自引力玻色-爱因斯坦凝聚体中与集体模式耦合的两个量子化涡旋的相关性

Kenta Asakawa, Makoto Tsubota
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摘要

我们利用格罗斯-皮塔耶夫斯基-泊松方程对自引力玻色-爱因斯坦凝聚态(BEC)中两个平行量子化涡旋的相关性进行了数值研究。长程引力吸引力相互作用使 BEC 无需外部势能就能自我约束,而引力势能的密度依赖性会诱发量子化涡旋的触发行为。本研究的目的是为理解引力相互作用影响下两个量子化涡旋的旋回提供线索。两个量子化涡旋的旋转与 BEC 的集体模式相耦合,这与在外部电势约束的典型 BEC 中观察到的行为明显不同。旋转周期随距离 BEC 中心的初始位置的增加而线性增加。这种与在均匀 BEC 中观察到的二次增加的偏差表明,引力相互作用对旋转的量子化涡旋产生了阻力效应。两个位置接近的量子化涡旋沿着椭圆轨道旋转,并伴有径向波动。然而,当量子化漩涡的初始位置超过与其核心大小相当的临界半径时,它们的轨迹会转变为向外的螺旋形,这意味着有效耗散的开始。我们的研究结果表明,量子化涡旋的径向波动与 BEC 的四极模式共振,从而产生了耗散机制。
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Corotation of two quantized vortices coupled with collective modes in self-gravitating Bose-Einstein condensates
We numerically examine the corotation of two parallel quantized vortices in a self-gravitating Bose-Einstein condensate (BEC) employing the Gross-Pitaevskii-Poisson equations. The long-range gravitationally attractive interaction allows the BEC to self-confine without the need for external potentials, while the density-dependence of the gravitational potential induces intriguing behaviors in the quantized vortices. The aim of this study is to provide a clue for understanding the corotation of two quantized vortices under the influence of gravitational interactions. The corotation of two quantized vortices is coupled with collective modes of the BEC, which markedly differs from the behavior observed in typical BECs confined by an external potential. The rotational period increases linearly with the initial position from the center of the BEC. This deviation from the quadratic increase observed in a uniform BEC suggests that the gravitational interaction exerts a drag effect on the rotating quantized vortices. The two closely positioned quantized vortices rotate along elliptical orbits with radial fluctuations. However, when the quantized vortices are initially positioned beyond a critical radius comparable to their core sizes, their trajectory transitions into an outward spiral, implying the onset of effective dissipation. Our findings demonstrate that the radial fluctuations of the quantized vortex resonate with the quadrupole mode of the BEC, giving rise to a dissipation mechanism.
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