| dc.contributor.author | Lewin, Mathieu | * |
| dc.contributor.author | Nam, Phan Thành | * |
| dc.contributor.author | Rougerie, Nicolas | * |
| dc.date.accessioned | 2018-09-05T12:13:59Z | |
| dc.date.available | 2018-09-05T12:13:59Z | |
| dc.date.issued | 2018 | |
| dc.identifier.uri | https://basepub.dauphine.fr/handle/123456789/17958 | |
| dc.language.iso | en | en |
| dc.subject | Bose gas | |
| dc.subject.ddc | 515 | en |
| dc.title | Blow-up profile of rotating 2D focusing Bose gases | |
| dc.type | Communication / Conférence | |
| dc.description.abstracten | We consider the Gross-Pitaevskii equation describing an attractive Bose gas trapped to a quasi 2D layer by means of a purely harmonic potential, and which rotates at a fixed speed of rotation Ω. First we study the behavior of the ground state when the coupling constant approaches a∗ , the critical strength of the cubic nonlinearity for the focusing nonlinear Schrödinger equation. We prove that blow-up always happens at the center of the trap, with the blow-up profile given by the Gagliardo-Nirenberg solution. In particular, the blow-up scenario is independent of Ω, to leading order. This generalizes results obtained by Guo and Seiringer (Lett. Math. Phys., 2014, vol. 104, p. 141–156) in the non-rotating case. In a second part we consider the many-particle Hamiltonian for N bosons, interacting with a potential rescaled in the mean-field manner −aNN2β−1w(Nβx),withwapositivefunctionsuchthat\int_{\mathbb{R}^2} w(x) dx = 1.Assumingthat\beta < 1/2andthata_N \to a_*sufficientlyslowly,weprovethatthemany−bodysystemisfullycondensedontheGross−PitaevskiigroundstateinthelimitN \to \infty$. | |
| dc.identifier.citationpages | 21 | |
| dc.relation.ispartoftitle | Macroscopic Limits of Quantum Systems. MaLiQS 2017. Springer Proceedings in Mathematics & Statistics, vol 270 | |
| dc.relation.ispartofeditor | Cadamuro, D., Duell, M., Dybalski, W., Simonella, S. | |
| dc.relation.ispartofpublname | Macroscopic Limits of Quantum Systems | |
| dc.relation.ispartofurl | https://doi.org/10.1007/978-3-030-01602-9 | |
| dc.subject.ddclabel | Analyse | en |
| dc.relation.ispartofisbn | 978-3-030-01601-2 | |
| dc.relation.confdate | 2018 | |
| dc.identifier.doi | 10.1007/978-3-030-01602-9_7 | |
| dc.description.ssrncandidate | non | |
| dc.description.halcandidate | non | |
| dc.description.readership | recherche | |
| dc.description.audience | International | |
| dc.date.updated | 2020-04-27T12:18:53Z | |
| hal.person.labIds | 60 | * |
| hal.person.labIds | 125566 | * |
| hal.person.labIds | 688 | * |
