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On the stability of 2D dipolar Bose-Einstein condensates

Mathematical Physics 2018-09-26 v2 Quantum Gases Analysis of PDEs math.MP

Abstract

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.

Keywords

Cite

@article{arxiv.1809.07085,
  title  = {On the stability of 2D dipolar Bose-Einstein condensates},
  author = {Arnaud Eychenne and Nicolas Rougerie},
  journal= {arXiv preprint arXiv:1809.07085},
  year   = {2018}
}
R2 v1 2026-06-23T04:11:18.063Z