Hydrodynamization in kinetic theory: Transient modes and the gradient expansion

Abstract

We explore the transition to hydrodynamics in a weakly-coupled model of quark-gluon plasma given by kinetic theory in the relaxation time approximation with conformal symmetry. We demonstrate that the gradient expansion in this model has a vanishing radius of convergence due to the presence of a transient (nonhydrodynamic) mode, in a way similar to results obtained earlier in strongly-coupled gauge theories. This suggests that the mechanism by which hydrodynamic behaviour emerges is the same, which we further corroborate by a novel comparison between solutions of different weakly and strongly coupled models. However, in contrast with other known cases, we find that not all the singularities of the analytic continuation of the Borel transform of the gradient expansion correspond to transient excitations of the microscopic system: some of them reflect analytic properties of the kinetic equation when the proper time is continued to complex values.

6 pages, 2 figures, v2: author added, major rewrite, mysterious off real axis singularities in the Borel plane explained (!), see also arXiv:1802.08225 [nucl-th] by Heller and Svensson; v3: references added, minor improvements in the text, first 426 terms from Eq. (8) included in the submission; v4: title changed, matches published version

References in corpus (22)

• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Holography and colliding gravitational shock waves in asymptotically AdS_5 spacetime
• New theories of relativistic hydrodynamics in the LHC era
• Fluid Dynamics far from Local Equilibrium
• Gauge/gravity duality and thermalization of a boost-invariant perfect fluid
• A numerical relativity approach to the initial value problem in asymptotically Anti-de Sitter spacetime for plasma thermalization - an ADM formulation
• The anisotropic non-equilibrium hydrodynamic attractor
• Approach to equilibrium in weakly coupled nonabelian plasmas
• Fluid dynamics of out of equilibrium boost invariant plasmas
• Entropy Production, Hydrodynamics, and Resurgence in the Primordial Quark-Gluon Plasma from Holography
• On the hydrodynamic attractor of Yang-Mills plasma
• From strong to weak coupling in holographic models of thermalization
• Do nuclear collisions create a locally equilibrated quark-gluon plasma?
• Relativistic Hydrodynamic Attractors with Broken Symmetries: Non-Conformal and Non-Homogeneous
• Analytical attractor and the divergence of the slow-roll expansion in relativistic hydrodynamics
• Equilibration rates in a strongly coupled nonconformal quark-gluon plasma
• Coupled kinetic equations for quarks and gluons in the relaxation time approximation
• Gradient expansion for anisotropic hydrodynamics
• Linearized nonequilibrium dynamics in nonconformal plasma
• Small systems and regulator dependence in relativistic hydrodynamics
• Statistics of thermalization in Bjorken Flow
• String-Theory-Based Predictions for Nonhydrodynamic Collective Modes in Strongly Interacting Fermi Gases

Cited by in corpus (101)

• New theories of relativistic hydrodynamics in the LHC era
• Causality and existence of solutions of relativistic viscous fluid dynamics with gravity
• QCD thermalization: Ab initio approaches and interdisciplinary connections
• Nonlinear causality of general first-order relativistic viscous hydrodynamics
• 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
• Relativistic dissipative spin dynamics in the relaxation time approximation
• What attracts to attractors?
• On the hydrodynamic attractor of Yang-Mills plasma
• The non-equilibrium attractor for kinetic theory in relaxation time approximation
• Hydrodynamic attractors, initial state energy and particle production in relativistic nuclear collisions
• Novel Relaxation Time Approximation to the Relativistic Boltzmann Equation
• Nonlinear Constraints on Relativistic Fluids Far From Equilibrium
• Chemical Equilibration in Hadronic Collisions
• Flow in AA and pA as an interplay of fluid-like and non-fluid like excitations
• Chemical Equilibration in Weakly Coupled QCD
• A Practical Mini-Course on Applied Holography
• The smallest fluid on earth
• How does relativistic kinetic theory remember about initial conditions?
• Non-equilibrium attractor in high-temperature QCD plasmas
• The Present and Future of QCD
• Exact hydrodynamic attractor of an ultrarelativistic gas of hard spheres
• Hydrodynamic attractors in heavy ion collisions: a review
• Exact solutions and attractors of higher-order viscous fluid dynamics for Bjorken flow
• Nearly isentropic flow at sizeable $\eta /s$
• Bounds on transport from univalence and pole-skipping
• Far-from-equilibrium search for the QCD critical point
• Hydrodynamic attractor and the fate of perturbative expansions in Gubser flow
• Quasinormal modes in charged fluids at complex momentum
• Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow
• Opacity dependence of elliptic flow in kinetic theory
• QCD Equation of State at Finite Chemical Potentials for Relativistic Nuclear Collisions
• A numerical exploration of first-order relativistic hydrodynamics
• Equilibration of the Quark-Gluon Plasma at finite net-baryon density in QCD kinetic theory
• Equilibration of weakly coupled QCD plasmas
• Non-perturbative rheological behavior of a far-from-equilibrium expanding plasma
• Adiabatic hydrodynamization in rapidly-expanding quark-gluon plasma
• Hydrodynamization and non-equilibrium Green's functions in kinetic theory
• On non-conformal kinetic theory and hydrodynamics for Bjorken flow
• Hydrodynamic gradient expansion in linear response theory
• Intermediate mass dileptons as pre-equilibrium probes in heavy ion collisions
• Hydrodynamics from free-streaming to thermalization and back again
• Holographic approach to compact stars and their binary mergers
• On higher order and anisotropic hydrodynamics for Bjorken and Gubser flows
• Hydrodynamic attractors in phase space
• Hydrodynamic attractors for Gubser flow
• SU(2) Gauge Theory in $2+1$ Dimensions on a Plaquette Chain Obeys the Eigenstate Thermalization Hypothesis
• Hydrodynamization in systems with detailed transverse profiles
• Analytical attractor for Bjorken expansion
• Convergence of hydrodynamic modes: insights from kinetic theory and holography
• Conservative finite volume scheme for first-order viscous relativistic hydrodynamics
• Extended relaxation time approximation and relativistic dissipative hydrodynamics
• Hydrodynamic Attractors in Ultrarelativistic Nuclear Collisions
• Critical lensing and kurtosis near a critical point in the QCD phase diagram in and out-of-equilibrium
• Homogeneous isotropization and equilibration of a strongly coupled plasma with a critical point
• Transasymptotics and hydrodynamization of the Fokker-Planck equation for gluons
• Equivalence between first-order causal and stable hydrodynamics and Israel-Stewart theory for boost-invariant systems with a constant relaxation time
• Non-local hydrodynamic transport and collective excitations in Dirac fluids
• Bjorken flow attractors with transverse dynamics
• Universal behaviour, transients and attractors in supersymmetric Yang-Mills plasma
• A fluid-dynamic approach to heavy-quark diffusion in the quark-gluon plasma
• Anisotropic fluid dynamical simulations of heavy-ion collisions
• Exponential Approach to the Hydrodynamic Attractor in Yang-Mills Kinetic Theory
• Resummed hydrodynamic expansion for a plasma of particles interacting with fields
• Holographic Bjorken Flow at Large-D
• Conformal Bjorken flow in the general frame and its attractor: Similarities and discrepancies with the Müller-Israel-Stewart formalism
• Some Aspects of the Theory of Heavy Ion Collisions
• Relativistic Hydrodynamics: A Singulant Perspective
• Hydrodynamic Gradient Expansion Diverges beyond Bjorken Flow
• Hydrodynamic Attractor in a Hubble Expansion
• Hydrodynamic attractor of a hybrid viscous fluid in Bjorken flow
• Limiting attractors in heavy-ion collisions
• Far-from-equilibrium attractors for massive kinetic theory in the relaxation time approximation
• Correspondence between Israel-Stewart and first-order casual and stable hydrodynamics for the boost-invariant massive case with zero baryon density
• Far-from-equilibrium kinetic dynamics of $\lambda {\varphi }^4$ theory in an expanding universe
• Dilepton polarization as a signature of plasma anisotropy
• Relativistic second-order viscous hydrodynamics from kinetic theory with extended relaxation-time approximation
• Hydrodynamic attractors for the speed of sound in holographic Bjorken flow
• Critical behaviour of hydrodynamic series
• Transverse mass scaling of dilepton radiation off a quark-gluon plasma
• Hydrodynamic generators in relativistic kinetic theory
• An improved anisotropic hydrodynamics ansatz
• Constraining the initial stages of ultrarelativistic nuclear collisions
• Hydrodynamization times of a holographic fluid far from equilibrium
• Hydrodynamic attractor in the non-conformal Bjorken flow
• Novel features of attractors and transseries in non-conformal Bjorken flows
• Aspects of relativistic heavy-ion collisions
• Transseries for causal diffusive systems
• Collective effects in nuclear collisions: theory overview
• Collective dynamics in heavy and light-ion collisions -- I) Kinetic Theory vs. Hydrodynamics
• Initial conditions for nuclear collisions: theory overview
• Mapping GENERIC hydrodynamics into Carter's multifluid theory
• Review of opportunities at the HESR-Collider with PANDA at FAIR
• Approach to thermalization and hydrodynamics
• Hydrodynamical attractor and thermal particle production in heavy-ion collision
• Thermal dilepton production within conformal viscous Gubser flow
• Correspondence between Israel-Stewart and first-order causal and stable hydrodynamics for Bjorken-expanding baryon-rich systems with vanishing particle masses
• Hydrodynamic attractor in periodically driven ultracold quantum gases
• Fluctuations in ultra-relativistic heavy ion collisions
• Effects of magnetic field on the evolution of energy density fluctuations
• Far-from-equilibrium hydrodynamic simulations of ultrarelativistic nuclear collisions