Early time behavior of spatial and momentum anisotropies in kinetic theory across different Knudsen numbers

TL;DR

This paper studies how spatial and momentum anisotropies develop early in a fireball's evolution across different interaction regimes, revealing a power-law behavior influenced by rescattering levels.

Contribution

It introduces a simple power-law model for early anisotropic flow development and provides semi-analytical calculations that match numerical simulations across regimes.

Findings

Early anisotropic flow follows a power-law with an exponent depending on rescatterings.

Semi-analytical calculations accurately reproduce numerical simulation results.

The onset of flow measures can be described across different Knudsen numbers.

Abstract

We investigate the early time development of the anisotropic transverse flow and spatial eccentricities of a fireball with various particle-based transport approaches using a fixed initial condition. In numerical simulations ranging from the quasi-collisionless case to the hydrodynamic regime, we find that the onset of $v_n$ and of related measures of anisotropic flow can be described with a simple power-law ansatz, with an exponent that depends on the amount of rescatterings in the system. In the few-rescatterings regime we perform semi-analytical calculations, based on a systematic expansion in powers of time and the cross section, which can reproduce the numerical findings.