Efficient and Accurate Computation of the Bogoliubov-De Gennes Excitations for the Quasi-2D Dipolar Bose-Einstein Condensates
Year: 2021
Author: Yuqing Zhang, Xin Liu, Manting Xie
East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.301120.250221
East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 4 : pp. 686–707
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Bogoliubov-de Gennes excitation Bose-Einstein condensate convolution-type nonlocal interaction spectral method kernel truncation method.