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Description
The measurement of the polarization of Lambda-hyperons in non-central heavy-ion collisions has shown that non-vanishing orbital momentum is converted into spin, which is a realization of the time-honored Barnett effect known from condensed-matter physics in strong-interaction matter. This observation has triggered a substantial effort from the theory side to describe the measured polarization signal, but so far without undisputed success. One obvious candidate to describe the experimental findings is a theory of spin hydrodynamics, i.e., ordinary hydrodynamics extended by spin degrees of freedom. In this talk, I will review the derivation of spin hydrodynamics from kinetic theory in the form of the Boltzmann equation. At next-to-leading order in Planck’s constant, the Boltzmann equation contains a novel non-local collision term, which provides a microscopic mechanism to convert orbital angular momentum into spin and vice versa. Applying the method of moments, the equations of motion for second-order dissipative spin hydrodynamics are derived. Dissipative spin degrees of freedom follow relaxation equations, similar to those for the ordinary dissipative quantities like the shear-stress tensor. The relaxation time scales for the dissipative spin degrees of freedom are shorter than those of the ordinary dissipative quantities, which warrants to approximate the former by their Navier-Stokes values. However, the spin potential, which is the Lagrange multiplier for the conservation of total angular momentum, follows a damped wave equations, where the damping time scale can be much longer than the shear-relaxation time scale. This implies that one has to solve the full system of evolution equations for spin hydrodynamics, before quantitative conclusions for polarization observables can be drawn. A prospect of how to achieve this is given at the end of the talk.
