# What attracts to attractors?

## TL;DR

This paper investigates how different theoretical models of heavy-ion collisions approach a universal attractor solution, revealing distinct early-time behaviors that could differentiate weakly and strongly coupled systems.

## Contribution

It demonstrates that in Israel-Stewart and kinetic theories, systems approach the attractor via power-law at early times, unlike in strongly coupled systems where approach coincides with hydrodynamization.

## Key findings

- Early-time approach is power-law in IS and kinetic theories.
- Late-time approach is exponential in these theories.
- In strongly coupled systems, the attractor coincides with hydrodynamization.

## Abstract

Whether, how, and to what extent solutions of Bjorken-expanding systems become insensitive to aspects of their initial conditions is of importance for heavy-ion collisions. Here we study 1+1D and phenomenologically relevant boost-invariant 3+1D systems in which initial conditions approach a universal attractor solution. In Israel-Stewart theory (IS) and kinetic theory where the universal attractor extends to arbitrarily early times, we show that all initial conditions approach the attractor at early times by a power-law while their approach is exponential at late times. In these theories, the physical mechanisms of hydrodynamization operational at late times do not drive the approach to the attractor at early times, and the early-time attractor is reached prior to hydrodynamization. In marked contrast, the attractor in strongly coupled systems is realized concurrent with hydrodynamization. This qualitative difference may offer a basis for discriminating weakly and strongly coupled scenarios of heavy-ion collisions.