标题： D维各向异性玻色-爱因斯坦凝聚体中的涡旋：具有超圆柱对称性的维度微扰理论 显示英文标题

标题： Vortices in D-dimensional anisotropic Bose-Einstein condensates: dimensional perturbation theory with hypercylindrical symmetry

摘要： 我们研究在超圆柱形势阱中沿z轴具有涡旋核心和量子化环流的D维原子玻色-爱因斯坦凝聚体。$\hbar m$。 我们使用维度微扰理论，以微扰参数$\delta=1/(D+2|m|-d)$，\textcolor{black}{其中$d$控制零阶动能的贡献}，对超圆柱形Gross-Pitaevskii方程进行解析近似。 我们推导出任意维度下凝聚体能量、密度、化学势和临界涡旋旋转速度的零阶（$\delta \to 0$）半经典近似。 我们研究势阱各向异性对有效维度降低的影响，并计算由合成维度和全息对偶研究所激发的高维涡旋特性，其中高维引力模型对应于低维量子模型。 在零阶近似中，我们观察到不同维度的能量级随相互作用强度和各向异性参数的变化而出现交叉。 显示英文摘要

摘要： We investigate D-dimensional atomic Bose-Einstein condensates in a hypercylindrical trap with a vortex core along the z-axis and quantized circulation $\hbar m$. We analytically approximate the hypercylindrical Gross-Pitaevskii equation using dimensional perturbation theory with perturbation parameter $\delta=1/(D+2|m|-d)$, \textcolor{black}{where $d$ controls the contribution of kinetic energy at zeroth order}. We derive the zeroth-order ($\delta \to 0$) semiclassical approximations for the condensate energy, density, chemical potential, and critical vortex rotation speed in arbitrary dimensions. We investigate the effect of trap anisotropy on lower effective dimensionality and compute properties of vortices in higher dimensions motivated by the study of synthetic dimensions and holographic duality, where a higher-dimensional gravitational model corresponds to a lower-dimensional quantum model. In the zeroth-order approximation, we observe crossings between energy levels for different dimensions as a function of interaction strength and anisotropy parameters.