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 self-consistent 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.

Ultrarelativistic quantum molecular dynamics phase-space coalescence calculations for the production of deuterons are compared with available data for various reactions from the Facility for Antiproton and Ion Research energy regime energy regime over the CERN Super Proton Synchrotron–Relativistic Heavy Ion Collider Beam Energy Scan region up to CERN Large Hadron Collider energies. It is found that the production process of deuterons, as reflected in their rapidity and transverse-momentum distributions in $p+p$, $p+A$, and $A+A$ collisions in the mentioned energy regime, are in good agreement with experimental data. We further explore the energy and centrality dependence of the $d$/$p$ and $\overline{d}/\overline{p}$ ratios and compare with thermal model results. Finally, we discuss antideuteron production for selected systems. Overall, a good description of the experimental data is observed. Most importantly this good description is based only on a single set of coalescence parameters that is independent of energy and system size and can also be applied for antideuterons.

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: noncritical 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 they develop clearly.

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 such as supercooling and domain formation occur when the system evolves through the first-order phase transition.

We explore the directed, elliptic, triangular and quadrangular flow of deuterons in Au+Au reactions at a beam energy of 1.23 AGeV within the UrQMD approach. These investigations are of direct relevance for the HADES experiment at GSI that has recently presented first data on the flow of light clusters in Au+Au collisions at 1.23 AGeV. To address the deuteron flow, UrQMD has been extended to include deuteron formation by coalescence. We find that this ansatz provides a very good description of the measured deuteron flow data, if a hard equation of state is used for the simulation. In addition we show that light cluster formation has a sizable impact on the proton flow and has to be taken into account to obtain reliable results in the forward/backward region. Based on the observed scaling of the flow, which is a natural result of coalescence, we conclude that deuteron production at GSI energies is a final state recombination effect. Finally, we also discuss the scaling relations of the higher order flow components up to v ₄. We show that v ₃ ∼ v ₁ v ₂ and v 4 ∼ v 2 2 as function of transverse momentum and that the integrated v 2 2 ∼ v 4 over the investigated energy range from E _lab = 0.1 AGeV to 40 AGeV.

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