# Stochastic hydrodynamics and long time tails of an expanding conformal charged fluid

Martinez, M. (Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA) ; Schäfer, T. (Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA)

06 May 2019

Abstract: We investigate the impact of hydrodynamic fluctuations on correlation functions in a scale invariant fluid with a conserved $\text{U}\left(1\right)$ 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 nonanalytic contributions to the energy-momentum tensor as well as the $\text{U}\left(1\right)$ 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 hydrokinetic 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 $O\left({\left(\tau T\right)}^{-3/2}\right)$ correction to the $\text{U}\left(1\right)$ current and compare with the first-order gradient term.

Published in: Physical Review C 99 (2019)