Kinetic approach to a relativistic BEC with inelastic processes

Abstract

The phenomenon of Bose-Einstein condensation is investigated in the context of the Color-Glass-Condensate description of the initial state of ultrarelativistic heavy-ion collisions. For the first time, in this paper we study the influence of particle-number changing 2 ↔ 3 processes on the transient formation of a Bose-Einstein Condensate within an isotropic system of scalar bosons by including 2 ↔ 3 interactions of massive bosons with constant and isotropic cross sections, following a Boltzmann equation. The one-particle distribution function is decomposed in a condensate part and a non-zero momentum part of excited modes, leading to coupled integro-differential equations for the time evolution of the condensate and phase-space distribution function, which are then solved numerically. Our simulations converge to the expected equilibrium state, and only for σ 23 /σ 22 1 we find that a Bose-Einstein condensate emerges and decays within a finite lifetime in contrast to the case where only binary scattering processes are taken into account, and the condensate is stable due to particle-number conservation. Our calculations demonstrate that Bose-Einstein Condensates in the very early stage of heavy-ion collisions are highly unlikely, if inelastic collisions are significantly participating in the dynamical gluonic evolution.

Towards a full solution of the relativistic Boltzmann equation for quark-gluon matter on GPUs

“…[49][50][51][52][53]. However, it is argued that the inelastic scattering processes may strongly hinder the effect of gluon condensation [54,55]. In fact, the role of inelastic scatterings in the thermalization is still not quite clear so far.…”

Kinetic theory of overpopulated gluon systems with inelastic processes

“…Based on the two-particle irreducible (2PI) formalism to next-to-leading order in the 1/N expansion, the study in [19] show that the formation of a BEC is hindered by particle number changing processes. And recently, within a kinetic approach by including interactions of massive bosons with constant and isotropic cross sections, the simulations in [20] demonstrate that BECs are highly unlikely if inelastic collisions are significantly participating in the dynamical gluonic evolution. Different from the above mentioned works focusing on the dynamical formation of a transient BEC, we calclu-tate the net rate of the condensation ( net condensation rate ) for an overoccupied gluon system in thermal equilibrium, which can in turn give a hint whether a BEC can be formed.…”