科研之友
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摘要
We describe a novel two-parameter continuation method combined with a spectral-collocation method (SCM) for computing the ground state and excited-state solutions of spin-1 Bose-Einstein condensates (EEC), where the second kind Chebyshev polynomials are used as the basis functions for the trial function space. To compute the ground state solution of spin-1 EEC, we implement the single parameter continuation algorithm with the chemical potential mu as the continuation parameter, and trace the first solution branch of the Gross-Pitaevskii equations (GPEs). When the curve-tracing is close enough to the target point, where the normalization condition of the wave function is going to be satisfied, we add the magnetic potential lambda as the second continuation parameter with the magnetization M as the additional constraint condition. Then we implement the two-parameter continuation algorithm until the target point is reached, and the ground state solution of the GPEs is obtained. The excited state solutions of the GPEs can be treated in a similar way. Some numerical experiments on Na-23 and Rb-87 are reported. The numerical results on the spin-1 EEC are the same as those reported in [10]. Further numerical experiments on excited-state solutions of spin-1 EEC suffice to show the robustness and efficiency of the proposed two-parameter continuation algorithm.
- 出版日期2014-1-1
