2022/08/17 by Van Duong Dinh, Dinh, Van Duong, Dinh-Thi Nguyen +3
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Laser-Matter Interactions and Applications #Quantum optics and atomic interactions
paper · pdf · doi:10.48550/arxiv.2208.08317
We study the ground states of a 2D focusing non-linear Schrödinger 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.