Author

Shi-Xin Zheng

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Preprint Oct 2026

Riemannian Hessian analysis of Sobolev gradient flows for the Gross--Pitaevskii ground state problem

Sobolev gradient flows for the Gross--Pitaevskii ground state problem are Riemannian gradient descent methods on the sphere under a metric induced by a discrete elliptic operator. We analyze their convergence through the condition number of the Riemannian Hessian at the ground state. Bounds of the Rayleigh quotient of...

Shi-Xin Zheng, Xiang-Xiong Zhang · 0 citations

Preprint Sep 2026

Global convergence of an efficient splitting method for the defocusing Gross--Pitaevskii ground state problem

For computing the ground state of the defocusing Gross--Pitaevskii energy, we propose and analyze two efficient schemes based on the Davis--Yin three-operator splitting, which treats the potential and interaction terms explicitly, and the kinetic energy by a resolvent. One iteration costs one inversion of $I-\gamma\Del...

Jia-Xing Li, Shi-Xin Zheng, Xiang-Xiong Zhang · 0 citations