Response of a weakly magnetized hot QCD medium to inhomogeneous electric field

The electric charge transport in a weakly magnetized hot QCD medium has been investigated in the presence of an external inhomogeneous electric field. The current densities induced by the inhomogeneous electric field have been estimated in the regime where space-time inhomogeneity of the field is small so that the collisional effect in the medium cannot be neglected. The collisional aspect of the medium has been captured by employing both relaxation time approximation and Bhatnagar-Gross-Krook collision kernels in the relativistic Boltzmann equation. The magnetic field and quark chemical potential dependences of the electric current and Hall current densities have been explored, and the impact on the respective conductivities have been studied. Both the inhomogeneity of the field and collisional effects seem to have sizable effects on the electromagnetic responses of the medium.