Global flow structure and exact formal transseries of the Gubser flow in kinetic theory
arXiv:1911.06406 · doi:10.1007/JHEP07(2020)226
Abstract
In this work we introduce the generic conditions for the existence of a non-equilibrium attractor that is an invariant manifold determined by the long-wavelength modes of the physical system. We investigate the topological properties of the global flow structure of the Gubser flow for the Israel-Stewart theory and a kinetic model for the Boltzmann equation by employing Morse-Smale theory. We present a complete classification of the invariant submanifolds of the flow and determine all the possible flow lines connecting any pair of UV/IR fixed points. The formal transseries solutions to the Gubser dynamical system around the early-time (UV) and late-time (IR) fixed points are constructed and analyzed. It is proven that these solutions are purely perturbative (or power-law asymptotic) series with a finite radius of convergence. Based on these analyses, we find that Gubser-like expanding kinetic systems do not hydrodynamize owing to the failure of the hydrodynamization process which heavily relies on the classification of (non)hydrodynamic modes in the IR regime. This is in contrast to longitudinal boost-invariant plasmas where the asymptotic dynamics is described by a few terms of the hydrodynamic gradient expansion. We finally compare our results for both Bjorken and Gubser conformal kinetic models.
arXiv comment46 pages, 5 figures, 1 table. Minor changes in the text and modifications in Fig.3
References in corpus (48)
- Dissipative Dynamics of Highly Anisotropic Systems
- The characteristics of thermalization of boost-invariant plasma from holography
- Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation
- Isotropization and hydrodynamization in weakly coupled heavy-ion collisions
- Boost invariant flow, black hole formation, and far-from-equilibrium dynamics in N = 4 supersymmetric Yang-Mills theory
- 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 TeV
- Novel Collective Phenomena in High-Energy Proton-Proton and Proton-Nucleus Collisions
- Fluid Dynamics far from Local Equilibrium
- Testing viscous and anisotropic hydrodynamics in an exactly solvable case
- Conformal hydrodynamics in Minkowski and de Sitter spacetimes
- The anisotropic non-equilibrium hydrodynamic attractor
- Anisotropic Hydrodynamics for Rapidly Expanding Systems
- The complex life of hydrodynamic modes
- A new exact solution of the relativistic Boltzmann equation and its hydrodynamic limit
- On the convergence of the gradient expansion in hydrodynamics
- Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation
- Fluid dynamics of out of equilibrium boost invariant plasmas
- What attracts to attractors?
- The non-equilibrium attractor for kinetic theory in relaxation time approximation
- Retarded Correlators in Kinetic Theory: Branch Cuts, Poles and Hydrodynamic Onset Transitions
- Boost-invariant early time dynamics from AdS/CFT
- Relativistic Hydrodynamic Attractors with Broken Symmetries: Non-Conformal and Non-Homogeneous
- Chemical Equilibration in Hadronic Collisions
- Holographic thermalization with radial flow
- Chemical Equilibration in Weakly Coupled QCD
- Solutions of Conformal Israel-Stewart Relativistic Viscous Fluid Dynamics
- Hydrodynamics, resurgence and trans-asymptotics
- How does relativistic kinetic theory remember about initial conditions?
- Short-lived modes from hydrodynamic dispersion relations
- Exact hydrodynamic attractor of an ultrarelativistic gas of hard spheres
- Exact solutions and attractors of higher-order viscous fluid dynamics for Bjorken flow
- How big are the smallest drops of quark-gluon plasma?
- Hilbert's 6th Problem: Exact and Approximate Hydrodynamic Manifolds for Kinetic Equations
- Resurgence and Hydrodynamic Attractors in Gauss-Bonnet Holography
- 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
- Non-perturbative rheological behavior of a far-from-equilibrium expanding plasma
- Anisotropic fluid dynamics for Gubser flow
- Onset of hydrodynamics for a quark-gluon plasma from the evolution of moments of distribution functions
- Exact solution for the non-equilibrium attractor in number-conserving relaxation time approximation
- Anisotropic hydrodynamics with a scalar collisional kernel
- Homogeneous isotropization and equilibration of a strongly coupled plasma with a critical point
- Universal behaviour, transients and attractors in supersymmetric Yang-Mills plasma
- First-principle Derivation of Stable First-order Generic-frame Relativistic Dissipative Hydrodynamic Equations from Kinetic Theory by Renormalization-group Method
- Collective flow from AA, pA to pp collisions - Toward a unified paradigm
- Existence of global attractor for a nonautonomous state-dependent delay differential equation of neuronal type
Cited by in corpus (27)
- The smallest fluid on earth
- Non-equilibrium attractor in high-temperature QCD plasmas
- 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
- Hydrodynamic attractors in phase space
- Hydrodynamic Attractors in Ultrarelativistic Nuclear Collisions
- Analytic solutions of relativistic dissipative spin hydrodynamics with radial expansion in Gubser flow
- Transasymptotics and hydrodynamization of the Fokker-Planck equation for gluons
- Bjorken flow attractors with transverse dynamics
- Opacity dependence of transverse flow, pre-equilibrium and applicability of hydrodynamics in heavy-ion collisions
- Conformal Bjorken flow in the general frame and its attractor: Similarities and discrepancies with the Müller-Israel-Stewart formalism
- Relativistic Hydrodynamics: A Singulant Perspective
- Hydrodynamic Attractor in a Hubble Expansion
- Hydrodynamic Gradient Expansion Diverges beyond Bjorken Flow
- Far-from-equilibrium attractors for massive kinetic theory in the relaxation time approximation
- An improved anisotropic hydrodynamics ansatz
- Pre-Equilibrium Evolution of Conserved Charges with ICCING Initial Conditions
- Novel features of attractors and transseries in non-conformal Bjorken flows
- High-order Shakhov-like extension of the relaxation time approximation in relativistic kinetic theory
- The late to early time behaviour of an expanding plasma: hydrodynamisation from exponential asymptotics
- How Gubser flow ends in a holographic conformal theory
- Holographic Gubser flow: A combined analytic and numerical study
- Resurgence for the non-conformal Bjorken flow with Fermi-Dirac and Bose-Einstein statistics
- Maximally Symmetric Boost-Invariant Solutions of the Boltzmann Equation in Foliated Geometries
- Non-perturbative Origin of the Electroweak Scale: RGE in Strongly-coupled Dark Gauge Theories via Dyson-Schwinger