Global flow structure and exact formal transseries of the Gubser flow in kinetic theory

TL;DR

This paper analyzes the global flow structure of Gubser flow in kinetic theory, classifies invariant manifolds, constructs formal solutions, and shows that Gubser-like systems do not hydrodynamize, contrasting with simpler plasma models.

Contribution

It provides a comprehensive topological classification of the flow and formal transseries solutions for Gubser flow, revealing the failure of hydrodynamization in these systems.

Findings

Gubser flow has a complex invariant manifold structure.

Formal transseries solutions are purely perturbative with finite convergence.

Gubser-like systems do not hydrodynamize, unlike simpler plasma models.

Abstract

In this work we introduce the generic conditions for the existence of a non-equilibrium attractor that is an invariant manifold determined by the long-wavelength modes of the physical system. We investigate the topological properties of the global flow structure of the Gubser flow for the Israel-Stewart theory and a kinetic model for the Boltzmann equation by employing Morse-Smale theory. We present a complete classification of the invariant submanifolds of the flow and determine all the possible flow lines connecting any pair of UV/IR fixed points. The formal transseries solutions to the Gubser dynamical system around the early-time (UV) and late-time (IR) fixed points are constructed and analyzed. It is proven that these solutions are purely perturbative (or power-law asymptotic) series with a finite radius of convergence. Based on these analyses, we find that Gubser-like expanding kinetic systems do not hydrodynamize owing to the failure of the hydrodynamization process which heavily relies on the classification of (non)hydrodynamic modes in the IR regime. This is in contrast to longitudinal boost-invariant plasmas where the asymptotic dynamics is described by a few terms of the hydrodynamic gradient expansion. We finally compare our results for both Bjorken and Gubser conformal kinetic models.