Far-from-equilibrium attractors with a realistic non-conformal equation of state

TL;DR

This paper investigates the early and late-time attractor behaviors in non-conformal hydrodynamic systems with realistic equations of state, revealing universal and semi-universal features in their evolution.

Contribution

It demonstrates for the first time the absence of strict late-time attractors in systems with realistic equations of state, extending previous constant-mass studies.

Findings

Longitudinal pressure evolution converges to a universal early-time curve.

Bulk and shear viscous corrections do not exhibit early-time attractor behavior.

Late-time evolution shows semi-universal features despite the absence of strict attractors.

Abstract

Using anisotropic hydrodynamics, we examine the existence of early-time attractors of non-conformal systems undergoing Bjorken expansion. In the case of a constant mass, we find that the evolution of the scaled longitudinal pressure is insensitive to variations of initial conditions converging onto an early-time universal curve and eventually merging with the late-time Navier-Stokes attractor (the hydrodynamic attractor). On the other hand, the bulk and the shear viscous corrections do not show an early-time attractor behavior. These results are consistent with previous studies considering a constant mass. When a realistic equation of state is included in the dynamics with a thermal mass, we demonstrate for the first time the absence of strict late-time universal attractors. However, a semi-universal feature of the evolution at very late times remains.