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We derive the collision term in the Boltzmann equation using the equation of motion for the Wigner function of massive spin-1/2 particles. To next-to-lowest order in h, it contains a nonlocal contribution, which is responsible for the conversion of orbital into spin angular momentum. In a proper choice of pseudogauge, the antisymmetric part of the energy-momentum tensor arises solely from this nonlocal contribution. We show that the collision term vanishes in global equilibrium and that the spin potential is, then, equal to the thermal vorticity. In the nonrelativistic limit, the equations of motion for the energy-momentum and spin tensors reduce to the well-known form for hydrodynamics for micropolar fluids.
We compute neutrino emissivities, specific heat, and the resulting cooling rates in four spin-one color superconductors: color-spin locked, planar, polar, and A phases. In particular, the role of anisotropies and point nodes in the quasiparticle excitation spectra are investigated. Furthermore, it is shown that the A phase exhibits a helicity order, giving rise to a reflection asymmetry in the neutrino emissivity.
We compute the fermion spin distribution in the vortical fluid created in off-central high energy heavy-ion collisions. We employ the event-by-event (3+1)D viscous hydrodynamic model. The spin polarization density is proportional to the local fluid vorticity in quantum kinetic theory. As a result of strong collectivity, the spatial distribution of the local vorticity on the freeze-out hyper-surface strongly correlates to the rapidity and azimuthal angle distribution of fermion spins. We investigate the sensitivity of the local polarization to the initial fluid velocity in the hydrodynamic model and compute the global polarization of Λ hyperons by the AMPT model. The energy dependence of the global polarization agrees with the STAR data.