On the Stability of 2D Dipolar Bose--Einstein Condensates

We study the existence of energy minimizers for a Bose-Einstein condensate with dipole-dipole interactions, tightly confined to a plane. The problem is critical in that the kinetic energy and the (partially attractive) interaction energy behave the same under mass-preserving scalings of the wave-fun...

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Veröffentlicht in:SIAM journal on mathematical analysis 2019-01, Vol.51 (2), p.1371-1386
Hauptverfasser: Eychenne, Arnaud, Rougerie, Nicolas
Format: Artikel
Sprache:eng
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Zusammenfassung:We study the existence of energy minimizers for a Bose-Einstein condensate with dipole-dipole interactions, tightly confined to a plane. The problem is critical in that the kinetic energy and the (partially attractive) interaction energy behave the same under mass-preserving scalings of the wave-function. We obtain a sharp criterion for the existence of ground states, involving the optimal constant of a certain generalized Gagliardo-Nirenberg inequality.
ISSN:0036-1410
1095-7154
DOI:10.1137/18M1216663