arXiv 1709.050972017-09-15cond-mat.quant-gasnlin.PS

高斯密度下玻色-爱因斯坦凝聚体中的非定常涡环

Non-stationary vortex ring in a Bose-Einstein condensate with Gaussian density

Victor P. Ruban

备注：: 3 pages, 3 figures

摘要：

在空间非均匀密度背景$ρ({\bf r})$上，近似描述囚禁玻色-爱因斯坦凝聚体中量子化涡丝动力学的局域感应方程，取无量纲形式${\mathbf R}_t=\varkappa {\mathbf b}+[\nabla\lnρ({\mathbf R})\times {\boldsymbol τ}]$（其中$\varkappa$是细丝的局部曲率，${\mathbf b}$是单位副法线向量，以及${\boldsymbol τ}$是单位切向量），示出承认有限维减少，如果密度分布是各向同性高斯，$ρ\propto\exp(-|{\bf r}|^2/2)$。这种减少对应于以位置${\bf A}(t)$为中心的几何上完美的涡环，其方向和大小都由矢量${\bf B}(t)$确定。参数${\bf A}$和${\bf B}$表现出与3D中牛顿粒子的速度和位置相同的动力学：$\dot {\bf A}={\bf B}/|{\bf B}|^2-{\bf B}$和$\dot {\bf B}={\bf A}$。

英文摘要：

The local induction equation, approximately describing dynamics of a quantized vortex filament in a trapped Bose-Einstein condensate in the Thomas-Fermi regime on a spatially nonuniform density background $ρ({\bf r})$ and taking dimensionless form ${\mathbf R}_t=\varkappa {\mathbf b}+[\nabla\lnρ({\mathbf R})\times {\boldsymbol τ}]$ (where $\varkappa$ is a local curvature of the filament, ${\mathbf b}$ is the unit binormal vector, and ${\boldsymbol τ}$ is the unit tangent vector), is shown to admit a finite-dimensional reduction if the density profile is an isotropic Gaussian, $ρ\propto\exp(-|{\bf r}|^2/2)$. The reduction corresponds to a geometrically perfect vortex ring centered at position ${\bf A}(t)$, with orientation and size both determined by a vector ${\bf B}(t)$. Parameters ${\bf A}$ and ${\bf B}$ exhibit the same dynamics as velocity and position of a Newtonian particle do in 3D: $\dot {\bf A}={\bf B}/|{\bf B}|^2-{\bf B}$, and $\dot {\bf B}={\bf A}$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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