Far-from-equilibrium attractors with Full Relativistic Boltzmann approach in 3+1 D: moments of distribution function and anisotropic flows $v_n$

TL;DR

This study uses the Full Relativistic Boltzmann Transport approach in 3+1D to analyze universal behaviors in moments of distribution functions and anisotropic flows, revealing attractor phenomena and the influence of system size and interaction strength.

Contribution

It introduces a detailed analysis of universality classes, attractor behaviors, and the effects of system size and shear viscosity on flow harmonics in relativistic systems.

Findings

Universal early-time behavior of momentum moments and inverse Reynolds number.

Identification of attractor behavior in normalized elliptic flow $v_2/v_{2,eq}$.

Dependence of flow harmonics and azimuthal correlation dissipation on system size and $oldsymbol{rac{ ext{shear viscosity}}{ ext{entropy density}}}$.

Abstract

We employ the Full Relativistic Boltzmann Transport approach for a conformal system in 3+1D to study the universal behaviour in moments of the distribution function and anisotropic flows. We investigate different transverse system sizes $R$ and interaction strength $\eta/s$ and identify universality classes based upon the interplay between $R$ and the mean free path; we show that each of this classes can be identified by a particular value of the opacity $\hat \gamma$, which has been previously introduced in literature. Our results highlight that, at early times, the inverse Reynolds number and momentum moments of the distribution function display universal behaviour, converging to a 1D attractor driven by longitudinal expansion. This indicates that systems of different sizes and interaction strengths tend to approach equilibrium in a similar manner. We provide a detailed analysis of how the onset of transverse flow affects these moments at later times. Moreover, we investigate the system size and $\eta/s$ dependence for the harmonic flows $v_2$, $v_3$, $v_4$ and their response functions, along with the impact of the $\eta/s$ and the system transverse size on the dissipation of initial azimuthal correlations in momentum space. Finally, we introduce the normalised elliptic flow $v_2/v_{2,eq}$, showing the emergence of attractor behaviour in the regime of large opacity. These results offer new insights into how different systems evolve towards equilibrium and the role that system size and interaction play in this process.