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

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.