On stability of rotational 2D binary Bose-Einstein condensates

TL;DR

This paper analyzes the orbital stability of energy minimizers in a 2D nonlinear Schrödinger model for rotational binary Bose-Einstein condensates with a logarithmic nonlinearity, focusing on the critical case where potential and rotation effects balance.

Contribution

It introduces a stability analysis for the critical case of the model, employing magnetic Schrödinger operator techniques, which is a novel approach in this context.

Findings

Orbital stability is established in the critical case where potential and rotation effects balance.

Standard techniques are insufficient due to the combined effects of potential and rotation, requiring new methods.

The analysis provides insights into the stability of energy minimizers under different physical parameters.

Abstract

We consider a two-dimensional nonlinear Schr{\"o}dinger equation proposed in Physics to model rotational binary Bose-Einstein condensates. The nonlinearity is a logarithmic modification of the usual cubic nonlinearity. The presence of both the external confining potential and rotating frame makes it difficult to apply standard techniques to directly construct ground states, as we explain in an appendix. The goal of the present paper is to analyze the orbital stability of the set of energy minimizers under mass constraint, according to the relative strength of the confining potential compared to the angular frequency. The main novelty concerns the critical case (lowest Landau Level) where these two effects compensate exactly, and orbital stability is established by using techniques related to magnetic Schr{\"o}dinger operators.