arXiv 1401.41382014-01cond-mat.quant-gasnlin.PS

两个分布的故事：准二维玻色-爱因斯坦凝聚体中从少到多的涡旋

A Tale of Two Distributions: From Few To Many Vortices In Quasi-Two-Dimensional Bose-Einstein Condensates

T. Kolokolnikov, P. G. Kevrekidis, R. Carretero-Gonzalez

备注：: 15 pages, 2 figures
发表信息：: Proc. R. Soc. A 470 (2014) 20140048
DOI：: 10.1098/rspa.2014.0048

摘要：

受最近粒子模型在捕捉准二维玻色-爱因斯坦凝聚体中涡旋结构的进动和相互作用方面的成功的启发，我们重新审视了相关的常微分方程组。我们考虑的涡旋数$N$作为一个参数，并探讨的原型配置（“基态“）的情况下出现的几个或多个涡旋。在涡量较少的情况下，我们修正了Havelock [Phil. Mag. ${\bf 11}$，617（1931）]，说明了对于$N \geq7$，环形的涡旋多边形是不稳定的。此外，我们调和这种修改与最近的对称性破缺分岔的情况下，$N=2,\dots,5$识别。我们还简要地讨论了一个中心涡周围的涡环的情况（所谓的$N+1$配置）。最后，我们检查大$N$的相反限制，并说明如何粗粒化，连续的方法，使准确识别的径向分布的旋涡在该限制。

英文摘要：

Motivated by the recent successes of particle models in capturing the precession and interactions of vortex structures in quasi-two-dimensional Bose-Einstein condensates, we revisit the relevant systems of ordinary differential equations. We consider the number of vortices $N$ as a parameter and explore the prototypical configurations ("ground states") that arise in the case of few or many vortices. In the case of few vortices, we modify the classical result of Havelock [Phil. Mag. ${\bf 11}$, 617 (1931)] illustrating that vortex polygons in the form of a ring are unstable for $N \geq7$. Additionally, we reconcile this modification with the recent identification of symmetry breaking bifurcations for the cases of $N=2,\dots,5$. We also briefly discuss the case of a ring of vortices surrounding a central vortex (so-called $N+1$ configuration). We finally examine the opposite limit of large $N$ and illustrate how a coarse-graining, continuum approach enables the accurate identification of the radial distribution of vortices in that limit.

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英文摘要：

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