Simulating Ground States Of Rotating Spin-2 Bose-einstein Condensates

The purpose of this paper is to design efficient and accurate numerical methods to simulate ground states of rotating Spin-2 Bose-Einstein Condensates(BEC).Combined with the two constraint conditions of total mass and total magnetization,three additional projection conditions or normalized conditions are introduced by exploring implicit relationship between the projection coefficients to overcome the difficulty that the inherent conservation conditions are not enough to determine all the projection coefficients.Therefore,a normalized gradient flow with Lagrange multipliers(GFLM)is successfully designed to simulate the ground states of rotating Spin-2 BECs.The full discretization scheme of the GFLM is presented.Actually,the backward Euler semi-implicit scheme is adopted in the time direction,and the discrete fast Fourier transformation method is adopted in the spatial direction.In order to further improve the efficiency of simulating ground states,a preconditioned conjugate gradient(PCG)method is proposed with three different preconditioned operators.Based on extensive numerical experiments,the ground states of rotating Spin-2 BECs with the ferromagnetic,nematic and cyclic parameters are computed.Then,the feasibility of the two numerical methods are tested,and their efficiency are compared.Moreover,some new physical phenomena about the ground state of rotating Spin-2 BECs are also studied.