Modeling the diffusive dynamics of critical fluctuations near the QCD critical point

TL;DR

This paper develops a stochastic fluid dynamical model to study critical fluctuations near the QCD critical point, accounting for conservation laws, finite size effects, and nonlinearities, with implications for heavy-ion collision experiments.

Contribution

It introduces a stochastic diffusion model with nonlinear coupling for critical fluctuations, including finite size effects and conservation laws, advancing the modeling of QCD critical phenomena.

Findings

Net-baryon conservation causes anticorrelations at large distances.

Non-Gaussian fluctuations are observed near the critical point.

Critical slowing down affects fluctuation signals in dynamical scenarios.

Abstract

The experimental search for the QCD critical point by means of relativistic heavy-ion collisions necessitates the development of dynamical models of fluctuations. In this work we study the fluctuations of the net-baryon density near the critical point. Due to net-baryon number conservation the correct dynamics is given by the fluid dynamical diffusion equation, which we extend by a white noise stochastic term to include intrinsic fluctuations. We quantify finite resolution and finite size effects by comparing our numerical results to analytic expectations for the structure factor and the equal-time correlation function. In small systems the net-baryon number conservation turns out to be quantitatively and qualitatively important, as it introduces anticorrelations at larger distances. Including nonlinear coupling terms in the form of a Ginzburg-Landau free energy functional we observe non-Gaussian fluctuations quantified by the excess kurtosis. We study the dynamical properties of the system close to equilibrium, for a sudden quench in temperature and a Hubble-like temperature evolution. In the real-time dynamical systems we find the important dynamical effects of critical slowing down, weakening of the extremal value and retardation of the fluctuation signal. In this work we establish a set of general tests, which should be met by any model propagating fluctuations, including upcoming $3+1$ dimensional fluctuating fluid dynamics.