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

Autor:	Dinh, Van Duong, Nguyen, Dinh-Thi, Rougerie, Nicolas
Rok vydání:	2022
Předmět:	Mathematics - Analysis of PDEs Mathematical Physics 35Q40 35Q51 35Q55
Druh dokumentu:	Working Paper
Popis:	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. Comment: 20 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2208.08317 Zobrazit plný text záznamu View this record from Arxiv