Kinetic approach to a relativistic Bose-Einstein condensate

TL;DR

This paper develops a kinetic model for a relativistic Bose-Einstein condensate using Boltzmann equations, compares it with Monte Carlo simulations, and explores turbulent cascades in overpopulated scalar boson systems.

Contribution

It introduces a coupled set of evolution equations for a relativistic BEC and demonstrates their efficiency and accuracy through comparison with Monte Carlo simulations.

Findings

Observation of self-similar particle cascade evolution.

Identification of non-relativistic turbulent scaling in the infrared.

Confirmation of relativistic energy cascade and weak wave turbulence.

Abstract

We apply a Boltzmann approach to the kinetic regime of a relativistic Bose-Einstein condensate of scalar bosons by decomposing the one-particle distribution function in a condensate part and a non-zero momentum part of excited modes, leading to a coupled set of evolution equations which are then solved efficiently with an adaptive higher order Runge-Kutta scheme. We compare our results to the partonic cascade Monte-Carlo simulation BAMPS for a critical but far from equilibrium case of massless bosons. Motivated by the color glass condensate initial conditions in QCD with a strongly overpopulated initial glasma state, we also discuss the time evolution starting from an overpopulated initial distribution function of massive scalar bosons. In this system a self-similar evolution of the particle cascade with a non-relativistic turbulent scaling in the infrared sector is observed as well as a relativistic exponent for the direct energy cascade, confirming a weak wave turbulence in the ultraviolet region.