Normalized Gradient Flow with Lagrange Multiplier for Computing Ground States of Bose--Einstein Condensates

2021 ◽  
Vol 43 (1) ◽  
pp. B219-B242 ◽  
Author(s):  
Wei Liu ◽  
Yongyong Cai
Keyword(s):  
Lagrange Multiplier ◽  
Ground States ◽  
Gradient Flow ◽  
Normalized Gradient ◽  
Bose Einstein

Ground States of Two-component Bose-Einstein Condensates with an Internal Atomic Josephson Junction

2011 ◽  
Vol 1 (1) ◽  
pp. 49-81 ◽  
Author(s):  
Weizhu Bao ◽  
Yongyong Cai
Keyword(s):  
Numerical Methods ◽  
Josephson Junction ◽  
Ground States ◽  
Gradient Flow ◽  
Limiting Behavior ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Backward Euler ◽  
Two Component ◽  
Bose Einstein

AbstractIn this paper, we prove existence and uniqueness results for the ground states of the coupled Gross-Pitaevskii equations for describing two-component Bose-Einstein condensates with an internal atomic Josephson junction, and obtain the limiting behavior of the ground states with large parameters. Efficient and accurate numerical methods based on continuous normalized gradient flow and gradient flow with discrete normalization are presented, for computing the ground states numerically. A modified backward Euler finite difference scheme is proposed to discretize the gradient flows. Numerical results are reported, to demonstrate the efficiency and accuracy of the numerical methods and show the rich phenomena of the ground sates in the problem.

scholarly journals Ground states of Bose–Einstein condensates with higher order interaction

2019 ◽  
Vol 386-387 ◽  
pp. 38-48 ◽  
Author(s):  
Weizhu Bao ◽  
Yongyong Cai ◽  
Xinran Ruan
Keyword(s):  
Ground States ◽  
Higher Order ◽  
Order Interaction ◽  
Bose Einstein

scholarly journals Accurate and Efficient Numerical Methods for Computing Ground States and Dynamics of Dipolar Bose-Einstein Condensates via the Nonuniform FFT

2016 ◽  
Vol 19 (5) ◽  
pp. 1141-1166 ◽  
Author(s):  
Weizhu Bao ◽  
Qinglin Tang ◽  
Yong Zhang
Keyword(s):  
Numerical Methods ◽  
Ground State ◽  
High Efficiency ◽  
Three Dimensional ◽  
Ground States ◽  
Dipole Interaction ◽  
Polar Coordinates ◽  
Pitaevskii Equation ◽  
Nonuniform Fft ◽  
Bose Einstein

AbstractWe propose efficient and accurate numerical methods for computing the ground state and dynamics of the dipolar Bose-Einstein condensates utilising a newly developed dipole-dipole interaction (DDI) solver that is implemented with the non-uniform fast Fourier transform (NUFFT) algorithm. We begin with the three-dimensional (3D) Gross-Pitaevskii equation (GPE) with a DDI term and present the corresponding two-dimensional (2D) model under a strongly anisotropic confining potential. Different from existing methods, the NUFFT based DDI solver removes the singularity by adopting the spherical/polar coordinates in the Fourier space in 3D/2D, respectively, thus it can achieve spectral accuracy in space and simultaneously maintain high efficiency by making full use of FFT and NUFFT whenever it is necessary and/or needed. Then, we incorporate this solver into existing successful methods for computing the ground state and dynamics of GPE with a DDI for dipolar BEC. Extensive numerical comparisons with existing methods are carried out for computing the DDI, ground states and dynamics of the dipolar BEC. Numerical results show that our new methods outperform existing methods in terms of both accuracy and efficiency.

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