We demonstrate that the diffusion currents do not depend only on gradients of their corresponding charge density, but that the different diffusion charge currents are coupled. This happens in such a way that it is possible for density gradients of a given charge to generate dissipative currents of another charge. Within this scheme, the charge diffusion coefficient is best viewed as a matrix, in which the diagonal terms correspond to the usual charge diffusion coefficients, while the off-diagonal terms describe the coupling between the different currents. In this Letter, we calculate for the first time the complete diffusion matrix for hot and dense nuclear matter, including baryon, electric, and strangeness charges. We find that the baryon diffusion current is strongly affected by baryon charge gradients but also by its coupling to gradients in strangeness. The electric charge diffusion current is found to be strongly affected by electric and strangeness gradients, whereas strangeness currents depend mostly on strange and baryon gradients.

The bulk nuclear matter produced in heavy ion collisions carries a multitude of conserved quantum numbers: electric charge, baryon number, and strangeness. Therefore, the diffusion processes associated to these conserved charges cannot occur independently and must be described in terms of a set of coupled diffusion equations. This physics is implemented by replacing the traditional diffusion coefficients for each conserved charge by a diffusion coefficient matrix, which quantifies the coupling between the conserved quantum numbers. The diagonal coefficients of this matrix are the usual charge diffusion coefficients, while the off-diagonal entries describe the diffusive coupling of the charge currents. In this paper, we show how to calculate this diffusion coefficient matrix from kinetic theory and provide results for a hadron resonance gas and a gas of partons. We further find that the off-diagonal entries can reach similar magnitudes compared to the diagonal entries. In order to provide some insight on the influence that the coupling between the net charge diffusion currents can have on heavy ion observables, we present first results for the diffusive evolution of a hadronic system in a simple (1+1)D-fluid dynamics approach, and study different configurations of the diffusion matrix.

Electric conductivity is sensitive to effective cross sections among the particles of the partonic medium. We investigate the electric conductivity of a hot plasma of quarks and gluons, solving the relativistic Boltzmann equation. In order to extract this transport coefficient, we employ the Green-Kubo formalism and, independently, a method motivated by the classical definition of electric conductivity. To this end we evaluate the static electric diffusion current upon the influence of an electric field. Both methods give identical results. For the first time, we obtain numerically the Drude electric conductivity formula for an ultrarelativistic gas of quarks and gluons employing constant isotropic binary cross sections. Furthermore, we extract the electric conductivity for a system of massless quarks and gluons including screened binary and inelastic, radiative 2 ↔ 3 perturbative QCD scattering. Comparing with recent lattice results, we find an agreement in the temperature dependence of the conductivity.

An error was found in the labeling of hadronic cross sections, shown in Fig. 3(b) of this paper. The corrected calculations are shown here in the left panel of Fig. 1 and display minor differences from the original results. In the paper, Fig. 4 shows the result for all 11 species and the full set of cross sections in Table I. We argued that the dip at about T ¼ 100 MeV came from resonance peaks in the cross sections; however, it was found that it was due to a small numerical error. We show the corrected result in the right panel of Fig. 1 (red solid curve). We emphasize that no qualitative differences exist and the numerical errors did not affect any of the conclusions reached in this paper. Note that in the right panel of Fig. 1 we changed the unit of the temperature axis from GeV to the critical temperature T c to better compare to other results (e.g., lattice), which are sometimes exclusively given in units of a critical temperature. (For the calculations that do not have an intrinsic critical temperature, like ours, we use T c ¼ 160 MeV.) The lattice QCD results are from Refs. [1-3], and all other references are given in the original publication. Note that we only compute a hadron resonance gas, and all results above T ¼ T c are merely to show how our hadronic system would extrapolate at higher temperatures.

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