A two-parameter continuation method for computing numerical solutions of spin-1 Bose–Einstein condensates

Journal Article · Wed Jan 01 04:00:00 EST 2014 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2013.08.056· OSTI ID:22230835

Wang, Y. -S.

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 (BEC), 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 BEC, we implement the single parameter continuation algorithm with the chemical potential μ 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 λ 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 {sup 23}Na and {sup 87}Rb are reported. The numerical results on the spin-1 BEC are the same as those reported in [10]. Further numerical experiments on excited-state solutions of spin-1 BEC suffice to show the robustness and efficiency of the proposed two-parameter continuation algorithm.

• OSTI ID: 22230835
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 256; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
97 MATHEMATICS AND COMPUTING
ALGORITHMS
BOSE-EINSTEIN CONDENSATION
EXCITED STATES
GROUND STATES
NUMERICAL SOLUTION
POLYNOMIALS
RUBIDIUM 87
SODIUM 23
SPIN
WAVE FUNCTIONS