Far-from-Equilibrium Attractors and Universality in Ultra-Relativistic Heavy-Ion Collisions within Relativistic Kinetic Theory

TL;DR

This work investigates how ultra-relativistic heavy-ion collisions exhibit attractor dynamics and universal behavior when described by relativistic kinetic theory, bridging pre-equilibrium dynamics and hydrodynamic-like collectivity. By deploying the Relativistic Boltzmann Transport (RBT) code with full collision integrals, it demonstrates forward and pull-back attractors across 0+1D, 1+1D, and 3+1D settings, and analyzes how Knudsen number and opacity govern the approach to equilibrium. It reveals that universality emerges in conformal systems and partly persists in non-conformal cases when the speed of sound and proper time scaling are accounted for; in 3+1D, transverse dynamics introduce a pull-back attractor structure tied to Kn^{-1}_R, with event-by-event fluctuations generally preserving attractor trends in averaged observables. The findings provide a mesoscopic framework linking kinetic theory to hydrodynamics, clarifying when and how collective flows arise, and offering a scalable classification of collision systems by opacity/Knudsen scaling that informs interpretation of small-system collectivity and QGP phenomenology.

Abstract

This PhD Thesis is devoted to the study of the emergence of attractors, universality and collectivity in ultra-relativistic collisions by means of relativistic kinetic theory. After an introduction about Quantum Chromodynamics (QCD), Quark-Gluon Plasma (QGP) and the importance of heavy-ion collisions to investigate both, we give an overview about the two main models able to describe the hot QCD matter collective behaviour, namely kinetic theory and hydrodynamics. Afterwards, the Relativistic Boltzmann Transport (RBT) model, which has been employed to obtain most part of the results of this thesis, is carefully described, from the numerical and physical perspectives. The study of attractors and universality proceeds then by starting from a simple one-dimensional massless model, moving to increasingly more complex scenarios, involving the full 3+1D setup, non-conformal systems and realistic event-by-event fluctuations. Particular attention is paid to the physical scales which govern the system collectivity and their interplay. We show that a very good description of collective behaviour can be carried out by means of a few variables which characterise the systems under study.

Figures (56)

• Figure 1: Experimental determinations on the running $\alpha_s(Q)$ compared to the predictions computed at five loops taking as an input the current PDG average, $\alpha_s(m^2_Z) = 0.1180\pm0.0009$ParticleDataGroup:2024cfk.
• Figure 2: Summary of the hadron spectrum at the state-of-the-art point, where $m_\pi, m_K$ and $m_\Omega$ are used as inputs, while the others are accurately predicted by the theory. Figure from Ref.Aoyama:2024pts
• Figure 3: Signatures of collectivity in $pA$ (left panel, from CMS:2012qk) and high multiplicity $pp$ (right panel. from ALICE:2012eyl).
• Figure 4: Schematic picture of an uRHIC as pictured by Bjorken in the '80s Bjorken:1982qr in the left panel and as nowadays conceived in the right panel Braun-Munzinger:2018hat.
• Figure 5: A hand-written phase diagram ($T$ vs $P$) by Enrico Fermi in which nothing was predicted beyond $10^{12}$ K $\approx 200$ MeV, since the inverse of this energy scale is approximately the size of a proton (1 fm), which was then considered an elementary particle. Notice that there is a typo in the $x$ axis label (it is dyne/cm$^2$) fermi1966notes.