Evolution of Non-Gaussian Hydrodynamic Fluctuations

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.

Automated summary

In the search for the QCD critical point using non-Gaussian fluctuations, evolution equations for non-Gaussian cumulants were obtained to the leading order of systematic expansion, with leading order contributions given by tree diagrams. A diagrammatic technique was developed for multipoint correlators using a Wigner transform, deriving evolution equations for three- and four-point Wigner functions for nonlinear stochastic diffusion with multiplicative noise.