论文标题

量子流体中涡流的识别:有限元算法和程序

Identification of vortices in quantum fluids: finite element algorithms and programs

论文作者

Kalt, Victor, Sadaka, Georges, Danaila, Ionut, Hecht, Frédéric

论文摘要

我们提出了有限元数值算法,用于鉴定由宏观复杂波函数描述的量子流体中的涡流。他们使用Free Software FreeFem ++的实现将本文作为后处理工具箱分发,可用于分析数值或实验数据。提出了Bose-Einstein冷凝水(BEC)和超流体氦气流的应用。使用求解gross-pitaevskii方程或旋转BEC的实验图像获得的数值数据对程序进行测试和验证。当使用数值数据时,将涡流位置计算为波函数的拓扑缺陷(零)。对于实验图像,我们将涡旋位置计算为原子密度的局部最小值,并在简单的图像处理后提取。一旦确定了涡旋中心,我们就会使用高斯拟合到精确估计涡旋半径。对于涡旋晶格,还计算了晶格参数(涡流距离)。后处理工具箱提供了超级流体中涡旋配置的完整描述。测试二维(旋转BEC中的巨型涡流,实验性BEC中的Abrikosov Vortex晶格)和三维(涡流环,开尔文波和超氟化氦中的量子湍流场)显示了软件的鲁棒性。提供数值或实验波函数字段的程序的通信非常简单且直观。后处理工具箱也可以应用于超导体中涡流的识别。

We present finite-element numerical algorithms for the identification of vortices in quantum fluids described by a macroscopic complex wave function. Their implementation using the free software FreeFem++ is distributed with this paper as a post-processing toolbox that can be used to analyse numerical or experimental data. Applications for Bose-Einstein condensates (BEC) and superfluid helium flows are presented. Programs are tested and validated using either numerical data obtained by solving the Gross-Pitaevskii equation or experimental images of rotating BEC. Vortex positions are computed as topological defects (zeros) of the wave function when numerical data are used. For experimental images, we compute vortex positions as local minima of the atomic density, extracted after a simple image processing. Once vortex centers are identified, we use a fit with a Gaussian to precisely estimate vortex radius. For vortex lattices, the lattice parameter (inter-vortex distance) is also computed. The post-processing toolbox offers a complete description of vortex configurations in superfluids. Tests for two-dimensional (giant vortex in rotating BEC, Abrikosov vortex lattice in experimental BEC) and three-dimensional (vortex rings, Kelvin waves and quantum turbulence fields in superfluid helium) configurations show the robustness of the software. The communication with programs providing the numerical or experimental wave function field is simple and intuitive. The post-processing toolbox can be also applied for the identification of vortices in superconductors.

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