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Home > Physical Review C (APS) > 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 $O({\left(\tau T\right)}^{-3/2})$ correction to the $\text{U}\left(1\right)$ current and compare with the first-order gradient term.

**Published in: ****Physical Review C 99 (2019)**
**Published by: **APS

**DOI: **10.1103/PhysRevC.99.054902

**arXiv: **1812.05279

**License: **CC-BY-4.0