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

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.

References in corpus (75)

• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• Collective flow and viscosity in relativistic heavy-ion collisions
• Signatures of the Tricritical Point in QCD
• The phase diagram of dense QCD
• Event-by-Event Fluctuations in Heavy Ion Collisions and the QCD Critical Point
• Heavy Ion Collisions: The Big Picture, and the Big Questions
• Non-Gaussian fluctuations near the QCD critical point
• On the Phase Diagram of QCD
• 3+1D hydrodynamic simulation of relativistic heavy-ion collisions
• Color Superconductivity and Chiral Symmetry Restoration at Nonzero Baryon Density and Temperature
• Static and Dynamic Critical Phenomena at a Second Order QCD Phase Transition
• Energy Dependence of Moments of Net-proton Multiplicity Distributions at RHIC
• Mapping the Phases of Quantum Chromodynamics with Beam Energy Scan
• On the sign of kurtosis near the QCD critical point
• Lectures on hydrodynamic fluctuations in relativistic theories
• Search for the QCD Critical Point with Fluctuations of Conserved Quantities in Relativistic Heavy-Ion Collisions at RHIC : An Overview
• Properties of hot and dense matter from relativistic heavy ion collisions
• Slowing Out of Equilibrium Near the QCD Critical Point
• Third moments of conserved charges as probes of QCD phase structure
• Review of Jet Measurements in Heavy Ion Collisions
• 3D Ising Model:The Scaling Equation of State
• A 3+1 dimensional viscous hydrodynamic code for relativistic heavy ion collisions
• Hydro+: hydrodynamics with parametric slowing down and fluctuations near the critical point
• Dynamic universality class of the QCD critical point
• Hydrodynamical evolution near the QCD critical end point
• Hydrodynamic Approaches in Relativistic Heavy Ion Reactions
• Real time evolution of non-Gaussian cumulants in the QCD critical regime
• Hydrodynamic Fluctuations, Long-time Tails, and Supersymmetry
• Nonequilibrium chiral fluid dynamics including dissipation and noise
• Relativistic viscous hydrodynamics for heavy-ion collisions with ECHO-QGP
• Exploring the QCD Phase Structure with Beam Energy Scan in Heavy-ion Collisions
• Fluctuations of conserved charges in relativistic heavy ion collisions: An introduction
• A kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion
• Sigma and hydrodynamic modes along the critical line
• Diffusive dynamics of critical fluctuations near the QCD critical point
• Proton number fluctuations in $\sqrt{s_{NN}}$ = 2.4 GeV Au+Au collisions studied with HADES
• An Experimental Exploration of the QCD Phase Diagram: The Search for the Critical Point and the Onset of De-confinement
• Universal off-equilibrium scaling of critical cumulants in the QCD phase diagram
• Relativistic Hydrodynamic Fluctuations
• Dynamical net-proton fluctuations near a QCD critical point
• Viscous Hydrodynamics and the Quark Gluon Plasma
• Chiral fluid dynamics with explicit propagation of the Polyakov loop
• A Study of the Properties of the QCD Phase Diagram in High-Energy Nuclear Collisions
• Fluid Dynamics and Viscosity in Strongly Correlated Fluids
• Hydro+ in Action: Understanding the Out-of-Equilibrium Dynamics Near a Critical Point in the QCD Phase Diagram
• Fluctuation dynamics in a relativistic fluid with a critical point
• Transits of the QCD Critical Point
• Equilibration and relaxation times at the chiral phase transition including reheating
• Hydrodynamic Fluctuations in Relativistic Heavy-Ion Collisions
• Fluctuation dynamics near the QCD critical point
• Microscopic models and effective equation of state in nuclear collisions at FAIR energies
• Stochastic hydrodynamics and long time tails of an expanding conformal charged fluid
• Hydrodynamic fluctuations and dissipation in an integrated dynamical model
• Nonequilibrium time evolution of higher order cumulants of conserved charges and event-by-event analysis
• A kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion
• Effects of global charge conservation on time evolution of cumulants of conserved charges in relativistic heavy ion collisions
• Dynamical evolution of critical fluctuations and its observation in heavy ion collisions
• Numerical integration of thermal noise in relativistic hydrodynamics
• Rapidity decorrelation of anisotropic flow caused by hydrodynamic fluctuations
• Effective Potential for Scalar Field in Three Dimensions: Ising Model in the Ferromagnetic Phase
• Impact of resonance decays on critical point signals in net-proton fluctuations
• Finite element discretization of non-linear diffusion equations with thermal fluctuations
• Net-baryon number variance and kurtosis within nonequilibrium chiral fluid dynamics
• Time-evolution of fluctuations as signal of the phase transition dynamics in a QCD-assisted transport approach
• Entropy production and reheating at the chiral phase transition
• Hydrodynamic fluctuations of entropy in one-dimensionally expanding system
• Fluctuating fluid dynamics for the QGP in the LHC and BES era
• Broadening of the chiral critical region in a hydrodynamically expanding medium
• Dynamics of critical fluctuations: Theory -- phenomenology -- heavy-ion collisions
• Influence of an inhomogeneous and expanding medium on signals of the QCD phase transition
• Critical fluctuations in a dynamically expanding heavy-ion collision
• Phenomena at the QCD phase transition in nonequilibrium chiral fluid dynamics (N$\chi$FD)
• Baryon number diffusion with critical fluctuations
• On the Accuracy of Finite-Volume Schemes for Fluctuating Hydrodynamics
• Behavior of universal critical parameters in the QCD phase diagram

Cited by in corpus (21)

• The Present and Future of QCD
• Search for the QCD Critical Point in High Energy Nuclear Collisions
• Freezing Out Fluctuations in Hydro+ Near the QCD Critical Point
• Baryon transport and the QCD critical point
• Progress and Challenges in Small Systems
• Critical net-baryon fluctuations in an expanding system
• Effects of QCD critical point on light nuclei production
• Holographic approach of the spinodal instability to criticality
• Stochastic hydrodynamics and hydro-kinetics: Similarities and differences
• Rapidity scan approach for net-baryon cumulants with a statistical thermal model
• Dynamical critical fluctuations near the QCD critical point with hydrodynamic cooling rate
• The BEST framework for the search for the QCD critical point and the chiral magnetic effect
• Hydrodynamic description of the baryon-charged quark-gluon plasma
• Enhanced pion-to-proton ratio at the onset of the QCD phase transition
• Non-equilibrium cumulants within model A from crossover to first-order phase transition side
• Net-proton number cumulant ratios as function of beam energy from an expanding nonequilibrium chiral fluid
• Role of slow, out-of-equilibrium modes on the dynamic structure factor near the QCD critical point
• Dynamics of the conserved net-baryon density near QCD critical point within inhomogeneous quark-gluon plasma profile
• Chiral phase transition: effective field theory and holography
• Cumulants of the chiral order parameter at lower RHIC energies
• Dynamic modeling for heavy-ion collisions