环形约束与超越：双极$^{164}$Dy量子滴的涡量定义形态
Toroidal Confinement and Beyond: Vorticity-Defined Morphologies of Dipolar $^{164}$Dy Quantum Droplets
AI总结：
研究非旋转双极玻色-爱因斯坦凝聚体中环形和多重极涡旋量子滴的形成、稳定性和动力学，揭示了LHY修正和DDI各向异性在维持复杂QD状态中的作用。
摘要：
我们研究了非旋转双极玻色-爱因斯坦凝聚体中三维环形和多重极涡旋量子滴（QDs）的形成、稳定性和动力学。在扩展的格鲁斯-皮塔耶夫斯基方程框架下，研究了QD的动力学，该方程包括长程偶极子-偶极子相互作用（DDI）和超越平均场李-黄-杨（LHY）项，揭示了自束缚态的出现。对于不同拓扑电荷（涡量$S$）值的多重极QDs，稳定的稳态解呈现项链状模式，其中“珠子”（多重极的阶数）$n=2S$，最大到$S=6$。多重极的稳定性区域随着$S$的增加而缩小。对于较高的$S$值，与相位缠绕相关的离心效应破坏了环形密度，并驱动了碎片化多重极滴状态的形成。化学势、总能量和峰值密度对规范（粒子数）和$S$的依赖性被产生。这些发现揭示了LHY修正和DDI各向异性在非旋转配置中维持复杂QD状态的稳定作用。
英文摘要：
We investigate the formation, stability, and dynamics of 3D ring-shaped and multipole vortical quantum droplets (QDs) in non-rotating dipolar Bose-Einstein condensates held in a toroidal trapping potential. The QD dynamics are investigated in the framework of the extended Gross-Pitaevskii equation, which includes long-range dipole-dipole interactions (DDI) and the beyond-mean-field Lee-Huang-Yang (LHY) term, revealing the emergence of self-bound states. Stable stationary solutions for multipole QDs with different values of the topological charge (vorticity $S$) are shaped as necklace-like modes, with the number of \textquotedblleft beads" (multipole's order) $n=2S$, up to $S=6$. The stability area of the multipoles shrinks with the increase of $S$. For higher values of $S$ the centrifugal effect associated with the phase winding destabilizes the annular density and drives the formation of fragmented multipole droplet states. The dependence of the chemical potential, total energy and peak density on the norm (number of particles) and $S$ is produced. These findings uncover the stabilizing effect of the LHY correction and DDI anisotropy in maintaining complex QD states in the non-rotating configurations.
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