论文标题
无限旋转2D玻色气体中预测的总毛的数值方法
Numerical method for the projected Gross--Pitaevskii equation in an infinite rotating 2D Bose gas
论文作者
论文摘要
我们提出了一种在无限旋转的玻璃纤维凝结物中进化的方法，它是在无限旋转的bose-Einstein冷凝物中进化的，其基态是涡旋晶格。在没有边界和边缘效应的情况下，我们使用准周期边界条件来研究该系统中块状超氟的行为。我们还为受这些边界条件的BEC阶段提供了Landau仪表的表达。我们的频谱表示使用单体哈密顿量的本征函数作为基础函数。由于这些基础函数没有已知的确切正交规则，因此我们大约实现了与能量截止相关的投影，但是表明，通过选择适当的良好空间电网，可以使结果误差可以忽略不计。我们展示了该模型的收敛性如何受模拟参数（例如空间网格的大小和Landau水平的数量）的影响。添加耗散，我们使用我们的方法来找到$ n $涡流的晶格基态。然后，我们可以扰动地面，以研究晶格的熔化。
We present a method for evolving the projected Gross-Pitaevskii equation in an infinite rotating Bose-Einstein condensate, the ground state of which is a vortex lattice. We use quasi-periodic boundary conditions to investigate the behaviour of the bulk superfluid in this system, in the absence of boundaries and edge effects. We also give the Landau gauge expression for the phase of a BEC subjected to these boundary conditions. Our spectral representation uses the eigenfunctions of the one-body Hamiltonian as basis functions. Since there is no known exact quadrature rule for these basis functions we approximately implement the projection associated with the energy cut-off, but show that by choosing a suitably fine spatial grid the resulting error can be made negligible. We show how the convergence of this model is affected by simulation parameters such as the size of the spatial grid and the number of Landau levels. Adding dissipation, we use our method to find the lattice ground state for $N$ vortices. We can then perturb the ground-state, in order to investigate the melting of the lattice.
