  Despite its importance for subjects ranging from cosmology to plasma physics,
first principle simulations of the dynamics associated with a U(1) chiral
anomaly have been started only recently. In this work, we report on the current
status of these investigations. We discuss a possible set-up and highlight some
results. We present a determination of the Chern-Simons diffusion rate, which
shows some discrepancy with the usual effective description which is anomalous
magnetohydrodynamic. We also present some exploratory results on the behaviour
of an initial chiral chemical potential.
