磁振子玻色-爱因斯坦凝聚的Ginzburg-Landau模型
The Ginzburg-Landau model of Bose-Einstein condensation of magnons
摘要：
本文介绍了一维磁振子玻色-爱因斯坦凝聚体的唯象方程组。为右和左行波的振幅编写的非线性耦合方程结合了Gross-Pitaevskii模型和复Ginzburg-Landau模型的基本特征。它们包括局域源项，以代表微波磁振子泵浦场。用$δ$ -函数表示源，我们得到了磁振子凝聚对称局域态的解析解。我们还预测了两个分量的振幅不等的非对称状态的存在。数值模拟表明，所有解析解是稳定的。随着$δ$函数项被更广泛的来源所取代，模拟揭示了从单峰稳态对称态到多峰稳态对称态的转变，这是由扩展非线性波模式的调制不稳定性产生的。在模拟中，对称的初始条件总是收敛到对称的平稳模式。另一方面，非对称输入可能会产生非平稳的非对称局部解，其形式为行波或驻波。与实验结果的比较表明，唯象方程为描述磁振子凝聚的时空动力学提供了一个相当好的模型。
英文摘要：
We introduce a system of phenomenological equations for Bose-Einstein condensates of magnons in the one-dimensional setting. The nonlinearly coupled equations, written for amplitudes of the right-and left-traveling waves, combine basic features of the Gross-Pitaevskii and complex Ginzburg-Landau models. They include localized source terms, to represent the microwave magnon-pumping field. With the source represented by the $δ$-functions, we find analytical solutions for symmetric localized states of the magnon condensates. We also predict the existence of asymmetric states with unequal amplitudes of the two components. Numerical simulations demonstrate that all analytically found solutions are stable. With the $δ$-function terms replaced by broader sources, the simulations reveal a transition from the single-peak stationary symmetric states to multi-peak ones, generated by the modulational instability of extended nonlinear-wave patterns. In the simulations, symmetric initial conditions always converge to symmetric stationary patterns. On the other hand, asymmetric inputs may generate nonstationary asymmetric localized solutions, in the form of traveling or standing waves. Comparison with experimental results demonstrates that the phenomenological equations provide for a reasonably good model for the description of the spatiotemporal dynamics of magnon condensates.
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