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We study the dynamical evolution of the so-called chiral magnetic effect inan electromagnetic conductor. To this end, we consider the coupled set ofcorresponding Maxwell and chiral anomaly equations, and we prove that these canbe derived from chiral kinetic theory. After integrating the chiral anomalyequation over space in a closed volume, it leads to a quantum conservation lawof the total helicity of the system. A change in the magnetic helicity densitycomes together with a modification of the chiral fermion density. We study inFourier space the coupled set of anomalous equations and we obtain thedynamical evolution of the magnetic fields, magnetic helicity density, andchiral fermion imbalance. Depending on the initial conditions we observe howthe helicity might be transferred from the fermions to the magnetic fields, orvice versa, and find that the rate of this transfer also depends on the scaleof wavelengths of the gauge fields in consideration. We then focus ourattention on the quark-gluon plasma phase, and analyze the dynamical evolutionof the chiral magnetic effect in a very simple toy model. We conclude that anexisting chiral fermion imbalance in peripheral heavy ion collisions wouldaffect the magnetic field dynamics, and consequently, the charge dependentcorrelations measured in these experiments.

Dynamical evolution of the chiral magnetic effect: Applications to the quark-gluon plasma