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 $\mathbf{k}\to 0$ 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.

一旦考虑了随机波动的影响，就经典的流体力学提供的关于耗散输运现象的，接近热平衡的许多人体系统的有效低能量后期描述得到了重要的修正。一种这样的物理效应是在守恒电流的相关函数中出现了长时间的幂定律尾部。在水力状态下$\mathbf{ķ}\to 0$这等于相关函数对频率ω的非解析依赖性。在本文中，我们考虑相对论流体，其具有守恒的整体$ü（\mathrm{1个}）$在存在强背景磁场的情况下进行充电，并计算应力张量的相关函数中的长时间拖尾。磁场的存在使系统各向异性。在没有磁场的情况下，在流体动力导数膨胀中一阶出现三个不平衡的输运参数，所有这些都是耗散的。在存在背景磁场的情况下，一阶有十个独立的失衡传输参数，其中三个是非耗散的，其余的是耗散的。我们提供了有关给定的热平衡状态的最通用线性化方程，该方程涉及在磁场存在下的各种传输参数，并使用它们来计算流体的长时间拖尾。