Novel hydrodynamic features in dissipative spin-polarized fluids
We investigate an extension of perfect spin hydrodynamics that includes dissipation in the spin sector. The presence of dissipation implies that antisymmetric parts of the energy-momentum tensor should be taken into account. Their form follows from the Navier-Stokes or Israel-Stewart theory, which introduces a priori unknown kinetic coefficients and relaxation times. We find that the inclusion of the antisymmetric parts of the energy-momentum tensor has twofold effects: i) they form source terms for the spin tensor allowing for the transfer between the spin and orbital parts of the total angular momentum (spin-orbit interaction) and ii) they appear in the conservation laws for the energy and linear momentum, indirectly affecting the spin dynamics. Numerical results are obtained for two boost-invariant expansion geometries: one-dimensional longitudinal motion (Bjorken model) and two-dimensional boost-invariant and cylindrically symmetric expansion. They indicate (for various choices of the spin kinetic coefficients and the relaxation times) that the spin polarization tensor approaches thermal vorticity. We also observe that Israel-Stewart dynamics on the way to local equilibrium approaches first the Navier-Stokes regime. In general, we find that the Israel-Stewart formalism naturally helps to consistently combine the conservation laws for linear and angular momentum, while the Navier-Stokes framework itself can lead to a disruption in the structure of the equations through the inclusion of terms involving derivatives of an order higher than one.