自旋磁流体动力学中的各向异性线性波与动量展开的失效
Anisotropic linear waves and breakdown of the momentum expansion in spin magnetohydrodynamics
AI总结：
本文构建自旋磁流体动力学框架，通过线性模式分析揭示小动量展开在临界角失效，并提出替代级数解，同时探讨弛豫动力学对一阶解的影响。
摘要：
我们在流体动力学框架中纳入磁通量和总角动量守恒定律，从而构建了自旋磁流体动力学（MHD）。为了明确局部角动量守恒，我们选择了完全反对称的自旋流。熵流分析允许存在十个耗散性一阶输运系数，包括各向异性自旋弛豫率、涡度（剪切）与对称应力（反对称力矩）之间的转换率，以及各向异性粘度和电阻率。通过采用线性模式分析，我们求解一阶自旋MHD方程，以确定保留了完整各向异性信息的色散关系。我们的解析解表明，当动量与磁场之间的夹角接近直角时，高阶项的发散会破坏小动量展开。这也揭示了另一个展开参数的存在，鉴于此，我们提供了在临界角之外的另一种级数表达式中的解。我们确认，与数值结果相比，这两个级数展开在适当的角度范围内表现良好。基于我们关于一阶理论中小动量展开失效的发现，我们进一步讨论了在以色列-斯图尔特框架中纳入耗散模式的弛豫动力学时，这些一阶解如何被修正。我们发现，由于一阶解中存在临界行为，即使在引入弛豫动力学之后，仍然存在一个扩散窗口。
英文摘要：
We formulate spin magnetohydrodynamics (MHD) by including the magnetic-flux and total angular momentum conservation laws in the hydrodynamic framework. To specify the local angular momentum conservation, we choose the totally antisymmetric spin current. The entropy-current analysis allows for ten dissipative first-order transport coefficients including anisotropic spin relaxation rates and the conversion rate between a vorticity (shear) to a symmetric stress (antisymmetric torque), as well as anisotropic viscosities and resistivities. By employing the linear-mode analysis, we solve the first-order spin MHD equations to determine the dispersion relations with the complete information of anisotropy retained. Our analytic solutions indicate that the small-momentum expansion is spoiled by blow up of the higher-order terms when the angle between the momentum and the magnetic field approaches the right angle. This also reveals the existence of another expansion parameter, and, in light of it, we provide solutions in an alternative series expression beyond the critical angle. We confirm that these two series expansions work well in the appropriate angle ranges as compared with numerical results. Building on our findings regarding the breakdown of the small-momentum expansion in first-order theory, we proceed to discussing how these first-order solutions are modified when we include the relaxation dynamics for dissipative modes with the Israel-Stewart framework. We find that, due to the presence of the critical behavior in the first-order solutions, there remains a diffusive window even after the relaxation dynamics is introduced.
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