Analytical attractor for Bjorken flows

Jean-Paul Blaizot,Li Yan

doi:10.1016/j.physletb.2021.136478

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.

Highlights

We present an analytic solution of a simple set of equations that govern the expansion of boostinvariant plasmas of massless particles
While hydrodynamics is often viewed as an effective theory for long wavelength modes with microscopic degrees of freedom near local equilibrium, implying small gradients and small mean free paths, a number of recent studies suggest that it may work even when these conditions are not fully satisfied
It was found for instance that viscous corrections can account for the large pressure anisotropy in the longitudinally expanding plasma formed in heavy ion collisions, for either a strongly coupled system in holography [3], or a weakly coupled system in kinetic theory [4]

Summary

Introduction

We present an analytic solution of a simple set of equations that govern the expansion of boostinvariant plasmas of massless particles. An important progress has been the identification of attractor solutions in dynamical equations whose late time behavior is hydrodynamical [5,6,7,8]. This letter aims to contribute to this general discussion by providing an explicit analytical solution for a simple set of equations that describes the transition from kinetics to hydrodynamics for a rapidly expanding plasma of massless particles.

Objectives

Results

Conclusion