Electromagnetic response in an expanding quark-gluon plasma

The validity of conventional Ohm's law is tested in the context of a rapidly evolving quark-gluon plasma produced in heavy-ion collisions. Here we discuss the electromagnetic response using an analytical solution in kinetic theory. As conjectured previously, after switching on an electric field in a nonexpanding plasma, the time-dependent current is given by $\mathbf{J}(t)=(1-e^{-t/\tau_0}) \sigma_{0} \mathbf{E}$, where $\tau_0$ is the transport relaxation time and $\sigma_{0}$ is the steady-state electrical conductivity. Such an incomplete electromagnetic response reduces the efficiency of the magnetic flux trapping in the quark-gluon plasma and may prevent the observation of the chiral magnetic effect. Here we extend the study to the case of a rapidly expanding plasma. We find that the decreasing temperature and the increasing transport relaxation time have opposite effects on the electromagnetic response. While the former suppresses the time-dependent conductivity, the latter enhances it.