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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.10851 |
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| _version_ | 1866910626372124672 |
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| author | Hu, Guanghui Li, Ruo Zhan, Hongfei |
| author_facet | Hu, Guanghui Li, Ruo Zhan, Hongfei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10851 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A gradient flow model for ground state calculations in Wigner formalism based on density functional theory Hu, Guanghui Li, Ruo Zhan, Hongfei Computational Physics Mathematical Physics 65M70, 70G60, 81S30 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. |
| title | A gradient flow model for ground state calculations in Wigner formalism based on density functional theory |
| topic | Computational Physics Mathematical Physics 65M70, 70G60, 81S30 |
| url | https://arxiv.org/abs/2409.10851 |