Studying Properties Of Ground States Of Spin-2 Bose-Einstein Condensates And The Corresponding Efficient Numerical Methods

Since under the ferromagnetic,nematic and cyclic parameters,the ground states of Spin-2 Bose-Einstein Condensates possess important properties,i.e.,all the component wave functions of the Spin-2 BEC ground states are proportional,or only two component of wave functions are non-zero,the simplified Spin-2 BEC models are obtained in this paper.Thus,the traditional Spin-2BEC models with five equations are reduced to one component BEC models or two component BEC models.Based on this,the normalized gradient flow method with Lagrange multipliers(GFLM)and the preconditioned conjugate gradient(PCG)method are designed to simulate the ground states of simplified Spin-2 BEC models as well as the traditional Spin-2 BEC models.The numerical results show that the ground state solutions of the simplified Spin-2BEC models are the same as that of the corresponding traditional models.However,the cpu time and iterations cost by the simplified models is less than that of the traditional models,which illustrates the feasibility and high efficiency of using the simplified Spin-2 BEC models to compute the ground states.Meanwhile,when the PCG method and GFLM method are applied to simulate the ground states of the same Spin-2 BEC model,the former is more efficient than the latter.Moreover,by simulating the ground states of Spin-2BEC models under different parameters,some new properties of the ground states of Spin-2 BECs,such as the changing of the ground state energies and eigenvalues with different parameters,are numerically studied.In addition,some new physical phenomena are demonstrated.