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

报告题目:A Spectrally Accurate Numerical Method For Computing The Bogoliubov-De Gennes Excitations Of Dipolar Bose-Einstein Condensates

报 告 人: 张勇 教授

报告时间: 6月17日16:00-18:00

报告地点: 明理楼C302B

报告人简介:

张勇，2007年本科毕业于天津大学数学系，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, SIAM journal on Applied Mathematics, Multiscale Modeling and Simulation, Mathematics of Computation, Journal of Computational Physics, Computer Physics Communication等计算数学顶尖杂志。

报告内容摘要:

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.

主办单位:理学院､人工智能研究院､非线性动力系统研究所､

数理力学研究中心 ､科学技术发展研究院