Response of a weakly magnetized hot QCD medium to an 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 (electric and Hall) 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 a relaxation-time approximation and a Bhatnagar-Gross-Krook collision kernel in the relativistic Boltzmann equation. The magnetic field, momentum anisotropy, and quark chemical potential dependences of the electric current and Hall current densities have been explored, and the impacts on the respective conductivities have been studied. The inhomogeneities of the field are seen to have sizable effects on the electromagnetic responses of the collisional medium.