Kinetic theory of a longitudinally expanding system of scalar particles

TL;DR

This paper investigates the limitations of the classical approximation in describing the evolution of an anisotropic scalar particle system undergoing longitudinal expansion, using the Boltzmann equation with Bose-Einstein condensate formation.

Contribution

It provides a quantitative analysis of the Boltzmann equation for an expanding scalar system, highlighting the inadequacy of the classical approximation in certain high-occupancy regimes.

Findings

Classical approximation may be insufficient for anisotropic expanding systems.

Full Boltzmann solutions do not follow classical attractor behavior under certain conditions.

Bose-Einstein condensate formation is considered in the kinetic evolution.

Abstract

A simple kinematical argument suggests that the classical approximation may be inadequate to describe the evolution of a system with an anisotropic particle distribution. In order to verify this quantitatively, we study the Boltzmann equation for a longitudinally expanding system of scalar particles interacting with a $\phi^4$ coupling, that mimics the kinematics of a heavy ion collision at very high energy. We consider only elastic $2\to 2$ scatterings, and we allow the formation of a Bose-Einstein condensate in overpopulated situations by solving the coupled equations for the particle distribution and the particle density in the zero mode. For generic CGC-like initial conditions with a large occupation number and a moderate coupling, the solutions of the full Boltzmann equation do not follow a classical attractor behavior.