论文标题
Bose-Einstein冷凝物中涡流动力学的一种方法：相奇数轨迹的分析方程
A method for the dynamics of vortices in a Bose-Einstein condensate: analytical equations of the trajectories of phase singularities
论文作者
论文摘要
我们提出了一种研究准二维的玻色网凝结物的动力学方法，该凝结物最初在任意位置包含许多涡旋。我们首先在均匀培养基和抛物线陷阱中的动力学分析解决方案，以实现理想的非相互作用情况。对于同质情况，这是在光子学的背景下引入的。在这里，我们在Bose-Einstein冷凝物的背景下讨论了这一病例，并首次将分析解决方案扩展到了被困的情况。这种线性案例允许人们在初始冷凝物中获得相位奇异性位置的轨迹以及时间。同样，它允许人们预测一定数量的兴趣，例如初始冷凝水中包含的涡流和抗变量的时间。其次，该方法与非线性情况的数值模拟相辅相成。我们使用非线性GROSS-PITAEVSKII方程的数值拆分模拟来确定相互作用的存在如何更改这些轨迹和量的量。我们用几个简单的案例中的均质和抛物困难系统中的几个简单案例说明了这种方法。
We present a method to study the dynamics of a quasi-two dimensional Bose-Einstein condensate which contains initially many vortices at arbitrary locations. We present first the analytical solution of the dynamics in a homogeneous medium and in a parabolic trap for the ideal non-interacting case. For the homogeneous case this was introduced in the context of photonics. Here we discuss this case in the context of Bose-Einstein condensates and extend the analytical solution to the trapped case, for the first time. This linear case allows one to obtain the trajectories of the position of phase singularities present in the initial condensate along with time. Also, it allows one to predict some quantities of interest, such as the time at which a vortex and an antivortex contained in the initial condensate will merge. Secondly, the method is complemented with numerical simulations of the non-linear case. We use a numerical split-step simulation of the non-linear Gross-Pitaevskii equation to determine how these trajectories and quantities of interest are changed by the presence of interactions. We illustrate the method with several simple cases of interest both in the homogeneous and parabolically trapped systems.
