On non-conformal kinetic theory and hydrodynamics for Bjorken flow

TL;DR

This paper compares kinetic theory and second-order hydrodynamics in non-conformal Bjorken flow, revealing differences in attractor behavior and proposing a modified anisotropic hydrodynamics model that aligns well with kinetic theory.

Contribution

It introduces a new fixed point in free-streaming dynamics and demonstrates the limitations of second-order hydrodynamics in capturing far-from-equilibrium attractors.

Findings

Identification of fixed lines as early-time attractors and repellors.

Absence of attractor behavior in normalized shear stress channel.

Modified anisotropic hydrodynamics accurately reproduces kinetic theory results.

Abstract

Using and comparing kinetic theory and second-order Chapman-Enskog hydrodynamics, we study the non-conformal dynamics of a system undergoing Bjorken expansion. We use the concept of `free-streaming fixed lines' for scaled shear and bulk stresses in non-conformal kinetic theory and hydrodynamics, and show that these `fixed lines' behave as early-time attractors and repellors of the evolution. In the conformal limit, the free-streaming fixed lines reduce to the well-known fixed points of conformal Bjorken dynamics. A new fixed point in the free streaming regime is identified which lies at the intersection of these fixed lines. Contrary to the conformal scenario, both kinetic theory and hydrodynamics predict the absence of attractor behavior in the normalised shear stress channel. In kinetic theory a far-off-equilibrium attractor is found for the normalised effective longitudinal pressure, driven by rapid longitudinal expansion. Second-order viscous hydrodynamics fails to accurately describe this attractor. From a thorough analysis of the free-streaming dynamics in Chapman-Enskog hydrodynamics we conclude that this failure results from an inaccurate approximation of the fixed lines and a related incorrect description of the nature of the fixed point. A modified anisotropic hydrodynamic description is presented that provides excellent agreement with kinetic theory results and reproduces the far-from-equilibrium attractor for the scaled longitudinal pressure.