Analytic solutions of relativistic dissipative spin hydrodynamics with Bjorken expansion
Dong-Lin Wang, Shuo Fang, Shi Pu
Abstract
We have studied analytically the longitudinally boost-invariant motion of a relativistic dissipative fluid with spin. We have derived the analytic solutions of spin density and spin chemical potential as a function of proper time $\ensuremath{\tau}$ in the presence of the viscous tensor and the second order relaxation time corrections for spin. Interestingly, analogous to the ordinary particle number density and chemical potential, we find that the spin density and spin chemical potential decay as $\ensuremath{\sim}{\ensuremath{\tau}}^{\ensuremath{-}1}$ and $\ensuremath{\sim}{\ensuremath{\tau}}^{\ensuremath{-}1/3}$, respectively. These solutions can serve both to gain insight on the dynamics of spin polarization in relativistic heavy-ion collisions and as test beds for further numerical codes.