Title: A gradient flow model for ground state calculations in Wigner formalism based on density functional theory Show Chinese title

Title: 基于密度泛函理论的Wigner形式中基态计算的梯度流模型

Abstract: In this paper, a gradient flow model is proposed for conducting ground state calculations in Wigner formalism of many-body system in the framework of density functional theory. More specifically, an energy functional for the ground state in Wigner formalism is proposed to provide a new perspective for ground state calculations of the Wigner function. Employing density functional theory, a gradient flow model is designed based on the energy functional to obtain the ground state Wigner function representing the whole many-body system. Subsequently, an efficient algorithm is developed using the operator splitting method and the Fourier spectral collocation method, whose numerical complexity of single iteration is $O(n_{\rm DoF}\log n_{\rm DoF})$. Numerical experiments demonstrate the anticipated accuracy, encompassing the one-dimensional system with up to $2^{21}$ particles and the three-dimensional system with defect, showcasing the potential of our approach to large-scale simulations and computations of systems with defect. Show Chinese abstract

Abstract: 在本文中，提出了一种梯度流模型，用于在密度泛函理论框架下进行多体系统的Wigner形式的基态计算。 更具体地说，提出了一个用于Wigner形式基态的能量泛函，以提供一种新的视角来计算Wigner函数的基态。 利用密度泛函理论，基于能量泛函设计了一个梯度流模型，以获得表示整个多体系统的基态Wigner函数。 随后，开发了一种高效的算法，该算法使用算子分裂方法和傅里叶谱插值方法，其单次迭代的数值复杂度为$O(n_{\rm DoF}\log n_{\rm DoF})$。 数值实验展示了预期的精度，包括最多含有$2^{21}$个粒子的一维系统和具有缺陷的三维系统，展示了我们方法在大规模模拟和计算有缺陷系统的潜力。