Stochastic hydrodynamics and long time tails of an expanding conformal charged fluid
Stochastic hydrodynamics and long time tails of an expanding conformal charged fluid
复制标题
膨胀保形带电流体的随机流体动力学和长时尾
作者：
M. Martinez;T. Schaefer
我们研究了具有守恒U（1）荷的标度不变流体中流体动力学涨落对关联函数的影响。在随机流体力学的框架内，推导了压力、动量和热能密度的两点函数的动力学方程。主要的非解析贡献的能量动量张量以及$U（1）$电流确定从这些动力学方程的解决方案。在一个静态均匀背景的情况下，我们表明，从流体动力学方程获得的长时间尾巴再现的单圈统计场理论的结果。我们使用这些结果来建立边界上的传输系数。我们推广的随机方程进行Bjorken扩展的背景流。我们计算领先的分数幂$mathcal{O}（ Au T）^{-3/2}）$校正，并与一阶梯度项进行比较。
We investigate the impact of hydrodynamic fluctuations on correlation functions in a scale invariant fluid with a conserved $U(1)$ charge. The kinetic equations for the two-point functions of pressure, momentum and heat energy densities are derived within the framework of stochastic hydrodynamics. The leading non-analytic contributions to the energy-momentum tensor as well as the $U(1)$ current are determined from the solutions to these kinetic equations. In the case of a static homogeneous background we show that the long time tails obtained from hydro-kinetic equations reproduce the one-loop results derived from statistical field theory. We use these results to establish bounds on transport coefficients. We generalize the stochastic equation to a background flow undergoing Bjorken expansion. We compute the leading fractional power $mathcal{O}(( au T)^{-3/2})$ correction to the $U(1)$ current and compare with the first order gradient term.