论文标题
Gross-Pitaevskii方程中量化涡流的高精度解决方案
High precision solutions to quantized vortices within Gross-Pitaevskii equation
论文作者
论文摘要
稀释原子的玻色子凝结物中涡流的动力学可以通过毛皮层的方程式很好地配制。为了更好地理解涡旋的属性，提出了一种将涡流的非线性微分方程求解为非常高精度的系统方法。通过两点垫$ \急性{\ text {e}} $近似值，这些解决方案是用简单的理性函数表示的，可用于模拟涡流动力学。解决方案的精度对连接参数和截断顺序敏感。通过合理函数顺序的合理扩展，可以显着改善它。讨论了解决方案的错误和两点垫的限制$ \ acute {\ text {e}} $近似值。这项研究可能会阐明非线性涡度方程的精确溶液。
The dynamics of vortices in Bose-Einstein condensates of dilute cold atoms can be well formulated by Gross-Pitaevskii equation. To better understand the properties of vortices, a systematic method to solve the nonlinear differential equation for the vortex to a very high precision is proposed. Through two-point Pad$\acute{\text{e}}$ approximants, these solutions are presented in terms of simple rational functions, which can be used in the simulation of vortex dynamics. The precision of the solutions is sensitive to the connecting parameter and the truncation orders. It can be improved significantly with a reasonable extension in the order of rational functions. The errors of the solutions and the limitation of two-point Pad$\acute{\text{e}}$ approximants are discussed. This investigation may shed light on the exact solution to the nonlinear vortex equation.
