报告题目：A preconditioned Riemannian conjugate gradient method for computing the ground states of arbitrary-angle rotating Bose-Einstein condensates

主讲人：张少波博士（四川大学）

时间：2025年4月15日（周二）15:00 p.m.

地点：北院卓远楼305会议室

主办单位：统计与数学学院

摘要：In this report, we investigate the ground states (GS) of arbitrary-angle rotating Bose-Einstein condensates (BECs), modeled by the three-dimensional Gross-Pitaevskii equation (GPE). Firstly, we establish the existence results of the ground states with rigorous proof. Secondly, we propose a preconditioned Riemannian conjugate gradient (pRCG) method coupled with the Fourier pseudo-spectral discretization to compute the ground states numerically. A robust and efficient preconditioner together with an adaptive stepsize control strategy is proposed to accelerate the convergence. Thirdly, utilizing the pRCG algorithm, we study the ground state patterns in various settings extensively. Particularly, we observe bent vortex lines, including U-shaped and S-shaped vortex lines, in the elongated BEC with arbitrary-angle rotation. We also study how the bent vortex line patterns change with the angle between the rotation axis and the elongated direction in detail. Lastly, we perform a comprehensive numerical study to confirm the spectral accuracy and showcase the great computational efficiency, and study the influences of physical parameters on GS patterns of BECs with arbitrary-angle rotation.

主讲人简介：

张少波，2018年本科毕业于山西大学数学科学学院，2024年在天津大学获得博士学位，现于四川大学从事博士后研究工作。研究方向主要是偏微分方程的数值计算和分析工作，专注于非局部卷积位势的快速高精度算法的设计以及旋转偶极BEC的动力学和基态计算。