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arXiv · 2510.15604

Convergence analysis of Sobolev Gradient flows for the rotating Gross-Pitaevskii energy functional

Chen Zhang·Patrick Henning·Mahima Yadav·Wenbin Chen
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Abstract

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.

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Chen Zhang, Patrick Henning, Mahima Yadav, Wenbin Chen. 2025-10-17. Convergence analysis of Sobolev Gradient flows for the rotating Gross-Pitaevskii energy functional. https://arxiv.org/abs/2510.15604

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