The anisotropic non-equilibrium hydrodynamic attractor

Abstract

We determine the dynamical attractors associated with anisotropic hydrodynamics (aHydro) and the DNMR equations for a 0+1d conformal system using kinetic theory in the relaxation time approximation. We compare our results to the non-equilibrium attractor obtained from exact solution of the 0+1d conformal Boltzmann equation, Navier-Stokes theory, and second-order Mueller-Israel-Stewart theory. We demonstrate that the aHydro attractor equation resums an infinite number of terms in the inverse Reynolds number. The resulting resummed aHydro attractor possesses a positive longitudinal to transverse pressure ratio and is virtually indistinguishable from the exact attractor. This suggests that kinetic theory involves not only a resummation in gradients (Knudsen number) but also a novel resummation in inverse Reynolds number. We also demonstrate that the DNMR result provides a better approximation to the exact kinetic theory attractor than Mueller-Israel-Stewart theory. Finally, we introduce a new method for obtaining approximate aHydro equations which relies solely on an expansion in inverse Reynolds number, carry out this expansion to third order, and compare these third-order results to the exact kinetic theory solution.