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|A mass and magnetization conservative and energy-diminishing numerical method for computing ground state of spin-1 Bose-Einstein condensates
|Bao, W., Wang, H. (2007). A mass and magnetization conservative and energy-diminishing numerical method for computing ground state of spin-1 Bose-Einstein condensates. SIAM Journal on Numerical Analysis 45 (5) : 2177-2200. ScholarBank@NUS Repository. https://doi.org/10.1137/070681624
|In this paper, a mass (or normalization) and magnetization conservative and energydiminishing numerical method is presented for computing the ground state of spin-1 (or F = 1 spinor) Bose-Einstein condensates (BECs). We begin with the coupled Gross-Pitaevskii equations, and the ground state is defined as the minimizer of the energy functional under two constraints on the mass and magnetization. By constructing a continuous normalized gradient flow (CNGF) which is mass and magnetization conservative and energy-diminishing, the ground state can be computed as the steady state solution of the CNGF. The CNGF is then discretized by the Crank-Nicolson finite difference method with a proper way to deal with the nonlinear terms, and we prove that the discretization is mass and magnetization conservative and energy-diminishing in the discretized level. Numerical results of the ground state and their energy of spin-1 BECs are reported to demonstrate the efficiency of the numerical method. © 2007 Society for Industrial and Applied Mathematics.
|Continuous normalized gradient flow
|Coupled Gross-Pitaevskii equations
|Mass and magnetization conservative
|Spin-1 Bose-Einstein condensate
|SIAM Journal on Numerical Analysis
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