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報(bào)告題目：An efficient compact splitting Fourier spectral method for computing the dynamics of rotating spin-orbit coupled spin-1 Bose-Einstein condensates

主講人：張勇教授（天津大學(xué)）

時(shí)間：2025年3月5日（周三）15:00 p.m.

地點(diǎn)：北院卓遠(yuǎn)樓305會(huì)議室

主辦單位：統(tǒng)計(jì)與數(shù)學(xué)學(xué)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.

主講人簡(jiǎn)介：

張勇，天津大學(xué)教授，2012年在清華大學(xué)獲得博士學(xué)位，曾先后在奧地利維也納大學(xué)，法國(guó)雷恩一大和美國(guó)紐約大學(xué)克朗所從事博士后研究工作。2015年7月獲得奧地利自然科學(xué)基金委支持的薛定諤基金，2018年入選國(guó)家高層次人才計(jì)劃。研究興趣主要是偏微分方程的數(shù)值計(jì)算和分析工作，尤其是快速算法的設(shè)計(jì)和應(yīng)用。迄今發(fā)表論文20余篇，主要發(fā)表在包括SIAM Journal on Scientific Computing, Mathematics of Computation, Journal of Computational Physics, Computer Physics Communication等計(jì)算數(shù)學(xué)權(quán)威雜志。