论文标题
Lifshitz中的杆子滑水和流体动力分析，广告$ _2 $和RINDLER GEOMERTIE
Pole-skipping and hydrodynamic analysis in Lifshitz, AdS$_2$ and Rindler geometries
论文作者
论文摘要
“杆子”现象反映出，在动量空间$（ω，k）$中，智障绿色的功能并非唯一。我们探索了不同几何形状的杆子的普遍性。在全息图中，近距离运动方程的近地平线分析是一种得出杆子的简单方法，我们在Lifshitz中使用此方法，ADS $ _2 $和RINDLER几何形状。我们还研究了复杂的流体动力学分析，并发现分散关系从无量纲变量来看$ \fracΩ{2πt} $和$ \ frac {\ vert k \ vert} {2πt} {2πt} $通过极点 - 杆 - - - 兼基化点$（ k_n \ vert} {2πt} $）在lifshitz背景中的小$ω$和$ k $。我们验证了杆子的位置不取决于ADS $ _2 \ times \ Mathbb {r}^{d-1} $ geetry中的边界理论中的标准量化或替代量化。在Rindler的几何形状中，我们找不到相应的绿色功能来计算杆子脱落点，因为很难强加边界条件。但是，我们可以在地平线附近获得“特殊点”，其中大块运动有两个传入的解决方案。这些“特殊点”从全息图的角度来看，对应于绿色功能的物理意义。
The "pole-skipping" phenomenon reflects that the retarded Green's function is not unique at a pole-skipping point in momentum space $(ω,k)$. We explore the universality of the pole-skipping in different geometries. In holography, near horizon analysis of the bulk equation of motion is a simpler way to derive a pole-skipping point and we use this method in Lifshitz, AdS$_2$ and Rindler geometries. We also study the complex hydrodynamic analyses and find that the dispersion relations in terms of dimensionless variables $\fracω{2πT}$ and $\frac{\vert k\vert}{2πT}$ pass through pole-skipping points $(\frac{ω_n}{2πT}, \frac{\vert k_n\vert}{2πT}$) at small $ω$ and $k$ in Lifshitz background. We verify that the position of the pole-skipping points does not depend on the standard quantization or alternative quantization in the boundary theory in AdS$_2\times\mathbb{R}^{d-1}$ geometry. In Rindler geometry, we cannot find the corresponding Green's function to calculate pole-skipping points because it is difficult to impose the boundary condition. However we can obtain "special points" near horizon where bulk equations of motion have two incoming solutions. These "special points" correspond to nonunique of the Green's function in physical meaning from the perspective of holography.
