论文标题
在毫无用的旋转速度下对2D有吸引力的Bose-Einstein凝结
Blow-up of 2D attractive Bose-Einstein condensates at the crittical rotational speed
论文作者
论文摘要
我们研究了旋转和谐波捕获的2D聚焦非线性Schrödinger方程的基态。当相互作用的强度从下方接近临界值时，系统崩溃到了从Gagliardo的优化器中获得的轮廓 - Nirenberg插值不平等。这是在固定旋转频率的情况下建立的。我们将结果扩展到接近甚至等于离心力补偿陷阱的临界频率的旋转频率。我们证明，爆炸的情况是领导不受这种强大的解密机制影响的秩序。特别是，爆破轮廓保持独立于旋转频率。
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.
