论文标题
在有限化学势的全息系统中，复杂的准模式和杆子铲
Complexified quasinormal modes and the pole-skipping in a holographic system at finite chemical potential
论文作者
论文摘要
我们开发了一种研究量规不变变量的耦合动力学，该变量是由ADS $ _5 $ reissner-Nordström-black Brane在ADS $ _5 $ _5 $ _5 $ _5 $的背景下构建的。使用这种方法，我们以$μ/t $非扰动的方式计算与自旋0、1和2波动相关的准模式的数值光谱。我们还通过分析计算在较小的化学势极限下计算流体动力激发的光谱。然后，通过研究每个自旋通道中复杂动量的光谱曲线，我们从数值上找到水动力和非流动力杆碰撞的点。我们讨论了这种碰撞点与流体动力衍生物扩张的收敛半径之间的关系。特别是在自旋0通道中，我们发现在$ 1.1 \ 1.1 \Lessimμ/t \ Lessim 2 $的范围内，流体动力学模式的收敛半径是由声极与水力动力学扩散极碰撞点的复合动量的绝对值来设定的。它表明，在有限化学势的全息系统中，上述范围中流体动力衍生物扩张的收敛性完全由流体动力信息控制。作为最后的结果，我们明确表明，可以从能量密度响应函数的杆子鞋底提取有关系统中有关量子混乱的相关信息。我们发现$μ/t $的阈值值低，低于可以在导数扩展中扰动地计算杆子的点。
We develop a method to study coupled dynamics of gauge-invariant variables, constructed out of metric and gauge field fluctuations on the background of a AdS$_5$ Reissner-Nordström black brane. Using this method, we compute the numerical spectrum of quasinormal modes associated with fluctuations of spin 0, 1 and 2, non-perturbatively in $μ/T$. We also analytically compute the spectrum of hydrodynamic excitations in the small chemical potential limit. Then, by studying the spectral curve at complex momenta in every spin channel, we numerically find points at which hydrodynamic and non-hydrodynamic poles collide. We discuss the relation between such collision points and the convergence radius of the hydrodynamic derivative expansion. Specifically in the spin 0 channel, we find that within the range $1.1\lesssim μ/T\lesssim 2$, the radius of convergence of the hydrodynamic sound mode is set by the absolute value of the complex momentum corresponding to the point at which the sound pole collides with the hydrodynamic diffusion pole. It shows that in holographic systems at finite chemical potential, the convergence of the hydrodynamic derivative expansion in the mentioned range is fully controlled by hydrodynamic information. As the last result, we explicitly show that the relevant information about quantum chaos in our system can be extracted from the pole-skipping points of energy density response function. We find a threshold value for $μ/T$, lower than which the pole-skipping points can be computed perturbatively in a derivative expansion.
