will give an overview on the relevance of anomalous and topological
effects in far-from-equilibrium situations such as heavy ion collisions.
To this end I present
a first-principles study of anomaly induced transport phenomena by
performing real-time lattice simulations with dynamical fermions coupled
simultaneously to non-Abelian SU(Nc) and Abelian U(1) gauge fields.
Investigating the behavior of vector and axial currents during a
sphaleron transition in the presence of an external magnetic field, I
demonstrate how the interplay of the chiral magnetic and chiral
separation effect leads to the formation of a propagating wave.
I will give an overview over perspectives and ideas behind the recently
proposed framework of chiral kinetic theory can be understood from fundamental
principles and comment on the role of geometric phases. While these
ideas might be used to connect various 'stages' of a heavy ion
collision, they might also be utilized in the context of chiral instabilities in a cosmological context.