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The numerical study for the ground and excited states of fractional Bose-Einstein condensates

机译:玻色-爱因斯坦分数凝聚态的基态和激发态的数值研究

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In this paper, we study the ground and first excited states of the fractional Bose-Einstein condensates (BEC) which is modeled by fractional Gross-Pitaevskii (GP) equation. We first introduce the normalized gradient flow method and prove its energy diminishing property. Then the weighted shifted Grunwald-Letnikov difference (WSGD) method is used to discretize the Gross-Pitaevskii equation. The corresponding normalization and energy diminishing property for the semi-discrete scheme are proved. For the time discretization, we use the implicit integration factor (IIF) method which decouples the diffusion and nonlinear terms separately. Finally the numerical methods are applied to compute the ground and first excited states of fractional BEC with harmonic oscillator, harmonic-plus-optical lattice and box potential. Our numerical results show that the ground and excited states in fractional GP equation differ from those of the standard (non-fractional) GP equation. (C) 2019 Elsevier Ltd. All rights reserved.
机译:在本文中,我们研究了分数Bose-Einstein凝聚物(BEC)的基态和第一激发态,这是通过分数Gross-Pitaevskii(GP)方程建模的。我们首先介绍归一化梯度流方法,并证明其能量递减特性。然后使用加权移位的格伦瓦尔德-列特尼科夫差分(WSGD)方法离散化Gross-Pitaevskii方程。证明了半离散方案的相应归一化和能量递减性质。对于时间离散化,我们使用隐式积分因子(IIF)方法,该方法分别将扩散项和非线性项解耦。最后,采用数值方法,利用谐波振荡器,谐波加光学晶格和盒势计算分数BEC的基态和第一激发态。我们的数值结果表明,分数GP方程的基态和激发态与标准(非分数)GP方程的基态和激发态不同。 (C)2019 Elsevier Ltd.保留所有权利。

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