We study the electric conductivity of hot QCD matter at various temperatures T within the off-shell parton-hadron-string dynamics transport approach for interacting partonic, hadronic or mixed systems in a finite box with periodic boundary conditions. The response of the strongly interacting system in equilibrium to an external electric field defines the electric conductivity σ(0). We find a sizable temperature dependence of the ratio σ(0)/T well in line with calculations in a relaxation time approach for T(c)

We study the effect of the chiral symmetry restoration (CSR) on heavy-ion collisions observables in the energy range √ sNN =3-20 GeV within the Parton-Hadron-String Dynamics (PHSD) transport approach. The PHSD includes the deconfinement phase transition as well as essential aspects of CSR in the dense and hot hadronic medium, which are incorporated in the Schwinger mechanism for the hadronic particle production. We adopt different parametrizations of the nuclear equation of state from the non-linear σ −ω model, which enter in the computation of the quark scalar density for the CSR mechanism, in order to estimate the uncertainty in our calculations. For the pion-nucleon Σ-term we adopt Σπ ≈ 45 MeV which corresponds to some 'world average'. Our systematic studies show that chiral symmetry restoration plays a crucial role in the description of heavy-ion collisions at √ sNN =3-20 GeV, realizing an increase of the hadronic particle production in the strangeness sector with respect to the non-strange one. We identify particle abundances and rapidity spectra to be suitable probes in order to extract information about CSR, while transverse mass spectra are less sensitive. Our results provide a microscopic explanation for the "horn" structure in the excitation function of the K + /π + ratio: the CSR in the hadronic phase produces the steep increase of this particle ratio up to √ sNN ≈ 7 GeV, while the drop at higher energies is associated to the appearance of a deconfined partonic medium. Furthermore, the appearance/disappearance of the 'horn'-structure is investigated as a function of the system size and collision centrality. We close this work by an analysis of strangeness production in the (T, µB)-plane (as extracted from the PHSD for central Au+Au collisions) and discuss the perspectives to identify a possible critical point in the phase diagram.PACS numbers: 25.75. Nq, 25.75.Ld, 24.85.+p, 12.38.Mh † In this work we adopt natural units, henceh = c = 1.

The direct photon spectra and flow (v2, v3) in heavy-ion collisions at SPS, RHIC and LHC energies are investigated within a relativistic transport approach incorporating both hadronic and partonic phases -the Parton-Hadron-String Dynamics (PHSD). In the present work, four extensions are introduced compared to our previous calculations: (i) going beyond the soft-photon approximation (SPA) in the calculation of the bremsstrahlung processes meson + meson → meson + meson + γ, (ii) quantifying the suppression due to the Landau-Pomeranchuk-Migdal (LPM) coherence effect, (iii) adding the additional channels V + N → N + γ and ∆ → N + γ and (iv) providing PHSD calculations for Pb+Pb collisions at √ sNN = 2.76 TeV. The first issue extends the applicability of the bremsstrahlung calculations to higher photon energies in order to understand the relevant sources in the region pT = 0.5−1.5 GeV, while the LPM correction turns out to be important for pT < 0.4 GeV in the partonic phase. The results suggest that a large elliptic flow v2 of the direct photons signals a significant contribution of photons produced in interactions of secondary mesons and baryons in the late (hadronic) stage of the heavy-ion collision. In order to further differentiate the origin of the direct photon azimuthal asymmetry (late hadron interactions vs electromagnetic fields in the initial stage), we provide predictions for the photon spectra, elliptic flow and triangular flow v3(pT ) of direct photons at different centralities to be tested by the experimental measurements at the LHC energies. Additionally, we illustrate the magnitude of the photon production in the partonic and hadronic phases as functions of time and local energy density. Finally, the 'cocktail' method for an estimation of the background photon elliptic flow, which is widely used in the experimental works, is supported by the calculations within the PHSD transport approach.

We study the electric conductivity as well as the magnetic response of hot QCD matter at various temperatures T and chemical potentials µq within the off-shell Parton-Hadron-String Dynamics (PHSD) transport approach for interacting partonic systems in a finite box with periodic boundary conditions. The response of the strongly-interacting system in equilibrium to an external electric field defines the electric conductivity σ0 whereas the response to a moderate external magnetic field defines the induced diamagnetic moment µL (T, µq) as well as the spin susceptibility χS(T, µq). We find a sizeable temperature dependence of the dimensionless ratio σ0/T well in line with calculations in a relaxation time approach for Tc < T < 2.5Tc as well as an increase of σ0 with µ 2 q /T 2 . Furthermore, the frequency dependence of the electric conductivity σ(Ω) shows a simple functional form well in line with results from the Dynamical QuasiParticle Model (DQPM). The spin susceptibility χS(T, µq) is found to increase with temperature T and to rise ∼ µ 2 q /T 2 , too. The actual values for the magnetic response of the QGP in the temperature range below 250 MeV show that the QGP should respond diamagnetically in actual ultra-relativistic heavy-ion collisions since the maximal magnetic fields created in these collisions are smaller than Bc(T ) which defines a boundary between diamagnetism and paramagnetism.

The properties of quantum-chromo dynamics (QCD) nowadays are accessable by lattice QCD calculations at vanishing quark chemical potential µq=0 but often lack a transparent physical interpretation. In this review we report about results from an extended dynamical quasiparticle model (DQPM * ) in which the effective parton propagators have a complex selfenergy that depends on the temperature T of the medium as well as on the chemical potential µq and the parton three-momentum p with respect to the medium at rest. It is demonstrated that this approach allows for a good description of QCD thermodynamics with respect to the entropy density, pressure etc. above the critical temperature Tc ≈ 158 MeV. Furthermore, the quark susceptibility χq and the quark number density nq are found to be reproduced simultaneously at zero and finite quark chemical potential. The shear and bulk viscosities η, ζ, and the electric conductivity σe from the DQPM * also turn out in close agreement with lattice results for µq =0. The DQPM * , furthermore, allows to evaluate the momentum p, T and µq dependencies of the partonic degrees of freedom also for larger µq which are mandatory for transport studies of heavy-ion collisions in the regime 5 GeV < √ s N N < 10 GeV. We finally calculate the charm quark diffusion coefficient Ds -evaluated from the differential cross sections * berrehrah@fias.uni-frankfurt.de † E.Bratkovskaya@gsi.de ‡ of partons in the medium for light and heavy quarks by employing the propagators and couplings from the DQPM -and compare to the available lattice data. It is argued that the complete set of observables allows for a transparent interpretation of the properties of hot QCD.