Spin kinetic theory with a nonlocal relaxation time approximation

We present a novel relaxation time approximation for kinetic theory with spin which takes into account the nonlocality of particle collisions. In particular, it models the property of the microscopic nonlocal collision term to vanish in global, but not in local equilibrium. We study the asymptotic distribution function obtained as the solution of the Boltzmann equation within the nonlocal relaxation time approximation in the limit of small gradients and short relaxation time. We show that the resulting polarization agrees with the one obtained from the Zubarev formalism for a certain value of a coefficient that determines the time scale on which orbital angular momentum is converted into spin. This coefficient can be identified with a parameter related to the pseudo gauge choice in the Zubarev formalism. Finally, we demonstrate how the nonlocal collision term generates polarization from vorticity by studying a nonrelativistic rotating cylinder both from kinetic and hydrodynamic approaches, which are shown to be equivalent in this example.