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.

14 pages, 14 figures

References in corpus (24)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Triangular flow in hydrodynamics and transport theory
• Imprints of fluctuating proton shapes on flow in proton-lead collisions at the LHC
• Collectivity and electromagnetic radiation in small systems
• Scalings of Elliptic Flow for a Fluid at Finite Shear Viscosity
• Electric Conductivity from the solution of the Relativistic Boltzmann Equation
• Relativistic Hydrodynamic Attractors with Broken Symmetries: Non-Conformal and Non-Homogeneous
• Bulk viscous evolution within anisotropic hydrodynamics
• Non-equilibrium attractor in high-temperature QCD plasmas
• Importance of initial and final state effects for azimuthal correlations in p+Pb collisions
• Hydrodynamization and non-equilibrium Green's functions in kinetic theory
• Establishing the Range of Applicability of Hydrodynamics in High-Energy Collisions
• Hydrodynamics from free-streaming to thermalization and back again
• Development of transverse flow at small and large opacities in conformal kinetic theory
• Relativistic Boltzmann transport approach with Bose-Einstein statistics and the onset of gluon condensation
• Hydrodynamic Attractors in Ultrarelativistic Nuclear Collisions
• Scaling and adiabaticity in a rapidly expanding gluon plasma
• Viscous corrections to anisotropic flow and transverse momentum spectra from transport theory
• Opacity dependence of transverse flow, pre-equilibrium and applicability of hydrodynamics in heavy-ion collisions
• Limiting attractors in heavy-ion collisions
• On differences between even and odd anisotropic-flow harmonics in non-equilibrated systems
• Early time behavior of spatial and momentum anisotropies in a kinetic approach to nuclear collisions
• Early time behavior of spatial and momentum anisotropies in kinetic theory across different Knudsen numbers
• Development of transverse flow for small and large systems in conformal kinetic theory

Cited by in corpus (2)

• Hydrodynamic attractor in periodically driven ultracold quantum gases
• Elliptic flow of charm quarks produced in the early stage of pA collisions