The Efficient Numerical Methods To Simulate Rotating Spin-1 Bose-Einstein Condensates

In this paper,the normalised gradient flow method and the preconditioned conjugate gradient?PCG?method are designed to calculate the ground state solutions of rotating spin-1 BECs.Based on this,we test the feasibility of the two numerical methods,compare their efficiency and accuracy of the two algorithms,then simulate the ground state solutions of the model problem with different parameters.As a result,new physical phenomena as well as the hidden relationships between the parameters and the physical phenomena are obtained.First of all,the mathematical model of the rotating spin-1 BECs,the GFDN method and PCG method for simulating the ground state solutions and the Fourier pseudo-spectral method used in spatial discretization are reviewed.Then,the GFDN and PCG are used to compute ground state solutions the model problem under different parameters.The numerical results show that the ground state solutions obtained by the two methods are the same,but the PCG is more efficient than the GFDN in calculating the ground state solutions of the model problem.Finally,the algorithms designed in this paper are used to calculate the ground state solutions of the model problems under different parameters in order to find new physical phenomena.The conclusions are obtained as:?1?when M =0,the component ???₁ and ???_-1 of the ground state solutions are equal to each other;?2?when ?_s>0,the component ???₀ of the ground state solutions is 0;?3?under the condition that the magnetization M is fixed,the larger the angular velocity ? is,the more vortices the ground state solutions possesses.