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报告题目：An efficient compact splitting Fourier spectral method for computing the dynamics of rotating spin-orbit coupled spin-1 Bose-Einstein condensates

主讲人：张勇教授（天津大学）

时间：2025年3月5日（周三）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：This talk focuses on the dynamic simulation of spin-1 Bose-Einstein condensates (BECs) with rotation and spin-orbit coupling (SOC), and presents a high-order compact splitting Fourier spectral method with favorable numerical properties. The Hamiltonian is split into a linear part, which consists of the Laplace, rotation and SOC terms, and a nonlinear part that includes all the remaining terms. The wave function is well approximated by the Fourier spectral method and is numerically accessed with discrete Fast Fourier transform (FFT). For the linear subproblem, we rotate the wave function by a function-rotation mapping, which is realized easily with purely FFT achieving almost optimal efficiency. The rotation term vanishes, but the SOC term becomes time-dependent. Using a time-dependent matrix decomposition and the function- rotation mapping, we can integrate the linear subproblem exactly and explicitly. The nonlinear subproblem is integrated analytically in physical space. Such “compact” splitting involves only two operators and facilitates the design of high-order splitting schemes. Our method is spectrally accurate in space and high order in time. It is efficient, explicit, unconditionally stable and simple to implement. In addition, we derive some dynamical properties and carry out a systematic study, including accuracy and efficiency tests, dynamical property verification, the SOC effects and dynamics of quantized vortices.

主讲人简介：

张勇，天津大学教授，2012年在清华大学获得博士学位，曾先后在奥地利维也纳大学，法国雷恩一大和美国纽约大学克朗所从事博士后研究工作。2015年7月获得奥地利自然科学基金委支持的薛定谔基金，2018年入选国家高层次人才计划。研究兴趣主要是偏微分方程的数值计算和分析工作，尤其是快速算法的设计和应用。迄今发表论文20余篇，主要发表在包括SIAM Journal on Scientific Computing, Mathematics of Computation, Journal of Computational Physics, Computer Physics Communication等计算数学权威杂志。