The chiral magnetic wave in an expanding QCD fluid

As a consequence of the chiral anomaly, the hydrodynamics of hot QCD matter coupled to QED allows for a long-wavelength mode of chiral charge density, the chiral magnetic wave (CMW), that provides for a mechanism of electric charge separation along the direction of an external magnetic field. Here, we investigate the efficiency of this mechanism for values of the time-dependent magnetic field and of the energy density attained in the hot QCD matter of ultra-relativistic heavy ion collisions. To this end, we derive the CMW equations of motion for expanding systems by treating the CMW as a charge perturbation on top of an expanding Bjorken-type background field in the limit of small chemical potential. Both, approximate analytical and full numerical solutions to these equations of motion indicate that for the lifetime and thermodynamic conditions of ultra-relativistic heavy ion collisions, the efficiency of CMW-induced electric charge separation decreases with increasing center of mass energy and that the effect is numerically very small. We note, however, that if sizable oriented asymmetries in the axial charge distribution (that are not induced by the CMW) are present in the early fluid dynamic evolution, then the mechanism of CMW-induced electric charge separation can be much more efficient.