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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.
A quantitatively reliable theoretical description of the dynamics of fluctuations in non-equilibrium is indispensable in the experimental search for the QCD critical point by means of ultra-relativistic heavy-ion collisions. In this work we consider
The evolution of non-hydrodynamic slow processes near the QCD critical point is explored with the novel Hydro+ framework, which extends the conventional hydrodynamic description by coupling it to additional explicitly evolving slow modes describing l
We present a fully dynamical model to study the chiral and deconfinement transition of QCD simultaneously. The quark degrees of freedom constitute a heat bath in local equilibrium for both order parameters, the sigma field and a dynamical Polyakov lo
Fireballs created in relativistic heavy-ion collisions at different beam energies have been argued to follow different trajectories in the QCD phase diagram in which the QCD critical point serves as a landmark. Using a (1+1)-dimensional model setting
The impact of the QCD critical point on the propagation of nonlinear waves has been studied. The effects have been investigated within the scope of second-order causal dissipative hydrodynamics by incorporating the critical point into the equation of