A G-FDTD scheme for solving multi-dimensional open dissipative Gross-Pitaevskii equations
A G-FDTD scheme for solving multi-dimensional open dissipative Gross-Pitaevskii equations
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DOI：
10.1016/j.jcp.2014.11.021
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发表时间：
2015-02
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影响因子：
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通讯作者：
F. Moxley;T. Byrnes;B. Ma;Yun Yan;W. Dai
中科院分区：
文献类型：
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作者：
F. Moxley;T. Byrnes;B. Ma;Yun Yan;W. Dai
在非平衡凝聚态中，暗孤子的传播、碰撞和涡旋形成的行为是值得研究的。这可以通过在多个维度上求解开放耗散Gross-Pitaevskii方程（dgpe）来实现，dgpe是标准Gross-Pitaevskii方程的推广，其中包括冷凝物增益和损失的影响。在本文中，我们提出了一种广义时域有限差分（G-FDTD）格式，它是明确的，稳定的，并且可以用简单的计算得到精确的解。通过求解非平衡凝结水的稳态问题对该方案进行了验证。此外，该方法的稳定性条件比常用的伪谱方法具有更宽松的时间步长限制。然后利用G-FDTD格式模拟了暗孤子的传播、碰撞和涡-反涡对的形成。
Behaviors of dark soliton propagation, collision, and vortex formation in the context of a non-equilibrium condensate are interesting to study. This can be achieved by solving open dissipative Gross–Pitaevskii equations (dGPEs) in multiple dimensions, which are a generalization of the standard Gross–Pitaevskii equation that includes effects of the condensate gain and loss. In this article, we present a generalized finite-difference time-domain (G-FDTD) scheme, which is explicit, stable, and permits an accurate solution with simple computation, for solving the multi-dimensional dGPE. The scheme is tested by solving a steady state problem in the non-equilibrium condensate. Moreover, it is shown that the stability condition for the scheme offers a more relaxed time step restriction than the popular pseudo-spectral method. The G-FDTD scheme is then employed to simulate the dark soliton propagation, collision, and the formation of vortex–antivortex pairs.