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 quasiperiodic boundary conditions to investigate the behavior 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 cutoff, but we 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, to investigate the melting of the lattice.

中文翻译：

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无限旋转二维玻色气体中投影Gross-Pitaevskii方程的数值方法

我们提出了一种在无限旋转的Bose-Einstein凝结水中发展投影Gross-Pitaevskii方程的方法，该凝结水的基态是涡旋晶格。在没有边界和边缘效应的情况下，我们使用拟周期边界条件来研究该系统中整体超流体的行为。我们还给出了在这些边界条件下BEC相的Landau规范表达式。我们的频谱表示使用一身哈密顿量的本征函数作为基本函数。由于对于这些基函数没有确切的正交规则，我们近似实现了与能量截止相关的投影，但是我们表明，通过选择适当的精细空间网格，可以使产生的误差忽略不计。我们展示了该模型的收敛性如何受到仿真参数的影响，例如空间网格的大小和Landau级别的数量。加上耗散，我们使用我们的方法找到晶格的基态$ñ$漩涡。然后，我们可以扰动基态，以研究晶格的熔化。