Non-Abelian chiral instabilities at high temperature on the lattice

We report on an exploratory lattice study on the phenomenon of chiral instabilities in non-abelian gauge theories at high temperature. it is based on a recently constructed anomalous langevin-type effective theory of classical soft gauge fields in the presence of a chiral number density n 5 = n r − n l. evaluated in thermal equilibrium using classical lattice techniques it reveals that the fluctuating soft fields indeed exhibit a rapid energy increase at early times and we observe a clear dependence of the diffusion rate of topological charge (sphaleron rate) on the the initial n 5, relevant in both early universe baryogenesis and relativistic heavy-ion collisions. the topological charge furthermore shows a drift among distinct vacuum sectors, roughly proportional to the initial n 5 and in turn the chiral imbalance is monotonously reduced as required by helicity conservation.