The anisotropic non-equilibrium hydrodynamic attractor

TL;DR

This paper investigates the dynamical attractors in anisotropic hydrodynamics and related theories for a 0+1d conformal system, showing that aHydro provides a near-perfect resummation of kinetic theory results, surpassing traditional second-order theories.

Contribution

It introduces a new method for deriving approximate anisotropic hydrodynamics equations based on inverse Reynolds number expansion and compares it with exact kinetic theory solutions.

Findings

aHydro attractor closely matches the exact kinetic theory attractor.

aHydro resums an infinite series of inverse Reynolds number terms.

DNMR theory outperforms Mueller-Israel-Stewart in approximating the exact 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.