Spin polarization induced by the hydrodynamic gradients

A bstract We systematically analyze the effects of derivatives hydrodynamic fields on axial Wigner function that describes spin polarization vector in phase space. have included all possible first-order derivative contributions are allowed by symmetry and compute associated transport functions at one-loop using linear response theory. In addition to reproducing known due temperature gradient vorticity, we identified a number potentially significant overlooked previously. particular, find shear strength, symmetric traceless part flow gradient, will induce quadrupole for Our results, together with gradients obtained from simulations, can be employed as basis interpretation ? (anti-?) measurement heavy-ion collisions.