Relativistic Hydrodynamic Fluctuations

Abstract

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). 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. We find that the equations for confluent Wigner functions not only resemble kinetic equations, but that the kinetic equation for phonons propagating on an arbitrary background nontrivially matches the equations for Wigner functions, 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.

29 pages, 3 figures; typos corrected and some notations optimized

References in corpus (5)

• The stickiness of sound: An absolute lower limit on viscosity and the breakdown of second order relativistic hydrodynamics
• A kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion
• Thermal Conductivity and Chiral Critical Point in Heavy Ion Collisions
• Thermally Fluctuating Second-Order Viscous Hydrodynamics and Heavy-Ion Collisions
• Stochastic hydrodynamics and long time tails of an expanding conformal charged fluid

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