Analytical attractor for Bjorken expansion

TL;DR

This paper derives an analytic attractor solution for the evolution of boost-invariant plasmas, bridging the collisionless early stage and hydrodynamic late stage, illustrating the application of resurgence theory in asymptotic series.

Contribution

It provides the first explicit analytic attractor solution for Bjorken flow, connecting collisionless and hydrodynamic regimes, and demonstrates resurgence theory in this context.

Findings

Explicit attractor solution connecting regimes

Application of resurgence theory to plasma dynamics

Unified description of early and late-time behavior

Abstract

We present an analytic solution of a simple set of equations that govern the expansion of boost-invariant plasmas of massless particles. These equations describe, approximately, the early time, collisionless regime, and the transition to hydrodynamics at late time. Their mathematical structure encompasses all versions of second order hydrodynamics when applied to Bjorken flows. The analytic solution provides an explicit expression for the attractor solution that connects the collisionless regime to hydrodynamics. It also constitutes a neat example of an application of the theory of resurgence in asymptotic series.