Chiral magnetic effect out of equilibrium

We consider relativistic fermionic systems in lattice regularization out of equilibrium. The chiral magnetic conductivity σCME is calculated in a spatially infinite system for the case when the chiral chemical potential depends on time, while the system initially was in thermal equilibrium at a small but nonzero temperature. We find that the frequency-dependent σCME(ω) for any nonzero ω both in the limits ω≪T and ω≫T is equal to its conventional value 1 when the lattice model approaches the continuum limit. Notice that σCME=0 for the case when the chiral chemical potential does not depend on time at all. We therefore confirm that the limit of vanishing ω is not regular for the spatially infinite systems of massless fermions.