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

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.