Evolution of Non-Gaussian Hydrodynamic Fluctuations

TL;DR

This paper develops a theoretical framework to describe the evolution of non-Gaussian fluctuations in hydrodynamics, aiding the search for the QCD critical point by deriving equations for higher-order cumulants.

Contribution

It introduces a diagrammatic method and Wigner transform approach to derive evolution equations for non-Gaussian cumulants in hydrodynamic fluctuations.

Findings

Derived leading-order evolution equations for non-Gaussian cumulants.

Developed a diagrammatic technique using tree diagrams.

Formulated Wigner transform for multipoint correlators.

Abstract

In the context of the search for the QCD critical point using non-Gaussian fluctuations, we obtain the evolution equations for non-Gaussian cumulants to the leading order of the systematic expansion in the magnitude of thermal fluctuations. We develop a diagrammatic technique in which the leading order contributions are given by tree diagrams. We introduce a Wigner transform for multipoint correlators and derive the evolution equations for three- and four-point Wigner functions for the problem of nonlinear stochastic diffusion with multiplicative noise.