報告題目:A Spectrally Accurate Numerical Method For Computing The Bogoliubov-De Gennes Excitations Of Dipolar Bose-Einstein Condensates

報 告 人: 張勇 教授

報告時間: 6月17日16:00-18:00

報告地點: 明理樓C302B

報告人簡介:

張勇，2007年本科畢業于天津大學數學系，2012年在清華大學獲得博士學位，曾先后在奧地利維也納大學，法國雷恩一大和美國紐約大學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基金委支持的薛定諤基金，2018年入選國家高層次人才計劃。研究興趣主要是偏微分方程的數值計算和分析工作，尤其是快速算法的設計和應用。迄今發表論文20余篇，主要發表在包括SIAM Journal on Scientific Computing, SIAM journal on Applied Mathematics, Multiscale Modeling and Simulation, Mathematics of Computation, Journal of Computational Physics, Computer Physics Communication等計算數學頂尖雜志。

報告內容摘要:

In this talk, we shall report an efficient and robust numerical method to study the ele- mentary excitation of dipolar Bose-Einstein condensates (BEC), which is governed by the Bogoliubov- de Gennes equations (BdGEs) with nonlocal dipole-dipole interaction, around the mean field ground state. Analytical properties of the BdGEs are investigated, which could serve as benchmarks for the numerical methods. To evaluate the nonlocal interactions accurately and efficiently, we propose a new Simple Fourier Spectral Convolution method (SFSC). Then, integrating SFSC with the stan- dard Fourier spectral method for spatial discretization and Implicitly Restarted Arnoldi Methods (IRAM) for the eigenvalue problem, we derive an efficient and spectrally accurate method, named as SFSC-IRAM method, for the BdGEs. Ample numerical tests are provided to illustrate the accuracy and efficiency. Finally, we apply the new method to study systematically the excitation spectrum and Bogoliubov amplitudes around the ground state with different parameters in different spatial dimensions.

主辦單位:理學院?人工智能研究院?非線性動力系統研究所?

數理力學研究中心 ?科學技術發展研究院