Electric and magnetic response of hot QCD matter

We study the electric conductivity as well as the magnetic response of hot QCD matter at various temperatures $T$ and chemical potentials $μ_q$ 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 $σ_0$ whereas the response to a moderate external magnetic field defines the induced diamagnetic moment $μ_L$ ($T, μ_q$) as well as the spin susceptibility $χ_S(T, μ_q)$. We find a sizeable temperature dependence of the dimensionless ratio $σ_0/T$ well in line with calculations in a relaxation time approach for $T_c \! < \! T < \! 2.5 \!\, T_c$ as well as an increase of $σ_0$ with $μ_q^2/T^2$. 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 $χ_S(T,μ_q)$ is found to increase with temperature $T$ and to rise $\sim μ_q ^2/T^2$, 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 $B_c(T)$ which defines a boundary between diamagnetism and paramagnetism.

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