Scaling and adiabaticity in a rapidly expanding gluon plasma

Abstract

In this work we aim to gain qualitative insight on the far-from-equilibrium behavior of the gluon plasma produced in the early stages of a heavy-ion collision. It was recently discovered arXiv:1810.10554 that the distribution functions of quarks and gluons in QCD effective kinetic theory (EKT) exhibit self-similar "scaling" evolution with time-dependent scaling exponents long before those exponents reach their pre-hydrodynamic fixed-point values. In this work we shed light on the origin of this time-dependent scaling phenomenon in the small-angle approximation to the Boltzmann equation. We first solve the Boltzmann equation numerically and find that time-dependent scaling is a feature of this kinetic theory, and that it captures key qualitative features of the scaling of hard gluons in QCD EKT. We then proceed to study scaling analytically and semi-analytically in this equation. We find that an appropriate momentum rescaling allows the scaling distribution to be identified as the instantaneous ground state of the operator describing the evolution of the distribution function, and the approach to the scaling function is described by the decay of the excited states. That is to say, there is a frame in which the system evolves adiabatically. Furthermore, from the conditions for adiabaticity we can derive evolution equations for the time-dependent scaling exponents. In addition to the known free-streaming and BMSS fixed points, we identify a new "dilute" fixed point when the number density becomes small before hydrodynamization. Corrections to the fixed point exponents in the small-angle approximation agree quantitatively with those found previously in QCD EKT and arise from the evolution of the ratio between hard and soft scales.

38 pages, 8 figures

References in corpus (5)

• The Color Glass Condensate
• On the equivalence between the Boltzmann equation and classical field theory at large occupation numbers
• The Hot QCD White Paper: Exploring the Phases of QCD at RHIC and the LHC
• Non-equilibrium attractor in high-temperature QCD plasmas
• QCD Splitting/Joining Functions at Finite Temperature in the Deep LPM Regime

Cited by in corpus (14)

• The Present and Future of QCD
• SU(2) Gauge Theory in $2+1$ Dimensions on a Plaquette Chain Obeys the Eigenstate Thermalization Hypothesis
• Hydrodynamic Attractors in Ultrarelativistic Nuclear Collisions
• Eigenstate Thermalization in 2+1 dimensional SU(2) Lattice Gauge Theory
• Universal dynamics and non-thermal fixed points in quantum fluids far from equilibrium
• Prescaling relaxation to nonthermal attractors
• Far-from-equilibrium attractors for massive kinetic theory in the relaxation time approximation
• Stable and unstable perturbations in universal scaling phenomena far from equilibrium
• Far-from-equilibrium attractors with Full Relativistic Boltzmann approach in 3+1 D: moments of distribution function and anisotropic flows $v_n$
• Soft-gluon exchange matters: isotropic screening in QCD kinetic theory
• Adiabatic Hydrodynamization and the Emergence of Attractors: a Unified Description of Hydrodynamization in Kinetic Theory
• Transport properties of the QCD medium
• Eigenstate Thermalization in 1+1-Dimensional SU(2) Lattice Gauge Theory Coupled with Dynamical Fermions
• Adiabatic hydrodynamization and quasinormal modes of nonthermal attractors