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.
Highlights
Introduction.—The recent resurgence of interest in the classic subject of hydrodynamics in general [1] and hydrodynamic fluctuations [2] in particular has been largely driven by the progress in heavy-ion collision experiments that create and study droplets of hot and dense matter governed by the physics of strong interactions described by quantum chromodynamics (QCD)
Most relevant for this work is the formalism describing the evolution of correlation functions coupled to the hydrodynamic background
We considered the problem of the diffusion of a conserved quantity and left the generalization to full stochastic hydrodynamics, including pressure and flow, to future work
Summary
Introduction.—The recent resurgence of interest in the classic subject of hydrodynamics in general [1] and hydrodynamic fluctuations [2] in particular has been largely driven by the progress in heavy-ion collision experiments that create and study droplets of hot and dense matter governed by the physics of strong interactions described by quantum chromodynamics (QCD). The experimental search for the QCD critical point relies heavily on such measures of non-Gaussianity [5,6,7,8] (which, similar to fluctuation magnitudes, depend on time evolution [10]). We obtain evolution equations for appropriate measures of non-Gaussianity in the hydrodynamic regime, that is, the regime where the ratio of correlation length to typical fluctuation wavelength is small.
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