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報告題目：A preconditioned Riemannian conjugate gradient method for computing the ground states of arbitrary-angle rotating Bose-Einstein condensates

主講人：張少波博士（四川大學）

時間：2025年4月15日（周二）15:00 p.m.

地點：北院卓遠樓305會議室

主辦單位：統(tǒng)計與數(shù)學學院

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.

主講人簡介：

張少波,，2018年本科畢業(yè)于山西大學數(shù)學科學學院，2024年在天津大學獲得博士學位,，現(xiàn)于四川大學從事博士后研究工作,。研究方向主要是偏微分方程的數(shù)值計算和分析工作，專注于非局部卷積位勢的快速高精度算法的設計以及旋轉(zhuǎn)偶極BEC的動力學和基態(tài)計算,。