Non-conformal attractor in boost-invariant plasmas

TL;DR

This paper investigates how non-zero particle mass affects the evolution and attractor behavior of expanding plasmas, revealing that mass significantly alters the approach to hydrodynamics and the nature of non-equilibrium attractors.

Contribution

It demonstrates that breaking conformal symmetry with mass modifies the attractor structure in expanding plasmas, especially affecting shear and bulk viscous pressures.

Findings

Mass induces a non-zero bulk viscous pressure.

Shear and bulk pressures relax slowly to attractors, approaching hydrodynamics late.

Longitudinal pressure shows early attractor behavior despite mass effects.

Abstract

We study the dissipative evolution of (0+1)-dimensionally expanding media with Bjorken symmetry using the Boltzmann equation for massive particles in relaxation-time approximation. Breaking conformal symmetry by a mass induces a non-zero bulk viscous pressure in the medium. It is shown that even a small mass (in units of the local temperature) drastically modifies the well-known attractor for the shear Reynolds number previously observed in massless systems. For generic nonzero particle mass, neither the shear nor the bulk viscous pressure relax quickly to a non-equilibrium attractor; they approach the hydrodynamic limit only late, at small values of the inverse Reynolds numbers. Only the longitudinal pressure, which is a combination of thermal, shear and bulk viscous pressures, continues to show early approach to a far-off-equilibrium attractor, driven by the rapid longitudinal expansion at early times. Second-order dissipative hydrodynamics based on a gradient expansion around locally isotropic thermal equilibrium fails to reproduce this attractor.