On the stability of 2D dipolar Bose-Einstein condensates

TL;DR

This paper investigates the conditions under which stable ground states exist for two-dimensional dipolar Bose-Einstein condensates, focusing on the critical balance between kinetic and interaction energies.

Contribution

It provides a sharp criterion for the existence of energy minimizers in 2D dipolar BECs, linking stability to a generalized Gagliardo-Nirenberg inequality.

Findings

Derived a criterion involving the optimal constant of a Gagliardo-Nirenberg inequality.

Identified conditions for the existence of ground states in 2D dipolar BECs.

Analyzed the critical behavior of kinetic and interaction energies under scaling.

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.