About PHSD-PHQMD

PHSD-PHQMD is a Fortran-based unified transport simulation framework for relativistic nucleus-nucleus collisions. It combines two complementary descriptions of baryon dynamics: PHSD, based on mean-field BUU transport, and PHQMD, which follows a Quantum Molecular Dynamics (QMD) n-body approach.

In both modes, the subsequent evolution includes quarks, gluons, mesons, and hadrons propagated within a nonequilibrium Kadanoff-Baym and BUU dynamics. Interactions are treated through a collision integral for off-shell hadrons and QGP partons, realized within the Dynamical QuasiParticle Model (DQPM), which describes the partonic medium consistently with lattice-QCD thermodynamics.

Final-state nuclear fragments and formed clusters can be reconstructed using MST (Minimum Spanning Tree), SACA (Simulated Annealing Cluster Algorithm), or coalescence-based algorithms. Simulated events can be exported in OSCAR, ROOT, and Rivet formats.

The Parton-Hadron-String Dynamics (PHSD) is a microscopic off-shell transport approach that consistently describes the full evolution of a relativistic heavy-ion collision from the initial hard scatterings and string formation through the dynamical deconfinement phase transition to the quark-gluon plasma, as well as hadronization and the subsequent interactions in the hadronic phase. It has been developed by the Giessen/Frankfurt groups on the basis of the Hadron-String Dynamics transport approach (HSD), and in the hadronic sector PHSD is equivalent to HSD.

In PHSD, the transition from the partonic (quarks and gluons) to hadronic degrees of freedom is described by covariant transition rates for the fusion of quark-antiquark pairs to mesonic resonances or three quarks (antiquarks) to baryonic states. This dynamical hadronization obeys flavor current conservation, color neutrality, and energy-momentum conservation. Two-particle correlations from finite parton spectral widths are treated dynamically by generalized off-shell transport equations that go beyond mean-field or Boltzmann approximations.

The transport-theoretical description of quarks and gluons in PHSD is based on the Dynamical Quasi-Particle Model (DQPM), constructed to reproduce lattice-QCD results for a quark-gluon plasma in thermodynamic equilibrium. The DQPM supplies mean fields for gluons and quarks, as well as effective two-body interactions implemented in PHSD. Close to the phase transition, dynamical quarks and antiquarks become massive, such that resonant pre-hadronic color-dipole states (q-qbar and qqq) are formed at large invariant mass and then decay sequentially to the meson and baryon octets. The resulting hadronization process increases total entropy and remains consistent with the second law of thermodynamics.

The PHSD approach has been applied to nucleus-nucleus collisions from low SPS to LHC energies to explore the space-time regions of partonic matter. It provides a consistent description of bulk observables in heavy-ion collisions, including rapidity spectra, transverse-mass distributions, and azimuthal asymmetries (v₁, v₂, v₃, v₄) for multiple particle species, and has also been used successfully for dilepton production analyses from hadronic and partonic sources at SPS, RHIC, and LHC energies.

Equilibrium properties of the QGP have also been studied with PHSD simulations in a finite box with periodic boundary conditions at fixed temperature T. In particular, the shear-viscosity to entropy-density ratio from PHSD shows a minimum of about 0.1 near the critical temperature T_c = 160 MeV and approaches the perturbative-QCD limit at higher temperatures, in line with lattice-QCD results. This supports a strongly interacting liquid-like QGP (sQGP) rather than a weakly interacting gas of partons.

The Parton-Hadron-Quantum-Molecular Dynamics (PHQMD) transport approach is designed to provide a microscopic description of nuclear cluster and hypernucleus formation, as well as general particle production, in heavy-ion reactions at relativistic energies.

In contrast to coalescence or statistical models often used for cluster formation, PHQMD forms clusters dynamically through interactions between baryons described within Quantum Molecular Dynamics (QMD), allowing the propagation of the n-body Wigner density and n-body phase-space correlations that are essential for cluster formation.

Clusters in PHQMD can be reconstructed using MST, SACA, or coalescence-based algorithms. At the same time, collisions among hadrons, quark-gluon-plasma formation, and parton dynamics are treated in the same way as in the established PHSD approach, making PHSD-PHQMD a consistent unified framework for both bulk particle production and cluster observables.