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 *
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