Chiral Fluid Dynamics Research Articles

Longitudinal dynamics from hydrodynamics with an order parameter * *This work is in part Supported by NSFC (11675274, 11735007)

We studied coupled dynamics of hydrodynamic fields and order parameter in the presence of nontrivial longitudinal flow using the chiral fluid dynamics model. We found that longitudinal expansion provides an effective relaxation for the order parameter, which equilibrates in an oscillatory fashion. Similar oscillations are also visible in hydrodynamic degrees of freedom through coupled dynamics. The oscillations are reduced when dissipation is present. We also found that the quark density, which initially peaked at the boundary of the boost invariant region, evolves toward forward rapidity with the peak velocity correlated with the velocity of longitudinal expansion. The peak broadens during this evolution. The corresponding chemical potential rises due to simultaneous decrease of density and temperature. We compared the cases with and without dissipation for the order parameter and also the standard hydrodynamics without order parameter. We found that the corresponding effects on temperature and chemical potential can be understood from the conservation laws and different speeds of equilibration of the order parameter in the three cases.

Time-evolution of fluctuations as signal of the phase transition dynamics in a QCD-assisted transport approach

For the understanding of fluctuation measurements in heavy-ion collisions it is crucial to develop quantitatively reliable dynamical descriptions which take the non-perturbative nature of QCD near the phase transition into account. We discuss a novel QCD-assisted transport approach based on non-equilibrium chiral fluid dynamics and the effective action of low energy QCD. In this framework, we study the time-evolution of fluctuation measures of the critical mode, notably the kurtosis, for a non-expanding system. From this, we can estimate the equilibration times of critical mode fluctuations in the QCD phase diagram. These allow us to identify both the phase boundary and the critical region near the QCD critical point.

Evolution of critical fluctuations in a heavy-ion collision scenario

We study fluctuations of the sigma field and the net-baryon number on the crossover side of the critical point within the model of nonequilibrium chiral fluid dynamics (NχFD). Herein, the sigma field as the chiral order parameter is propagated explicitly and coupled to a fluid of quarks. Before investigating these fluctuations in an expanding nonequilibrium medium, we scrutinize the NχFD model by comparing cumulants of the sigma fluctuations in a thermalized box to (ratios of) susceptibilities as they are obtained from derivatives of the grand canonical potential. The dynamically determined cumulants follow the trend of the thermodynamic susceptibilities. In an expanding inhomogeneous medium, however, the behavior of the fluctuations is shown to be different as a result of memory effects.

A particlization procedure for the NχFD model and the evolution of the net-proton kurtosis

We present an analysis of the net-proton kurtosis on the crossover side of the critical point within the model of nonequilibrium chiral fluid dynamics (NχFD). The chiral order parameter is propagated explicitly and coupled to an expanding fluid of quarks and gluons to describe the dynamical situation in a heavy-ion collision. After implementing a particlization routine into this model, we study the behavior of the net-proton kurtosis as driven by the characteristic structure of the net-baryon number susceptibility in the critical region.

Phenomena at the QCD phase transition in nonequilibrium chiral fluid dynamics (N $\chi$ FD)

Heavy-ion collisions performed in the beam energy range accessible by the NICA collider facility are expected to produce systems of extreme net-baryon densities and can thus reach yet unexplored regions of the QCD phase diagram. Here, one expects the phase transition between the plasma of deconfined quarks and gluons and the hadronic matter to be of first order. A discovery of the first-order phase transition would as well prove the existence of the QCD critical point, a landmark in the phase diagram. In order to understand possible signals of the first-order phase transition in heavy-ion collision experiments it is very important to develop dynamical models of the phase transition. Here, we discuss the opportunities of studying dynamical effects at the QCD first-order phase transition within our model of nonequilibrium chiral fluid dynamics.

Dynamical net-proton fluctuations near a QCD critical point

We investigate the evolution of the net-proton kurtosis and the kurtosis of the chiral order parameter near the critical point in the model of nonequilibrium chiral fluid dynamics. The order parameter is propagated explicitly and coupled to an expanding fluid of quarks and gluons in order to describe the dynamical situation in a heavy-ion collision. We study the critical region near the critical point on the crossover side. There are two sources of fluctuations: non-critical initial event-by-event fluctuations and critical fluctuations. These fluctuations can be distinguished by comparing a mean-field evolution of averaged thermodynamic quantities with the inclusion of fluctuations at the phase transition. We find that while the initial state fluctuations give rise to flat deviations from statistical fluctuations, critical fluctuations reveal a clear structure of the phase transition. The signals of the critical point in the net-proton and sigma field kurtosis are affected by the nonequilibrium dynamics and the inhomogeneity of the space-time evolution but develop clearly.

Dynamics and stability of chiral fluid

Starting from the linear sigma model with constituent quarks we derive hydrodynamic equations which are coupled to the order-parameter field, e.g. the chiral fluid dynamics. For a static system in thermal equilibrium this model leads to a chiral phase transition which, depending on the choice of the quark-meson coupling constant g, could be a crossover or a first order one. We investigate the stability of the chiral fluid in the static and expanding background by considering the evolution of perturbations with respect to the mean-field solution. In the static background the spectrum of plane-wave perturbations consists of two branches, one corresponding to the sound waves and another to the σ-meson excitations. For large g these two branches cross and the excitation spectrum acquires exponentially growing modes. The stability analysis is also done for the Bjorken-like background solution by explicitly solving the time-dependent differential equation for perturbations in the η space. In this case the growth rate of unstable modes is significantly reduced.

The QCD phase transition in a fully dynamical model of heavy-ion collisions

Experimental signals for a possible QCD critical point and first-order phase transition are strongly influenced by the rapid nonequilibrium dynamics during a heavy-ion collision. In order to estimate and understand these effects we study the cooling through the phase transition within a nonequilibrium chiral fluid dynamics model. The order parameters for the chiral and deconfinement transition are explicitly propagated, taking into account dissipation and fluctuation stemming from the interaction with a quark-antiquark fluid. In studies of single events, we demonstrate how the formation of domains in net-baryon density at the first-order phase transition leads to a clear enhancement of higher flow harmonics. For the detection of the critical point it is crucial that the relevant signal survives the rapid dynamics. We observe critical slowing down and long-wavelength fluctuations in the vicinity of the critical point.

How spinodal decomposition influences observables at FAIR energies

The FAIR facility will make the region of high net-baryon densities experimentally accessible, where a first-order phase transition is conjectured. We investigate the dynamics of chiral symmetry breaking and the onset of confinement during a heavy-ion collision at large baryochemical potentials within a nonequilibrium chiral fluid dynamics model including effects of dissipation and noise. The order parameters are explicitly propagated and coupled to a fluid dynamically expanding medium of quarks. We demonstrate that the coupled system is strongly influenced by the nonequilibrium dynamics, leading only to a weak growth of the correlation length near the critical point. At the first-order phase transition, spinodal instabilities create domains in the order parameters and large spatial fluctuations in the baryon density within single events. As a consequence we find a clear enhancement of higher flow harmonics in coordinate space at the first-order phase transition in comparison with transitions through the crossover or critical point.

The impact of dissipation and noise on fluctuations in chiral fluid dynamics

We investigate the nonequilibrium evolution of the sigma field coupled to a fluid dynamic expansion of a hot fireball to model the chiral phase transition in heavy-ion collisions. The dissipative processes and fluctuations are allowed under the assumption that the total energy of the coupled system is conserved. We use the linear sigma model with constituent quarks to investigate the effects of the chiral phase transition on the equilibration and excitation of the sigma modes. The quark fluid acts as a heat bath in local thermal equilibrium and the sigma field evolves according to a semiclassical stochastic Langevin equation of motion. The effects of supercooling and reheating of the fluid in a first order phase transition are observed via the delayed relaxation of the sigma field to a new equilibrium state. At the first order phase transition the nonequilibrium fluctuations are strongly enhanced.Communicated by Steffen Bass

Chiral fluid dynamics with explicit propagation of the Polyakov loop

We present a fully dynamical model to study nonequilibrium effects in both the chiral and the deconfinement phase transition. The sigma field and the Polyakov loop as the corresponding order parameters are propagated by Langevin equations of motion. The locally thermalized background is provided by a fluid of quarks and antiquarks. Allowing for an exchange of energy and momentum through dissipative and stochastic processes we ensure that the total energy of the coupled system remains conserved. We study its relaxational dynamics in different quench scenarios and are able to observe critical slowing down as well as the enhancement of long wavelength modes at the critical point. During the fluid dynamical expansion of a hot plasma fireball typical nonequilibrium effects like supercooling and domain formation occur when the system evolves through the first order phase transition.

Recent developments on the UrQMD hybrid model

We present recent results from the UrQMD hybrid approach investigating the influence of a deconfinement phase transition on the dynamics of hot and dense nuclear matter. In the hydrodynamic stage an equation of state that incorporates a critical end-point (CEP) in line with lattice data is used. The equation of state describes chiral restoration as well as the deconfinement phase transition. We compare the results from this new equation of state to results obtained by applying a hadron resonance gas equation of state, focusing on bulk observables. Furthermore we will discuss future improvements of the hydrodynamic model. This includes the formulation of chiral fluid dynamics to be able to study the effects of a chiral critical point as well as considerable improvements in terms of computational time which would open up possibilities for observables that require high statistics.

Nonequilibrium effects in dynamic symmetry breaking

We study the evolution of the sigma field fluctuations in a scenario featuring a critical point and a first order phase transition using the model of nonequilibrium chiral fluid dynamics (NχFD).

Nonequilibrium chiral fluid dynamics including dissipation and noise

We present a consistent theoretical approach for the study of nonequilibrium effects in chiral fluid dynamics within the framework of the linear sigma model with constituent quarks. Treating the quarks as an equilibrated heat bath we use the influence functional formalism to obtain a Langevin equation for the sigma field. This allows us to calculate the explicit form of the damping coefficient and the noise correlators. For a selfconsistent derivation of both the dynamics of the sigma field and the quark fluid we have to employ the 2PI (two-particle irreducible) effective action formalism. The energy dissipation from the field to the fluid is treated in the exact formalism of the 2PI effective action where a conserved energy-momentum tensor can be constructed. We derive its form and comment on approximations generating additional terms in the energy-momentum balance of the entire system.

The QCD Phase Diagram in Chiral Fluid Dynamics

We give a general overview about the approaches to study the phase diagram of QCD. Thereafter, we examine the evolution of a fireball in a chiral fluid dynamic model including nonequilibrium effects.

AN INTEGRATED HYDRO AND BOLTZMANN APPROACH TO HEAVY ION REACTIONS

Results on bulk particle observables, from a hybrid approach to relativistic heavy-ion collisions, are presented over a wide range of beam energies from E lab = 2 - 160 A GeV . In this model a hydrodynamic phase is integrated into a hadronic transport model. This setup enables us to study the effect of the equation of state of hot and dense nuclear matter on different observables from heavy-ion collider experiments. In addition we present a study on density fluctuations at a phase transition in the framework of chiral fluid dynamics.

Chiral Fluid Dynamics and Collapse of Vacuum Bubbles

We study the expansion dynamics of a quark-antiquark plasma droplet from an initial state with restored chiral symmetry. The calculations are made within the linear $\sigma$ model scaled with an additional scalar field representing the gluon condensate. We solve numerically the classical equations of motion for the meson fields coupled to the fluid-dynamical equations for the plasma. Strong space-time oscillations of the meson fields are observed in the course of the chiral transition. A new phenomenon, the formation and collapse of vacuum bubbles, is also predicted. The particle production due to the bremsstrahlung of the meson fields is estimated.

A FULL-ACCEPTANCE DETECTOR FOR SSC PHYSICS AT LOW AND INTERMEDIATE MASS SCALES: AN EXPRESSION OF INTEREST TO THE SSC

A FULL-ACCEPTANCE DETECTOR FOR SSC PHYSICS AT LOW AND INTERMEDIATE MASS SCALES: AN EXPRESSION OF INTEREST TO THE SSC