标题： 自引力玻色-爱因斯坦凝聚体中与集体模态耦合的两个量子涡旋的共转 显示英文标题

标题： Corotation of two quantized vortices coupled with collective modes in self-gravitating Bose-Einstein condensates

摘要： 我们通过Gross-Pitaevskii-Poisson方程数值研究了自引力玻色-爱因斯坦凝聚体（BEC）中两个平行量子涡旋的共转现象。 长程的引力吸引相互作用使得BEC能够在不需要外部势的情况下自我约束，而引力势的密度依赖性在量子涡旋中引起了有趣的行为。 本研究的目的是提供一个理解在引力相互作用影响下两个量子涡旋共转的线索。 两个量子涡旋的共转与BEC的集体模式耦合，这明显不同于在外部势约束下的典型BEC中观察到的行为。 旋转周期随着初始位置从BEC中心的距离线性增加。 这种与均匀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涡旋产生了阻力效应。 两个紧密放置的量子涡旋沿着具有径向波动的椭圆轨道旋转。 然而，当量子涡旋最初放置在与它们核心尺寸相当的临界半径之外时，其轨迹会转变为向外的螺旋，暗示有效耗散的开始。 我们的研究结果表明，量子涡旋的径向波动与BEC的四极模共振，从而产生了一种耗散机制。 显示英文摘要

摘要： 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.