Electric conductivity of the quark-gluon plasma investigated using a perturbative QCD based parton cascade

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 $2\leftrightarrow 3$ perturbative QCD scattering. Comparing with recent lattice results, we find an agreement in the temperature dependence of the conductivity.

Figure 1

Top: Examples of electric current autocorrelation functions $C(t)$ at different temperatures, with the standard error over the full sample (210 runs) shown for selected points. Bottom: Electric current fluctuation over time from a single run.

Figure 2

The variance of the correlation function from the analytic formula from Eq. (24) compared to numerical results, using constant isotropic binary cross sections.

Figure 3

The typical picture of static electric current densities, established by constant electric fields of different strengths. The BAMPS calculations use a constant isotropic cross section of 3 mb and a temperature of 0.4 GeV. Here we show the average of 70 simulations.

Figure 4

For different electric field strengths, the electric conductivity is calculated and averaged. The standard error of the averaged currents is very small. For comparison, the corresponding Green-Kubo value is also plotted.

Figure 5

Numerical results for the electric conductivity compared to analytic formulas. A constant isotropic binary cross section of 3 mb is used in the system. Both methods from Sec. 4 show identical results.

Figure 6

Numerical results for the electric conductivity (filled symbols) compared to recent results from literature. The open symbols represent results from lattice QCD: PHSD [21], SYM [54], a nonconformal holographic model [24], lattice A [15], lattice B [19], lattice C [20], lattice D [14], lattice E [16], lattice F [18], and lattice G [17]. The electric charge is explicitly multiplied out, $e^2=4\pi /137$. Around $T=0.3\mathrm{GeV}$, results from Ref. [29] (not shown), using a Dyson-Schwinger approach, are consistent with the results from Ref. [20].