/handle/123456789/20662 | |
| dc.language.iso | en | en |
| dc.subject | nonlinear Schrödinger equation | |
| dc.subject | Lieb-Thirring | |
| dc.subject.ddc | 520 | en |
| dc.title | The nonlinear Schrödinger equation for orthonormal functions: II. Application to Lieb-Thirring inequalities | |
| dc.type | Document de travail / Working paper | |
| dc.description.abstracten | We 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.city | Paris | en |
| dc.identifier.citationpages | 39 | |
| dc.relation.ispartofseriestitle | Cahier de recherche CEREMADE, Université Paris-Dauphine | |
| dc.identifier.urlsite | https://hal.archives-ouvertes.fr/hal-02477148 | |
| dc.subject.ddclabel | Sciences connexes (physique, astrophysique) | en |
| dc.description.ssrncandidate | non | |
| dc.description.halcandidate | non | |
| dc.description.readership | recherche | |
| dc.description.audience | International | |
| dc.date.updated | 2020-06-09T10:43:19Z | |
| hal.person.labIds | 224225 | * |
| hal.person.labIds | 60 | * |
| hal.person.labIds | 31$$$60 | * |
