Non-perturbative rheological behavior of a far-from-equilibrium expanding plasma

TL;DR

This paper develops a non-perturbative, renormalized approach to understanding the rheological behavior of a far-from-equilibrium expanding plasma, revealing insights into transient non-Newtonian dynamics beyond linear response.

Contribution

It introduces a trans-series framework for hydrodynamization, incorporating non-perturbative effects and a new renormalization scheme for transport coefficients in relativistic kinetic theory.

Findings

Renormalized transport coefficients exhibit a transition to equilibrium fixed points.

The effective theory accurately predicts numerical solutions of evolution equations.

Transient rheological behavior explains fluid dynamics far from equilibrium.

Abstract

For the Bjorken flow we investigate the hydrodynamization of different modes of the one-particle distribution function by analyzing its relativistic kinetic equations. We calculate the constitutive relations of each mode written as a multi-parameter trans-series encoding the non-perturbative dissipative contributions quantified by the Knudsen $Kn$ and inverse Reynolds $Re^{-1}$ numbers. At any given order in the asymptotic expansion of each mode, the transport coefficients get effectively renormalized by summing over all non-perturbative sectors appearing in the trans-series. This gives an effective description of the transport coefficients that provides a new renormalization scheme with an associated renormalization group equation, going beyond the realms of linear response theory. As a result, the renormalized transport coefficients feature a transition to their equilibrium fixed point, which is a neat diagnostics of transient non-Newtonian behavior. As a proof of principle, we verify the predictions of the effective theory with the numerical solutions of their corresponding evolution equations. Our studies strongly suggest that the phenomenological success of fluid dynamics far from local thermal equilibrium is due to the transient rheological behavior of the fluid.