Non-Gaussian fluctuations in relativistic hydrodynamics: Confluent equations for three-point correlations
Xin An, Gokce Basar, Mikhail Stephanov
TLDR
Derives deterministic equations for non-Gaussian fluctuations in relativistic stochastic hydrodynamics using a novel covariant formalism.
Key contributions
- Defines average local Landau frame and fluctuating hydrodynamic variables.
- Expresses nonlinear stochastic hydrodynamics in a unified multi-component matrix form.
- Introduces a relativistic SO(3)-covariant formalism for local spatial basis rotations.
- Derives evolution equations for three-point correlators including fluctuating velocity.
Why it matters
Understanding non-Gaussian fluctuations in relativistic fluids is crucial for accurate modeling in high-energy physics and astrophysics. This work provides a new framework to analyze complex correlations beyond Gaussian approximations.
Original Abstract
We derive deterministic equations for the evolution of non-Gaussian fluctuations in relativistic stochastic hydrodynamics. This is achieved by defining the average local Landau frame and corresponding fluctuating hydrodynamic variables. Fully nonlinear stochastic hydrodynamics is expressed in a unified multi-component matrix form. A novel relativistic formalism, also manifestly covariant under SO(3) rotations of the local spatial basis in the average local Landau frame, is introduced. The equations describe correlators of all hydrodynamic variables, including fluctuating velocity (or momentum density) -- a nontrivial problem in relativistic hydrodynamics.
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