论文标题
关于稳定的一阶相对论水动力学的相关功能
On the correlation functions in stable first-order relativistic hydrodynamics
论文作者
论文摘要
一般（流体动力）框架中的一阶相对论保形流体动力学的特征是剪切粘度系数和两个紫外线调节剂参数。在这些参数的一定范围内，平衡是稳定的，传播是因果关系。在这项工作中，我们研究了该理论波动的相关函数。我们首先计算线性响应方案中的流体动力相关功能。然后，我们使用线性响应结果来探索超出线性响应以外的响应函数的分析结构。开发了一种方法来计算众所周知的Landau方程的分支切割结构。我们将方法应用于剪切通道，并在不计算响应函数本身的情况下找到特定响应函数的分支切割。然后，我们通过分析求解Landau方程，并找到相同响应函数的阈值奇点。使用这些结果，我们在动量空间中实现了领先的奇异性，通过该空间，我们找到了相关函数的长期尾巴。结果证明，与有效野外理论中的循环计算完全一致。
First-order relativistic conformal hydrodynamics in a general (hydrodynamic) frame is characterized by a shear viscosity coefficient and two UV-regulator parameters. Within a certain range of these parameters, the equilibrium is stable and propagation is causal. In this work we study the correlation functions of fluctuations in this theory. We first compute hydrodynamic correlation functions in the linear response regime. Then we use the linear response results to explore the analytical structure of response functions beyond the linear response. A method is developed to numerically calculate the branch cut structure from the well-known Landau equations. We apply our method to the shear channel and find the branch cuts of a certain response function, without computing the response function itself. We then solve the Landau equations analytically and find the threshold singularities of the same response function. Using these results, we achieve the leading singularity in momentum space, by which, we find the long-time tail of the correlation function. The results turn out to be in complete agreement with the loop calculations in effective field theory.
