Hydro+ in Action: Understanding the Out-of-Equilibrium Dynamics Near a Critical Point in the QCD Phase Diagram

Abstract

Upcoming experimental programs will look for signatures of a possible critical point in the QCD phase diagram in fluctuation observables. To understand and predict these signatures, one must account for the fact that the dynamics of any critical fluctuations must be out-of-equilibrium: because of critical slowing down, the fluctuations cannot stay in equilibrium as the droplet of QGP produced in a collision expands and cools. Furthermore, their out-of-equilibrium dynamics must also influence the hydrodynamic evolution of the cooling droplet. The recently developed Hydro+ formalism allows for a consistent description of both the hydrodynamics and the out-of-equilibrium fluctuations, including the feedback between them. We shall explicitly demonstrate how this works, setting up a Hydro+ simulation in a simplified setting: a rapidity-independent fireball undergoing radial flow with an equation of state in which we imagine a critical point close to the ${\mu }_B=0$ axis of the phase diagram. Within this setup, we show that we can quantitatively capture non-equilibrium phenomena, including critical fluctuations over a range of scales and memory effects. Furthermore, we illustrate the interplay between the dynamics of the fluctuations and the hydrodynamic flow of the fireball: as the fluid cools and flows, the dynamical fluctuations lag relative to how they would evolve if they stayed in equilibrium; there is then a backreaction on the flow itself due to the out-of-equilibrium fluctuations; and, in addition, the radial flow transports fluctuations outwards by advection. Within our model, we find that the backreaction from the out-of-equilibrium fluctuations does not yield dramatically large effects in the hydrodynamic variables. Further work will be needed in order to check this quantitative conclusion in other settings but, if it persists, this will considerably simplify future modelling.

arXiv comment40 pages, 9 figures

References in corpus (54)

• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• The equation of state in (2+1)-flavor QCD
• The chiral and deconfinement aspects of the QCD transition
• Signatures of the Tricritical Point in QCD
• The phase diagram of dense QCD
• The QCD equation of state with dynamical quarks
• Event-by-Event Fluctuations in Heavy Ion Collisions and the QCD Critical Point
• Heavy Ion Collisions: The Big Picture, and the Big Questions
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Non-Gaussian fluctuations near the QCD critical point
• On the Phase Diagram of QCD
• Equation of state and QCD transition at finite temperature
• Color Superconductivity and Chiral Symmetry Restoration at Nonzero Baryon Density and Temperature
• Applying Bayesian parameter estimation to relativistic heavy-ion collisions: simultaneous characterization of the initial state and quark-gluon plasma medium
• Mapping the Phases of Quantum Chromodynamics with Beam Energy Scan
• On the sign of kurtosis near the QCD critical point
• Search for the QCD Critical Point with Fluctuations of Conserved Quantities in Relativistic Heavy-Ion Collisions at RHIC : An Overview
• The Condensed Matter Physics of QCD
• Challenges in QCD matter physics - The Compressed Baryonic Matter experiment at FAIR
• Slowing Out of Equilibrium Near the QCD Critical Point
• Dissipative Hydrodynamics and Heavy Ion Collisions
• 3D Ising Model:The Scaling Equation of State
• Hydro+: hydrodynamics with parametric slowing down and fluctuations near the critical point
• Dynamic universality class of the QCD critical point
• Dynamical initial state model for relativistic heavy-ion collisions
• Using Higher Moments of Fluctuations and their Ratios in the Search for the QCD Critical Point
• Net baryon diffusion in fluid dynamic simulations of relativistic heavy-ion collisions
• Real time evolution of non-Gaussian cumulants in the QCD critical regime
• Nonequilibrium chiral fluid dynamics including dissipation and noise
• Causal Viscous Hydrodynamics for Central Heavy-Ion Collisions
• A kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion
• Diffusive dynamics of critical fluctuations near the QCD critical point
• Causal Viscous Hydrodynamics for Central Heavy-Ion Collisions II: Meson Spectra and HBT Radii
• Proton number fluctuation as a signal of the QCD critical end-point
• Thermal Conductivity and Chiral Critical Point in Heavy Ion Collisions
• Relativistic Hydrodynamic Fluctuations
• Dynamical net-proton fluctuations near a QCD critical point
• (3+1)-dimensional dissipative relativistic fluid dynamics at non-zero net baryon density
• Fluctuation dynamics in a relativistic fluid with a critical point
• Phenomenological Consequences of Enhanced Bulk Viscosity Near the QCD Critical Point
• Transits of the QCD Critical Point
• Equilibration and relaxation times at the chiral phase transition including reheating
• Particlization with local event-by-event conservation laws
• Hydrodynamic Fluctuations in Relativistic Heavy-Ion Collisions
• Hydrodynamic fluctuations and dissipation in an integrated dynamical model
• Searching for the QCD critical point via the rapidity dependence of cumulants
• A kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion
• Critical behavior of the bulk viscosity in QCD
• Dynamical evolution of critical fluctuations and its observation in heavy ion collisions
• Dynamical initialization and hydrodynamic modeling of relativistic heavy-ion collisions
• Causal Electric Charge Diffusion and Balance Functions in Relativistic Heavy Ion Collisions
• Entropy production and reheating at the chiral phase transition
• Hydrodynamic fluctuations of entropy in one-dimensionally expanding system
• Soft Modes at the Critical End Point in the Chiral Effective Models

Cited by in corpus (40)

• Dense Nuclear Matter Equation of State from Heavy-Ion Collisions
• Cumulants and Correlation Functions of Net-proton, Proton and Antiproton Multiplicity Distributions in Au+Au Collisions at energies available at the BNL Relativistic Heavy Ion Collider
• A collision geometry-based 3D initial condition for relativistic heavy-ion collisions
• Phase Transitions in Particle Physics -- Results and Perspectives from Lattice Quantum Chromo-Dynamics
• A Study of the Properties of the QCD Phase Diagram in High-Energy Nuclear Collisions
• The Present and Future of QCD
• Proton number cumulants and correlation functions in Au-Au collisions at $\sqrt{s_{\mathrm{NN}}}=7.7-200$ GeV from hydrodynamics
• Fluctuation dynamics in a relativistic fluid with a critical point
• The QCD phase diagram and Beam Energy Scan physics: a theory overview
• Fluctuation dynamics near the QCD critical point
• Freezing Out Fluctuations in Hydro+ Near the QCD Critical Point
• Evolution of Non-Gaussian Hydrodynamic Fluctuations
• Modeling the diffusive dynamics of critical fluctuations near the QCD critical point
• Baryon transport and the QCD critical point
• Progress and Challenges in Small Systems
• Dynamical exploring the QCD matter at finite temperatures and densities-a short review
• Critical lensing and kurtosis near a critical point in the QCD phase diagram in and out-of-equilibrium
• Real-time methods for spectral functions
• Non-Gaussian fluctuation dynamics in relativistic fluids
• Effects of QCD critical point on light nuclei production
• Critical net-baryon fluctuations in an expanding system
• Off-equilibrium non-Gaussian fluctuations near the QCD critical point: an effective field theory perspective
• Dynamics of critical fluctuations: Theory -- phenomenology -- heavy-ion collisions
• Enhanced yield ratio of light nuclei in heavy ion collisions with a first-order QCD phase transition
• Suppression of thermal vorticity as an indicator of QCD critical point
• Stochastic hydrodynamics and hydro-kinetics: Similarities and differences
• Characteristic momentum of Hydro+ and a bound on the speed of sound near the QCD critical point
• Rapidity scan approach for net-baryon cumulants with a statistical thermal model
• The QCD critical point from the Nambu-Jona-Lasino model with a scalar-vector interaction
• 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
• Elliptic flow splittings in the Polyakov-looped Nambu-Jona Lasinio transport model
• The equilibrium and dynamical cumulants of QCD chiral order parameter with parametric Landau free energy
• Nonuniform-temperature effects on the phase transition in an Ising-like model
• Non-equilibrium cumulants within model A from crossover to first-order phase transition side
• Role of slow, out-of-equilibrium modes on the dynamic structure factor near the QCD critical point
• Investigations into the characteristics and influences of nonequilibrium evolution
• The effects of the QCD critical point on the spectra and flow coefficients of hadrons
• Dynamic modeling for heavy-ion collisions
• Entropy Production in Dissipationless Hydrodynamics with an order parameter