NT/RIKEN Seminar

We present a general systematic formalism for describing dynamics of fluctuations in an arbitrary relativistic hydrodynamic flow, including their feedback (known as long-time hydrodynamic tails) in a deterministic way. The fluctuations are described by two-point equal-time correlation functions. We introduce a definition of equal time in a situation where the local rest frame is determined by the local flow velocity, and a method of taking derivatives and Wigner transforms of such equal-time correlation functions, which we call confluent. The Wigner functions satisfy evolution equations that describes the relaxation of the out-of-equilibrium modes. We find that the equations for confluent Wigner functions nontrivially match with the kinetic equation for phonons propagating on an arbitrary background, including relativistic inertial and Coriolis forces due to acceleration and vorticity of the flow. We also describe the procedure of renormalization of short-distance singularities which eliminates cutoff dependence, allowing efficient numerical implementation of these equations.