论文标题
流体动力模式的收敛：动力学理论和全息图的见解
Convergence of hydrodynamic modes: insights from kinetic theory and holography
论文作者
论文摘要
我们研究了在松弛时间近似中动力学理论中流体动力分散关系收敛的半径。这引入了关于全息图的定性新功能：一个非流动力部门，该部门由延迟的绿色功能中的分支切开。与现有的全息示例相反，我们发现剪切通道中收敛的半径是通过与分支点的流体动力极的碰撞来设定的。在声音通道中，它是由绿色功能的非主要纸板上的杆极碰撞设置的。更普遍地，我们检查了隐式函数定理在流体动力学中的后果，并给出了处方以确定一组必然包含分散关系的所有复杂奇点的点。这可以用作有助于确定流体分散关系收敛半径的实用工具。
We study the mechanisms setting the radius of convergence of hydrodynamic dispersion relations in kinetic theory in the relaxation time approximation. This introduces a qualitatively new feature with respect to holography: a nonhydrodynamic sector represented by a branch cut in the retarded Green's function. In contrast with existing holographic examples, we find that the radius of convergence in the shear channel is set by a collision of the hydrodynamic pole with a branch point. In the sound channel it is set by a pole-pole collision on a non-principal sheet of the Green's function. More generally, we examine the consequences of the Implicit Function Theorem in hydrodynamics and give a prescription to determine a set of points that necessarily includes all complex singularities of the dispersion relation. This may be used as a practical tool to assist in determining the radius of convergence of hydrodynamic dispersion relations.
