Volume 11, Issue 4
Efficient and Accurate Computation of the Bogoliubov-De Gennes Excitations for the Quasi-2D Dipolar Bose-Einstein Condensates

Yuqing Zhang, Xin Liu & Manting Xie

East Asian J. Appl. Math., 11 (2021), pp. 686-707.

Published online: 2021-08

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  • Abstract

An efficient spectrally accurate multigrid method for the Bogoliubov-de Gennes excitations of the quasi-2D dipolar Bose-Einstein condensates is proposed. The wave functions/eigenmodes are spatially discretised by the Fourier spectral method. The convolution-type nonlocal potentials are computed in $\mathscr{O}(N log(N))$ operations with a spectral accuracy by the kernel truncation method. In addition, the influence of the model parameters on the eigenvalue distribution is studied and for various dipole orientations and an anisotropic external potential the phase diagrams of the eigenmodes are presented. Examples verify the spectral accuracy of the method.

  • Keywords

Bogoliubov-de Gennes excitation, Bose-Einstein condensate, convolution-type nonlocal interaction, spectral method, kernel truncation method.

  • AMS Subject Headings

35Q40, 35Q41, 65M70, 65T40, 65T50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-11-686, author = {Zhang , Yuqing and Liu , Xin and Xie , Manting}, title = {Efficient and Accurate Computation of the Bogoliubov-De Gennes Excitations for the Quasi-2D Dipolar Bose-Einstein Condensates}, journal = {East Asian Journal on Applied Mathematics}, year = {2021}, volume = {11}, number = {4}, pages = {686--707}, abstract = {

An efficient spectrally accurate multigrid method for the Bogoliubov-de Gennes excitations of the quasi-2D dipolar Bose-Einstein condensates is proposed. The wave functions/eigenmodes are spatially discretised by the Fourier spectral method. The convolution-type nonlocal potentials are computed in $\mathscr{O}(N log(N))$ operations with a spectral accuracy by the kernel truncation method. In addition, the influence of the model parameters on the eigenvalue distribution is studied and for various dipole orientations and an anisotropic external potential the phase diagrams of the eigenmodes are presented. Examples verify the spectral accuracy of the method.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.301120.250221}, url = {http://global-sci.org/intro/article_detail/eajam/19368.html} }
TY - JOUR T1 - Efficient and Accurate Computation of the Bogoliubov-De Gennes Excitations for the Quasi-2D Dipolar Bose-Einstein Condensates AU - Zhang , Yuqing AU - Liu , Xin AU - Xie , Manting JO - East Asian Journal on Applied Mathematics VL - 4 SP - 686 EP - 707 PY - 2021 DA - 2021/08 SN - 11 DO - http://doi.org/10.4208/eajam.301120.250221 UR - https://global-sci.org/intro/article_detail/eajam/19368.html KW - Bogoliubov-de Gennes excitation, Bose-Einstein condensate, convolution-type nonlocal interaction, spectral method, kernel truncation method. AB -

An efficient spectrally accurate multigrid method for the Bogoliubov-de Gennes excitations of the quasi-2D dipolar Bose-Einstein condensates is proposed. The wave functions/eigenmodes are spatially discretised by the Fourier spectral method. The convolution-type nonlocal potentials are computed in $\mathscr{O}(N log(N))$ operations with a spectral accuracy by the kernel truncation method. In addition, the influence of the model parameters on the eigenvalue distribution is studied and for various dipole orientations and an anisotropic external potential the phase diagrams of the eigenmodes are presented. Examples verify the spectral accuracy of the method.

Yuqing Zhang, Xin Liu & Manting Xie. (2021). Efficient and Accurate Computation of the Bogoliubov-De Gennes Excitations for the Quasi-2D Dipolar Bose-Einstein Condensates. East Asian Journal on Applied Mathematics. 11 (4). 686-707. doi:10.4208/eajam.301120.250221
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