Longitudinal conductivity of hot magnetized collisional QCD medium in the inhomogeneous electric field

The longitudinal current density induced by the inhomogeneous electric field in the hot magnetized quark-gluon plasma has been investigated and utilized in obtaining the conductivity of the medium. The analysis has been done in the regime where inhomogeneity of the field is small so that the collision effect could be significant. The modeling of the QCD medium is based on a quasiparticle description where the medium effects have been encoded in the effective quarks, antiquarks and gluons. The temperature dependence of the linear longitudinal current density (in terms of the electric field) and the additional components of current density due to the inhomogeneity of the electric field (in terms of its derivatives) have been obtained by solving the ($1+1$)-dimensional effective covariant kinetic theory with a proper collision term. The conductivity has been obtained from the current density in the presence of the inhomogeneous field. The collisional aspects of the medium have been captured by including both the thermal relaxation approximation and the Bhatnagar-Gross-Krook collision kernels in the analysis. Further, the hot QCD medium effects and higher Landau level contributions to the current density and the conductivity have been investigated. It has been seen that the effects of inhomogeneity of the field and the mean field corrections to the current density and the conductivity are more visible in the temperature regions which are not far from the transition temperature.

Figure 1

Temperature behavior of the ratio $R_{zz}$ at $|eB|=10m_{\pi }^2$ for RTA and BGK collision kernels considering up to 20 LLs.

Figure 2

Behavior of ${\sigma }_{zz}/T$ in the LLL approximation of quarks or antiquarks as a function of temperature at $|eB|=10m_{\pi }^2$ within the RTA. The one-loop LLL result for the linear component has been taken from [30] for the same value of the magnetic field.

Figure 3

(Left panel) The effect of HLLs on the temperature behavior of ${\sigma }_{zz}/T$ at $|eB|=10m_{\pi }^2$. (Right panel) Mean field corrections to ${\sigma }_{zz}/T$ with the RTA and BGK collision integrals considering up to 20 LLs. The results are also compared with the BAMPS estimation at $B=0$ [61].