构建高阶流体力学：第三阶
Constructing higher-order hydrodynamics: The third order
摘要：
流体动力学可以用描述近平衡流体流动的基本场的守恒流的梯度展开来表示。在相对论情况下，从应力-能量张量守恒到一阶导数，纳维-斯托克斯方程都成立。在本文中，我们超越了目前所理解的二阶流体动力学，并讨论了系统化获得的流体动力学扩展到任意高阶。作为我们提出的算法的一个例子，我们完全分类的梯度展开在第三阶的中性流体在四维，从而找到最普遍的下一个领先的阶修正相对论性纳维-斯托克斯方程在弯曲的时空。在这样做时，我们列出了共形情况下的$20$新的输运系数候选者和非共形情况下的$68$。由于我们不考虑任何可能由局部熵流分析产生的约束，因此这是中性三阶输运系数的最大可能集合。为了研究这些新的输运系数的物理意义，我们得到了三阶修正的线性色散关系，描述了相对论流体中的扩散和声波的传播。我们还计算了三阶应力-能量张量的标量（自旋- $2$）两点关联函数的修正。此外，作为一个非线性流体动力学流的例子，我们计算的三阶修正的能量密度的助推不变Bjorken流。最后，我们将我们的场论结果应用于$\mathcal{N}=4$超对称Yang-Mills流体，在无限t Hooft耦合和无限种颜色下，得到了共形输运系数的五种新的线性组合.
英文摘要：
Hydrodynamics can be formulated as the gradient expansion of conserved currents in terms of the fundamental fields describing the near-equilibrium fluid flow. In the relativistic case, the Navier-Stokes equations follow from the conservation of the stress-energy tensor to first order in derivatives. In this paper, we go beyond the presently understood second-order hydrodynamics and discuss the systematisation of obtaining the hydrodynamic expansion to an arbitrarily high order. As an example of the algorithm that we present, we fully classify the gradient expansion at third order for neutral fluids in four dimensions, thus finding the most general next-to-leading-order corrections to the relativistic Navier-Stokes equations in curved space-time. In doing so, we list $20$ new transport coefficient candidates in the conformal and $68$ in the non-conformal case. As we do not consider any constraints that could potentially arise from the local entropy current analysis, this is the maximal possible set of neutral third-order transport coefficients. To investigate the physical implications of these new transport coefficients, we obtain the third-order corrections to the linear dispersion relations that describe the propagation of diffusion and sound waves in relativistic fluids. We also compute the corrections to the scalar (spin-$2$) two-point correlation function of the third-order stress-energy tensor. Furthermore, as an example of a non-linear hydrodynamic flow, we calculate the third-order corrections to the energy density of a boost-invariant Bjorken flow. Finally, we apply our field theoretic results to the $\mathcal{N}=4$ supersymmetric Yang-Mills fluid at infinite 't Hooft coupling and infinite number of colours to find the values of five new linear combinations of the conformal transport coefficients.
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