Hydrodynamization in kinetic theory: Transient modes and the gradient expansion

TL;DR

This paper investigates how hydrodynamic behavior emerges from kinetic theory in quark-gluon plasma, revealing the role of transient modes and the nature of the gradient expansion's divergence.

Contribution

It demonstrates that the gradient expansion's divergence is due to transient modes and shows the emergence of hydrodynamics is similar in weakly and strongly coupled models.

Findings

Gradient expansion has zero radius of convergence due to transient modes.

Hydrodynamic behavior emerges via similar mechanisms in weakly and strongly coupled theories.

Not all singularities in the Borel plane correspond to physical transient modes.

Abstract

We explore the transition to hydrodynamics in a weakly-coupled model of quark-gluon plasma given by kinetic theory in the relaxation time approximation with conformal symmetry. We demonstrate that the gradient expansion in this model has a vanishing radius of convergence due to the presence of a transient (nonhydrodynamic) mode, in a way similar to results obtained earlier in strongly-coupled gauge theories. This suggests that the mechanism by which hydrodynamic behaviour emerges is the same, which we further corroborate by a novel comparison between solutions of different weakly and strongly coupled models. However, in contrast with other known cases, we find that not all the singularities of the analytic continuation of the Borel transform of the gradient expansion correspond to transient excitations of the microscopic system: some of them reflect analytic properties of the kinetic equation when the proper time is continued to complex values.