Attractors and Late Time Asymptotics in a Generalized Relativistic Second Order Spin Hydrodynamics

Abstract

We investigate the attractor of spin density in relativistic spin hydrodynamics using Zubarev's non-equilibrium statistical operator formalism in the spin probe limit. We derive the (0+1)D Bjorken flow equations and the associated attractor equation while retaining second order gradient corrections in the relevant relaxation constitutive equations including couplings associated with nonlinear response and nonlocal memory effects. We analyze the early time fixed point structure and analytically determine the early time attractor solution, thereby clarifying branch selection and the role of different dynamical corrections. We find that source-like driving terms modify the leading correction to the attractor solution without changing the fixed point structure, whereas self feedback terms involving the rotational stress tensor modify the dominant balance and modify the early time fixed point structure. We further analyze the late time asymptotics in the conformal limit and show that the newly added terms modify the algebraic prefactor and logarithmic phase shift, while leaving the leading late time decay unchanged. These results provide a unified picture of early time attractor and late time asymptotics in the conformal limit.