Transasymptotics and hydrodynamization of the Fokker-Planck equation for gluons

Abstract

We investigate the non-linear transport processes and hydrodynamization of a system of gluons undergoing longitudinal boost-invariant expansion. The dynamics is described within the framework of the Boltzmann equation in the small-angle approximation. The kinetic equations for a suitable set of moments of the one-particle distribution function are derived. By investigating the stability and asymptotic resurgent properties of this dynamical system, we demonstrate, that its solutions exhibit a rather different behavior for large (UV) and small (IR) effective Knudsen numbers. Close to the forward attractor in the IR regime the constitutive relations of each moment can be written as a multiparameter transseries. This resummation scheme allows us to extend the definition of a transport coefficient to the non-equilibrium regime naturally. Each transport coefficient is renormalized by the non-perturbative contributions of the non-hydrodynamic modes. The Knudsen number dependence of the transport coefficient is governed by the corresponding renormalization group flow equation. An interesting feature of the Yang-Mills plasma in this regime is that it exhibits transient non-Newtonian behavior while hydrodynamizing. In the UV regime the solution for the moments can be written as a power-law asymptotic series with a finite radius of convergence. We show that radius of convergence of the UV perturbative expansion grows linearly as a function of the shear viscosity to entropy density ratio. Finally, we compare the universal properties in the pullback and forward attracting regions to other kinetic models including the relaxation time approximation and the effective kinetic Arnold-Moore-Yaffe (AMY) theory.

arXiv commentv2: 23 pages + appendices, 7 figures, updated references. Added new subsection IVB which is related with transasymptotic matching and RG flow equations of 1st. and 2nd. order transport coefficients for the most general case. Accepted for publication in PRD

References in corpus (97)

• Collective flow and viscosity in relativistic heavy-ion collisions
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Long-range angular correlations on the near and away side in p-Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV
• Hydrodynamic Modeling of Heavy-Ion Collisions
• How Much do Heavy Quarks Thermalize in a Heavy Ion Collision?
• Observation of Associated Near-side and Away-side Long-range Correlations in sqrt(s_NN)=5.02 TeV Proton-lead Collisions with the ATLAS Detector
• Multiplicity and transverse-momentum dependence of two- and four-particle correlations in pPb and PbPb collisions
• Effective Kinetic Theory for High Temperature Gauge Theories
• New theories of relativistic hydrodynamics in the LHC era
• Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation
• Creating small circular, elliptical, and triangular droplets of quark-gluon plasma
• Quadrupole Anisotropy in Dihadron Azimuthal Correlations in Central $d$$+$Au Collisions at $\sqrt{s_{{}_{NN}}}$=200 GeV
• Isotropization and hydrodynamization in weakly coupled heavy-ion collisions
• Symmetry constraints on generalizations of Bjorken flow
• Dissipative relativistic fluid dynamics: a new way to derive the equations of motion from kinetic theory
• One fluid to rule them all: viscous hydrodynamic description of event-by-event central p+p, p+Pb and Pb+Pb collisions at $\sqrt{s}=5.02$ TeV
• Turbulent thermalization process in heavy-ion collisions at ultrarelativistic energies
• Universal attractor in a highly occupied non-Abelian plasma
• Fluid Dynamics far from Local Equilibrium
• Radiative energy loss and v2 spectra for viscous hydrodynamics
• Testing viscous and anisotropic hydrodynamics in an exactly solvable case
• Matching the Nonequilibrium Initial Stage of Heavy Ion Collisions to Hydrodynamics with QCD Kinetic Theory
• Effective kinetic description of event-by-event pre-equilibrium dynamics in high-energy heavy-ion collisions
• Elliptic Flow and HBT in non-central Nuclear Collisions
• Conformal hydrodynamics in Minkowski and de Sitter spacetimes
• Toward Equilibration in the Early Stages After a High Energy Heavy Ion Collision
• Anisotropic Hydrodynamics for Rapidly Expanding Systems
• Relativistic third-order dissipative fluid dynamics from kinetic theory
• A new exact solution of the relativistic Boltzmann equation and its hydrodynamic limit
• Origin of the Relaxation Time in Dissipative Fluid Dynamics
• Hydrodynamization in kinetic theory: Transient modes and the gradient expansion
• Relativistic dissipative hydrodynamics from kinetic theory with relaxation time approximation
• Derivation of fluid dynamics from kinetic theory with the 14--moment approximation
• Viscosities of Quark-Gluon Plasmas
• Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation
• Fluid dynamics of out of equilibrium boost invariant plasmas
• The First fm/c of Heavy-Ion Collisions
• Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow
• What attracts to attractors?
• The Boltzmann equation for gluons at early times after a heavy ion collision
• Entropy Production, Hydrodynamics, and Resurgence in the Primordial Quark-Gluon Plasma from Holography
• On the hydrodynamic attractor of Yang-Mills plasma
• Do nuclear collisions create a locally equilibrated quark-gluon plasma?
• Relativistic (Lattice) Boltzmann Equation with Non-Ideal Equation of State
• RG Flows and Bifurcations
• The non-equilibrium attractor for kinetic theory in relaxation time approximation
• Hydrodynamic attractors, initial state energy and particle production in relativistic nuclear collisions
• UV Cascade in Classical Yang-Mills via Kinetic Theory
• Exact solution of the (0+1)-dimensional Boltzmann equation for a massive gas
• Resurgence in Extended Hydrodynamics
• Flow in AA and pA as an interplay of fluid-like and non-fluid like excitations
• Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation
• On the formation of singularities of solutions of nonlinear differential systems in antistokes directions
• Gluon Transport Equation in the Small Angle Approximation and the Onset of Bose-Einstein Condensation
• Quark production, Bose-Einstein condensates and thermalization of the quark-gluon plasma
• Hydrodynamics, resurgence and trans-asymptotics
• Spectral densities for hot QCD plasmas in a leading log approximation
• Bjorken Flow, Plasma Instabilities, and Thermalization
• Non-equilibrium attractor in high-temperature QCD plasmas
• Shear-bulk coupling in nonconformal hydrodynamics
• Prescaling and far-from-equilibrium hydrodynamics in the quark-gluon plasma
• From colored glass condensate to gluon plasma: equilibration in high energy heavy ion collisions
• Relativistic third-order viscous corrections to the entropy four-current from kinetic theory
• Exact solutions and attractors of higher-order viscous fluid dynamics for Bjorken flow
• Anisotropic flow far from equilibrium
• Analytic solution of the Boltzmann equation in an expanding system
• Constraining relativistic viscous hydrodynamical evolution
• Resurgence and Hydrodynamic Attractors in Gauss-Bonnet Holography
• Emergence of hydrodynamical behavior in expanding quark-gluon plasmas
• Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow
• Opacity dependence of elliptic flow in kinetic theory
• Relativistic viscous hydrodynamics for heavy-ion collisions: A comparison between the Chapman-Enskog and Grad methods
• Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime
• Leading-order anisotropic hydrodynamics for systems with massive particles
• Non-perturbative rheological behavior of a far-from-equilibrium expanding plasma
• Azimuthal Anisotropies at High Momentum from Purely Non-Hydrodynamic Transport
• Hydrodynamization and non-equilibrium Green's functions in kinetic theory
• Anisotropic fluid dynamics for Gubser flow
• Second order viscous corrections to the harmonic spectrum in heavy ion collisions
• Onset of hydrodynamics for a quark-gluon plasma from the evolution of moments of distribution functions
• The large proper-time expansion of Yang-Mills plasma as a resurgent transseries
• Dissipative fluid dynamics for the dilute Fermi gas at unitarity: Anisotropic fluid dynamics
• Model-independent determination of the shear viscosity of a trapped unitary Fermi gas: Application to high temperature data
• Determination of the density and temperature dependence of the shear viscosity of a unitary Fermi gas based on hydrodynamic flow
• Counting RG flows
• Hydrodynamic attractors in phase space
• Exact solution for the non-equilibrium attractor in number-conserving relaxation time approximation
• Effective kinetic description of the expanding overoccupied Glasma
• Anisotropic hydrodynamics with a scalar collisional kernel
• Global flow structure and exact formal transseries of the Gubser flow in kinetic theory
• Testing different formulations of leading-order anisotropic hydrodynamics
• Universal behaviour, transients and attractors in supersymmetric Yang-Mills plasma
• Anisotropic hydrodynamics with number-conserving kernels
• A generalized Theory of Diffusion based on Kinetic Theory
• Angular mode expansion of the Boltzmann equation in the small-angle approximation
• Nonlocal wave turbulence in non-Abelian plasmas
• Anisotropic Flow and Viscous Hydrodynamics

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