On the stability of 2D dipolar Bose-Einstein condensates

2018/09/19 by Arnaud Eychenne, Eychenne, Arnaud, Nicolas Rougerie +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph) #Quantum Gases (cond-mat.quant-gas)

paper · doi:10.48550/arxiv.1809.07085

openalex publication_date 2018/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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