Electric conductivity and flavor diffusion in a viscous, resistive quark-gluon plasma for weak and strong magnetic fields

Abstract

We present a microscopic calculation of the electric conductivity and net-particle diffusion coefficients for a viscous and resistive ultra-relativistic plasma. Our results might be of interest for several astrophysical and cosmological problems, but the main physical application we have in mind is the hot deconfined matter produced in relativistic heavy-ion collisions. Accordingly, as charged particles of the medium we take three species (flavors) of light (massless for the sake of simplicity) quarks -- $u$, $d$ and $s$ -- and antiquarks, entailing the existence of three macroscopic conserved charges: baryon number ${\cal B}$, electric charge $Q$ and strangeness $S$. Our results are valid both in a weakly and in a strongly-magnetized plasma, where the energy stored in the magnetic field is comparable to the one carried by the medium particles. Actually, for a conformal fluid, the behavior of the system only depends on the ratio between the thermal and the magnetic pressure, the so-called plasma beta-parameter, acting as a scaling variable. Our calculation, starting from a relativistic Boltzmann-Vlasov equation, is based on a generalized Chapman-Enskog approach in which space-time gradients and the local electric field are treated as first-order quantities in a perturbative expansion, while terms containing magnetic corrections are considered of zeroth order and hence self-consistently resummed. We find that, also in the strong-field limit, for each conserved charge a generalized Wiedemann-Franz law, connecting charge conductivity and diffusion coefficient, exists. However these transport coefficients acquire a non-trivial tensor structure, reflecting the development of a longitudinal, a transverse and a Hall current as a response to electric fields or density gradients.