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dc.contributor.authorLewin, Mathieu*
dc.contributor.authorNam, Phan Thành*
dc.contributor.authorRougerie, Nicolas*
dc.date.accessioned2018-09-05T12:13:59Z
dc.date.available2018-09-05T12:13:59Z
dc.date.issued2018
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17958
dc.language.isoenen
dc.subjectBose gas
dc.subject.ddc515en
dc.titleBlow-up profile of rotating 2D focusing Bose gases
dc.typeCommunication / Conférence
dc.description.abstractenWe 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.citationpages21
dc.relation.ispartoftitleMacroscopic Limits of Quantum Systems. MaLiQS 2017. Springer Proceedings in Mathematics & Statistics, vol 270
dc.relation.ispartofeditorCadamuro, D., Duell, M., Dybalski, W., Simonella, S.
dc.relation.ispartofpublnameMacroscopic Limits of Quantum Systems
dc.relation.ispartofurlhttps://doi.org/10.1007/978-3-030-01602-9
dc.subject.ddclabelAnalyseen
dc.relation.ispartofisbn978-3-030-01601-2
dc.relation.confdate2018
dc.identifier.doi10.1007/978-3-030-01602-9_7
dc.description.ssrncandidatenon
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dc.description.audienceInternational
dc.date.updated2020-04-27T12:18:53Z
hal.person.labIds60*
hal.person.labIds125566*
hal.person.labIds688*


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