We will be giving an overview over topological and anomalous phenomena relevant for heavy ion collisions. To this end we 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, we demonstrate how the interplay of the chiral magnetic and chiral separation effect leads to the formation of a propagating wave. We further analyze the dependence of the magnitude of the induced vector current and the propagation of the wave on the amount of explicit chiral symmetry breaking due to finite quark masses. Further we perform simulations using overlap-fermions for the first time in real-time, showing that in the classical statistical regime they can be related to the Wilson formulation.
