Electric and magnetic response of hot QCD matter

Abstract

We study the electric conductivity as well as the magnetic response of hot QCD matter at various temperatures $T$ and chemical potentials $\mu_q$ 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 $\sigma_0$ whereas the response to a moderate external magnetic field defines the induced diamagnetic moment $\mu_L$ ($T, \mu_q$) as well as the spin susceptibility $\chi_S(T, \mu_q)$. We find a sizeable temperature dependence of the dimensionless ratio $\sigma_0/T$ well in line with calculations in a relaxation time approach for $T_c \! < \! T < \! 2.5 \!\, T_c$ as well as an increase of $\sigma_0$ with $\mu_q^2/T^2$. Furthermore, the frequency dependence of the electric conductivity $\sigma(\Omega)$ shows a simple functional form well in line with results from the Dynamical QuasiParticle Model (DQPM). The spin susceptibility $\chi_S(T,\mu_q)$ is found to increase with temperature $T$ and to rise $\sim \mu_q ^2/T^2$, 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.