Non-equilibrium Chiral Magnetic/Vortical Effects in Viscous Fluids

We utilize the chiral kinetic theory in a relaxation-time approximation to investigate the nonlinear anomalous responses of chiral fluids with viscous effects. Unlike the cases in equilibrium, it is found that the chiral magnetic effect and chiral vortical effect are modified by the shear and bulk strengths. Particularly, the shear strength could result in charged Hall currents for chiral magnetic and chiral vortical effects, which propagate perpendicular to applied magnetic fields and vorticity. These quantum corrections stemming from side jumps and anomalies are dissipative and pertinent to interactions. Although the non-equilibrium effects upon charge currents are dissipative, the second law of thermodynamics is still satisfied.