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.
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}
}