Hydrodynamic attractors for Gubser flow

Abstract

The Boltzmann equation is solved in the relaxation time approximation using a hierarchy of angular moments of the distribution function. Our solution is obtained for an azimuthally symmetric radially expanding boost-invariant conformal system that is undergoing Gubser flow. The solution of moments that we get after truncating the infinite set of equations at various orders is compared to the exact kinetic solution. The dynamics of transition is described by the presence of fixed points which describes the evolution of the system from an early time collisionless free streaming to the hydrodynamic regime at intermediate times and back to free streaming at late times. The attractor solution is found for various orders of moments as an interpolation between these fixed points. The relation of moments to various approximations of relativistic viscous hydrodynamics is investigated.

arXiv comment7 pages, 4 figures v2: major rewrite of hydrodynamic attractors section, new figures added, accepted for publication in Physics Letters B

References in corpus (30)

• Derivation of transient relativistic fluid dynamics from the Boltzmann equation
• Evidence for collectivity in pp collisions at the LHC
• New theories of relativistic hydrodynamics in the LHC era
• Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation
• Symmetry constraints on generalizations of Bjorken flow
• 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
• The "Ridge" in Proton-Proton Scattering at 7 TeV
• Conformal hydrodynamics in Minkowski and de Sitter spacetimes
• The anisotropic non-equilibrium hydrodynamic attractor
• A new exact solution of the relativistic Boltzmann equation and its hydrodynamic limit
• Hydrodynamization in kinetic theory: Transient modes and the gradient expansion
• Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation
• Fluid dynamics of out of equilibrium boost invariant plasmas
• Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow
• Do nuclear collisions create a locally equilibrated quark-gluon plasma?
• The non-equilibrium attractor for kinetic theory in relaxation time approximation
• Hydrodynamic attractors, initial state energy and particle production in relativistic nuclear collisions
• Resurgence in Extended Hydrodynamics
• Coupling hydrodynamics to nonequilibrium degrees of freedom in strongly interacting quark-gluon plasma
• Elliptic flow in proton-proton collisions at 7 TeV
• Exact solutions and attractors of higher-order viscous fluid dynamics for Bjorken flow
• Hydrodynamic attractor and the fate of perturbative expansions in Gubser flow
• Emergence of hydrodynamical behavior in expanding quark-gluon plasmas
• Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow
• Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime
• Coupled kinetic equations for quarks and gluons in the relaxation time approximation
• Onset of hydrodynamics for a quark-gluon plasma from the evolution of moments of distribution functions
• Hydrodynamics from free-streaming to thermalization and back again
• On higher order and anisotropic hydrodynamics for Bjorken and Gubser flows
• Divergence of the Chapman-Enskog expansion in relativistic kinetic theory

Cited by in corpus (24)

• Hydrodynamic attractors in heavy ion collisions: a review
• Spin polarization dynamics in the Gubser-expanding background
• Hydrodynamization and non-equilibrium Green's functions in kinetic theory
• On non-conformal kinetic theory and hydrodynamics for Bjorken flow
• On attractor and fixed points in Bjorken flows
• Hydrodynamic attractors in phase space
• Hydrodynamic Attractors in Ultrarelativistic Nuclear Collisions
• Extended relaxation time approximation and relativistic dissipative hydrodynamics
• Analytic solutions of relativistic dissipative spin hydrodynamics with radial expansion in Gubser flow
• Bjorken flow attractors with transverse dynamics
• Opacity dependence of transverse flow, pre-equilibrium and applicability of hydrodynamics in heavy-ion collisions
• Hydrodynamic Attractor in a Hubble Expansion
• Relativistic second-order viscous hydrodynamics from kinetic theory with extended relaxation-time approximation
• Relaxation time approximation with pair production and annihilation processes
• Pre-Equilibrium Evolution of Conserved Charges with ICCING Initial Conditions
• An improved anisotropic hydrodynamics ansatz
• Collective dynamics of polarized spin-half fermions in relativistic heavy-ion collisions
• Does Quarkonia Suppression serve as a probe for the deconfinement in small systems?
• How Gubser flow ends in a holographic conformal theory
• Holographic Gubser flow: A combined analytic and numerical study
• Exploring QGP-like phenomena with Charmonia in $p+p$ collisions at $\sqrt{s}=13$ TeV
• Superfluids in expanding backgrounds and attractor times
• Hydrodynamic attractor in periodically driven ultracold quantum gases
• New, spherical solutions of non-relativistic, dissipative hydrodynamics