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.

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流体动力学模式的收敛：来自动力学理论和全息术的见解

我们研究了在弛豫时间近似中设置动力学理论中流体动力色散关系收敛半径的机制。这在全息方面引入了一个全新的定性特征：由延迟格林函数中的分支切割表示的非流体动力扇区。与现有的全息示例相比，我们发现剪切通道中的会聚半径是由流体动力极与分支点的碰撞设置的。在声道中，它是通过格林函数的非主片上的极-极碰撞来设置的。更一般地说，我们检查了流体动力学中隐函数定理的结果，并给出了确定一组点的方法，这些点必须包括色散关系的所有复杂奇点。