A kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion

Understand

We develop a set of kinetic equations for hydrodynamic fluctuations which are equivalent to nonlinear hydrodynamics with noise.

• The hydro-kinetic equations can be coupled to existing second order hydrodynamic codes to incorporate the physics of these fluctuations.
• We first show that the kinetic response precisely reproduces the renormalization of the shear viscosity and the fractional power ($\propto \omega^{3/2}$) which characterizes equilibrium correlators of energy and momentum for a static fluid.
• Then we use the hydro-kinetic equations to analyze thermal fluctuations for a Bjorken expansion, evaluating the contribution of thermal noise from the earliest moments and at late times.