报告题目：A Spectrally Accurate Numerical Method for Computing the Bogoliubov De Gennes Excitations of Dipolar Bose-Einstein Condensates

报告时间：2022-12-09  10:00 - 11:30

报告人：张勇 教授  天津大学

腾讯会议ID：345 773 4983

报告链接：https://meeting.tencent.com/p/3457734983

Abstract：In this talk, we propose 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.