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.
Highlights
Introduction and motivationA long standing problem in the theoretical study of heavy ion collisions is the time evolution of the pressure tensor and its isotropization [1,2,3,4,5,6,7,8,9,10,11,12]
In order to verify this quantitatively, we study the Boltzmann equation for a longitudinally expanding system of scalar particles interacting with a φ4 coupling, that mimics the kinematics of a heavy ion collision at very high energy
This paper started with the qualitative observation that large-angle out-of-plane scatterings are artificially suppressed by the classical approximation of the collision term in the Boltzmann equation with 2 → 2 scatterings, when the particle distribution is anisotropic, as is generically the case for a system subject to a fast longitudinal expansion
Summary
A long standing problem in the theoretical study of heavy ion collisions is the time evolution of the pressure tensor and its isotropization [1,2,3,4,5,6,7,8,9,10,11,12]. On timescales of the order of a few Q−s 1 (Qs is the saturation momentum), the longitudinal pressure rises, and reaches a positive value of comparable magnitude to the transverse pressure It is unclear whether the scatterings are strong enough to sustain this mild anisotropy, or whether the longitudinal expansion wins and causes the anisotropy to increase. This regime may be addressed by various tools It corresponds to a period where the gluon occupation number is still large compared to 1, but small compared to the inverse coupling g−2 so that a quasi-particle picture may be valid. This means that the system could in principle be described either in terms of fields or in terms of particles. In a description in terms of particles, i.e. kinetic theory, this amounts to keeping in the collision integral of the Boltzmann equation only the terms that have the highest degree in the occupation number [21,22,23]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
