发表机构
Université Lyon 1, Centrale Lyon, INSA Lyon, Université Jean Monnet, CNRS, ICJ UMR5208; HSE University（里昂第一大学、中央里昂学院、里昂国立应用科学学院、让·莫内大学、法国国家科学研究中心、ICJ联合研究实验室; 高等经济大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对Gross-Pitaevskii基态计算，提出在固定TT秩单位范数流形上的一阶黎曼优化方法，保持质量约束与低秩，显著降低计算时间并保持精度。
AI 中文摘要
本文关注利用张量列（TT）格式数值计算Gross-Pitaevskii基态。我们将问题视为在单位质量约束下最小化Gross-Pitaevskii能量泛函，并提出一种一阶黎曼优化方案，该方案通过在固定TT秩的单位范数函数流形上操作，在整个优化过程中同时保持质量约束和低秩表示。在此流形上，我们推导出能量自适应黎曼梯度，并展示如何在TT格式中高效计算它。空间离散化采用带数值积分的谱方法，使得所需计算能够高效进行，同时保持低秩格式。结果表明，与全秩计算相比，该方法大幅减少了计算时间，同时保持了单分量和多分量Gross-Pitaevskii方程的精度。
英文摘要
This work is concerned with the numerical computation of Gross-Pitaevskii ground states using the tensor train (TT) format. We regard the problem as the minimization of the Gross-Pitaevskii energy functional under a unit mass constraint, and propose a first-order Riemannian optimization scheme that preserves both the mass constraint and the low-rank representation throughout the optimization, by operating on the manifold of unit-norm functions of fixed TT-rank. On this manifold, we derive the energy-adaptive Riemannian gradient and show how to compute it efficiently in the TT format. Spatial discretization is performed using a spectral method with numerical integration, which allows the required computations to be carried out efficiently while preserving the low-rank format. The method is shown to substantially reduce computational time compared to full-rank computations, while maintaining accuracy for both single- and multicomponent Gross-Pitaevskii equations.
