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Blow-up profile of rotating 2D focusing Bose gases

Lewin, Mathieu; Nam, Phan Thành; Rougerie, Nicolas (2018), Blow-up profile of rotating 2D focusing Bose gases, in Cadamuro, D., Duell, M., Dybalski, W., Simonella, S., Macroscopic Limits of Quantum Systems. MaLiQS 2017. Springer Proceedings in Mathematics & Statistics, vol 270, Macroscopic Limits of Quantum Systems, p. 21. 10.1007/978-3-030-01602-9_7

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Blowup-NLS-rev2.pdf (375.2Kb)
Type
Communication / Conférence
Date
2018
Conference date
2018
Book title
Macroscopic Limits of Quantum Systems. MaLiQS 2017. Springer Proceedings in Mathematics & Statistics, vol 270
Book author
Cadamuro, D., Duell, M., Dybalski, W., Simonella, S.
Publisher
Macroscopic Limits of Quantum Systems
ISBN
978-3-030-01601-2
Pages
21
Publication identifier
10.1007/978-3-030-01602-9_7
Metadata
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Author(s)
Lewin, Mathieu cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Nam, Phan Thành
Ludwig-Maximilians-Universität München
Rougerie, Nicolas
Laboratoire de physique et modélisation des milieux condensés [LPM2C]
Abstract (EN)
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$.
Subjects / Keywords
Bose gas

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