Convergence analysis of Sobolev Gradient flows for the rotating Gross-Pitaevskii energy functional
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909866934665216 |
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| author | Zhang, Chen Henning, Patrick Yadav, Mahima Chen, Wenbin |
| author_facet | Zhang, Chen Henning, Patrick Yadav, Mahima Chen, Wenbin |
| contents | This paper studies the numerical approximation of the ground state of rotating Bose--Einstein condensates, formulated as the minimization of the Gross--Pitaevskii energy functional under a mass conservation constraint. To solve this problem, we consider three Sobolev gradient flow schemes: the $H_0^1$ scheme, the $a_0$ scheme, and the $a_u$ scheme. Convergence of these schemes in the non-rotating case was established by Chen et al., and the rotating $a_u$ scheme was analyzed in Henning et al. In this work, we prove the global convergence of the $H_0^1$ and $a_0$ schemes in the rotating case, and establish local linear convergence for all three schemes near the ground state. Numerical experiments confirm our theoretical findings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_15604 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence analysis of Sobolev Gradient flows for the rotating Gross-Pitaevskii energy functional Zhang, Chen Henning, Patrick Yadav, Mahima Chen, Wenbin Numerical Analysis This paper studies the numerical approximation of the ground state of rotating Bose--Einstein condensates, formulated as the minimization of the Gross--Pitaevskii energy functional under a mass conservation constraint. To solve this problem, we consider three Sobolev gradient flow schemes: the $H_0^1$ scheme, the $a_0$ scheme, and the $a_u$ scheme. Convergence of these schemes in the non-rotating case was established by Chen et al., and the rotating $a_u$ scheme was analyzed in Henning et al. In this work, we prove the global convergence of the $H_0^1$ and $a_0$ schemes in the rotating case, and establish local linear convergence for all three schemes near the ground state. Numerical experiments confirm our theoretical findings. |
| title | Convergence analysis of Sobolev Gradient flows for the rotating Gross-Pitaevskii energy functional |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2510.15604 |