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 $T_c<T<2.5T_c$ 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.

Comments: 11 pages, 14 figures. arXiv admin note: text overlap with arXiv:1302.0906, matches published version