  We present first results of classical-statistical real-time simulations of
anomalous transport phenomena with overlap fermions. We find that even on small
lattices overlap fermions reproduce the real-time anomaly equation with much
better precision than Wilson-Dirac fermions on an order of magnitude larger
lattices. The difference becomes much more pronounced for quickly changing
electromagnetic fields, especially if one takes into account the back-reaction
of fermions on electromagnetism. As test cases, we consider chirality pumping
in parallel electric and magnetic fields and mixing between the plasmon and the
Chiral Magnetic Wave.
