各向异性背景下流体中的流体动力学涨落和长时间尾
Hydrodynamic fluctuations and long-time tails in a fluid on an anisotropic background
摘要：
许多身体系统附近的热平衡由经典流体力学耗散传输现象提供的有效的低能量后期时间的描述收到重要的修正，一旦随机波动的影响被考虑在内。一个这样的物理效应是守恒电流的关联函数中长时间幂律尾的出现。在流体动力学区域$\vec{k} \rightarrow 0$中，这相当于关联函数对频率$ω$的非解析依赖性。本文考虑了在强背景磁场中具有守恒整体$U(1)$电荷的相对论流体，计算了应力张量的关联函数中的长时尾.磁场的存在使系统呈现各向异性。在没有磁场的情况下，在流体动力学导数展开的一阶中出现三个非平衡输运参数，所有这些参数都是耗散的。在背景磁场的存在下，有十个独立的一级非平衡输运参数，其中三个是非耗散的，其余的是耗散的。我们提供了最一般的线性化方程关于一个给定的状态的热平衡，涉及各种传输参数的存在下，一个磁场，并使用它们来计算长时间的尾巴的流体。
英文摘要：
The effective low-energy late-time description of many body systems near thermal equilibrium provided by classical hydrodynamics in terms of dissipative transport phenomena receives important corrections once the effects of stochastic fluctuations are taken into account. One such physical effect is the occurrence of long-time power law tails in correlation functions of conserved currents. In the hydrodynamic regime $\vec{k} \rightarrow 0$ this amounts to non-analytic dependence of the correlation functions on the frequency $ω$. In this article, we consider a relativistic fluid with a conserved global $U(1)$ charge in the presence of a strong background magnetic field, and compute the long-time tails in correlation functions of the stress tensor. The presence of the magnetic field renders the system anisotropic. In the absence of the magnetic field, there are three out-of-equilibrium transport parameters that arise at the first order in the hydrodynamic derivative expansion, all of which are dissipative. In the presence of a background magnetic field, there are ten independent out-of-equilibrium transport parameters at the first order, three of which are non-dissipative and the rest are dissipative. We provide the most general linearized equations about a given state of thermal equilibrium involving the various transport parameters in the presence of a magnetic field, and use them to compute the long-time tails for the fluid.
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