Blow-up of 2D attractive Bose-Einstein condensates at the crittical rotational speed

TL;DR

This paper analyzes the collapse behavior of 2D attractive Bose-Einstein condensates under rotation, showing that the blow-up profile remains consistent even at critical rotational speeds where centrifugal forces counteract the trapping potential.

Contribution

It extends previous results by demonstrating that the blow-up profile of collapsing condensates is unaffected by rotation frequencies approaching the critical value, including the case of strong deconfinement.

Findings

Blow-up profile remains unchanged at critical rotation speeds.

Collapse occurs at a critical interaction strength from below.

Blow-up scenario is robust against centrifugal deconfinement.

Abstract

We study the ground states of a 2D focusing non-linear Schr\"odinger equation with rotation and harmonic trapping. When the strength of the interaction approaches a critical value from below, the system collapses to a profile obtained from the optimizer of a Gagliardo--Nirenberg interpolation inequality. This was established before in the case of fixed rotation frequency. We extend the result to rotation frequencies approaching, or even equal to, the critical frequency at which the centrifugal force compensates the trap. We prove that the blow-up scenario is to leading order unaffected by such a strong deconfinement mechanism. In particular the blow-up profile remains independent of the rotation frequency.