Please use this identifier to cite or link to this item: https://doi.org/10.1137/070681624
Title: A mass and magnetization conservative and energy-diminishing numerical method for computing ground state of spin-1 Bose-Einstein condensates
Authors: Bao, W. 
Wang, H.
Keywords: Continuous normalized gradient flow
Coupled Gross-Pitaevskii equations
Energy-diminishing
Ground state
Mass and magnetization conservative
Spin-1 Bose-Einstein condensate
Issue Date: 2007
Source: 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
Abstract: 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.
Source Title: SIAM Journal on Numerical Analysis
URI: http://scholarbank.nus.edu.sg/handle/10635/102673
ISSN: 00361429
DOI: 10.1137/070681624
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