Analytic solutions of relativistic dissipative spin hydrodynamics with Bjorken expansion

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 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 similar to tau-1 and similar to tau-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.

Automated summary

By studying analytically the longitudinally boost-invariant motion of a relativistic dissipative fluid with spin, we have derived analytic solutions for spin density and spin chemical potential as functions of proper time tau, showing that they decay at rates similar to tau-1 and tau-1/3, respectively. These solutions provide insights into spin polarization dynamics in relativistic heavy-ion collisions and serve as test beds for further numerical simulations.