Global flow structure and exact formal transseries of the Gubser flow in kinetic theory
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.
- Authors:
-
[1];
- North Carolina State Univ., Raleigh, NC (United States). Dept. of Physics
- North Carolina State Univ., Raleigh, NC (United States). Dept. of Physics; Jiangxi Normal Univ., Nanchang (China). College of Physics and Communication Electronics
- Publication Date:
- Research Org.:
- North Carolina State University, Raleigh, NC (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1800102
- Grant/Contract Number:
- FG02-03ER41260; SC0013036
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2020; Journal Issue: 7; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Berlin
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics
Citation Formats
Behtash, Alireza, Kamata, Syo, Martinez, Mauricio, and Shi, Haosheng. Global flow structure and exact formal transseries of the Gubser flow in kinetic theory. United States: N. p., 2020.
Web. doi:10.1007/jhep07(2020)226.
Behtash, Alireza, Kamata, Syo, Martinez, Mauricio, & Shi, Haosheng. Global flow structure and exact formal transseries of the Gubser flow in kinetic theory. United States. https://doi.org/10.1007/jhep07(2020)226
Behtash, Alireza, Kamata, Syo, Martinez, Mauricio, and Shi, Haosheng. Thu .
"Global flow structure and exact formal transseries of the Gubser flow in kinetic theory". United States. https://doi.org/10.1007/jhep07(2020)226. https://www.osti.gov/servlets/purl/1800102.
@article{osti_1800102,
title = {Global flow structure and exact formal transseries of the Gubser flow in kinetic theory},
author = {Behtash, Alireza and Kamata, Syo and Martinez, Mauricio and Shi, Haosheng},
abstractNote = {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.},
doi = {10.1007/jhep07(2020)226},
journal = {Journal of High Energy Physics (Online)},
number = 7,
volume = 2020,
place = {United States},
year = {Thu Jul 30 00:00:00 EDT 2020},
month = {Thu Jul 30 00:00:00 EDT 2020}
}
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Works referenced in this record:
Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation
journal, December 2014
- Denicol, Gabriel; Heinz, Ulrich; Martinez, Mauricio
- Physical Review D, Vol. 90, Issue 12
Characteristics of Thermalization of Boost-Invariant Plasma from Holography
journal, May 2012
- Heller, Michal P.; Janik, Romuald A.; Witaszczyk, Przemysław
- Physical Review Letters, Vol. 108, Issue 20
Conformal hydrodynamics in Minkowski and de Sitter spacetimes
journal, May 2011
- Gubser, Steven S.; Yarom, Amos
- Nuclear Physics B, Vol. 846, Issue 3
Exact Hydrodynamic Attractor of an Ultrarelativistic Gas of Hard Spheres
journal, April 2020
- Denicol, Gabriel S.; Noronha, Jorge
- Physical Review Letters, Vol. 124, Issue 15
Homogeneous isotropization and equilibration of a strongly coupled plasma with a critical point
journal, December 2017
- Critelli, Renato; Rougemont, Romulo; Noronha, Jorge
- Journal of High Energy Physics, Vol. 2017, Issue 12
One fluid to rule them all: Viscous hydrodynamic description of event-by-event central p+p, p+Pb and Pb+Pb collisions at TeV
journal, November 2017
- Weller, Ryan D.; Romatschke, Paul
- Physics Letters B, Vol. 774
Hilbert’s 6th Problem: exact and approximate hydrodynamic manifolds for kinetic equations
journal, November 2013
- Gorban, Alexander N.; Karlin, Ilya
- Bulletin of the American Mathematical Society, Vol. 51, Issue 2
Isotropization and Hydrodynamization in Weakly Coupled Heavy-Ion Collisions
journal, October 2015
- Kurkela, Aleksi; Zhu, Yan
- Physical Review Letters, Vol. 115, Issue 18
Non-perturbative rheological behavior of a far-from-equilibrium expanding plasma
journal, October 2019
- Behtash, Alireza; Cruz-Camacho, C. N.; Kamata, Syo
- Physics Letters B, Vol. 797
Chemical Equilibration in Hadronic Collisions
journal, April 2019
- Kurkela, Aleksi; Mazeliauskas, Aleksas
- Physical Review Letters, Vol. 122, Issue 14
A lemma in the theory of structural stability of differential equations
journal, April 1960
- Hartman, Philip
- Proceedings of the American Mathematical Society, Vol. 11, Issue 4
The complex life of hydrodynamic modes
journal, November 2019
- Grozdanov, Sašo; Kovtun, Pavel K.; Starinets, Andrei O.
- Journal of High Energy Physics, Vol. 2019, Issue 11
Symmetry constraints on generalizations of Bjorken flow
journal, October 2010
- Gubser, Steven S.
- Physical Review D, Vol. 82, Issue 8
Boost invariant flow, black hole formation, and far-from-equilibrium dynamics in supersymmetric Yang-Mills theory
journal, July 2010
- Chesler, Paul M.; Yaffe, Laurence G.
- Physical Review D, Vol. 82, Issue 2
Onset of hydrodynamics for a quark-gluon plasma from the evolution of moments of distribution functions
journal, November 2017
- Blaizot, Jean-Paul; Yan, Li
- Journal of High Energy Physics, Vol. 2017, Issue 11
Relativistic hydrodynamic attractors with broken symmetries: non-conformal and non-homogeneous
journal, December 2017
- Romatschke, Paul
- Journal of High Energy Physics, Vol. 2017, Issue 12
Chemical equilibration in weakly coupled QCD
journal, March 2019
- Kurkela, Aleksi; Mazeliauskas, Aleksas
- Physical Review D, Vol. 99, Issue 5
The Devil's Invention: Asymptotic, Superasymptotic and Hyperasymptotic Series
journal, March 1999
- Boyd, John P.
- Acta Applicandae Mathematicae, Vol. 56, Issue 1, p. 1-98
Transient relativistic thermodynamics and kinetic theory
journal, April 1979
- Israel, W.; Stewart, J. M.
- Annals of Physics, Vol. 118, Issue 2
Dissipative dynamics of highly anisotropic systems
journal, December 2010
- Martinez, Mauricio; Strickland, Michael
- Nuclear Physics A, Vol. 848, Issue 1-2
Lagrangian Coherent Structures
journal, January 2015
- Haller, George
- Annual Review of Fluid Mechanics, Vol. 47, Issue 1
Anisotropic fluid dynamics for Gubser flow
journal, May 2017
- Martinez, M.; McNelis, M.; Heinz, U.
- Physical Review C, Vol. 95, Issue 5
Anisotropic hydrodynamics with a scalar collisional kernel
journal, April 2018
- Almaalol, Dekrayat; Strickland, Michael
- Physical Review C, Vol. 97, Issue 4
Analytic structure of nonhydrodynamic modes in kinetic theory
journal, September 2019
- Kurkela, Aleksi; Wiedemann, Urs Achim
- The European Physical Journal C, Vol. 79, Issue 9
Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation
journal, August 2015
- Heller, Michal P.; Spaliński, Michał
- Physical Review Letters, Vol. 115, Issue 7
How big are the smallest drops of quark-gluon plasma?
journal, March 2016
- Chesler, Paul M.
- Journal of High Energy Physics, Vol. 2016, Issue 3
Early- and Late-Time Behavior of Attractors in Heavy-Ion Collisions
journal, March 2020
- Kurkela, Aleksi; van der Schee, Wilke; Wiedemann, Urs Achim
- Physical Review Letters, Vol. 124, Issue 10
Convergence of the Gradient Expansion in Hydrodynamics
journal, June 2019
- Grozdanov, Sašo; Kovtun, Pavel K.; Starinets, Andrei O.
- Physical Review Letters, Vol. 122, Issue 25
First-Principles Derivation of Stable First-Order Generic-Frame Relativistic Dissipative Hydrodynamic Equations from Kinetic Theory by Renormalization-Group Method
journal, November 2011
- Tsumura, K.; Kunihiro, T.
- Progress of Theoretical Physics, Vol. 126, Issue 5
A simple model of the derivation of fluid mechanics from the Boltzmann equation
journal, January 1969
- McKean Jr., H. P.
- Bulletin of the American Mathematical Society, Vol. 75, Issue 1
Universal behaviour, transients and attractors in supersymmetric Yang–Mills plasma
journal, September 2018
- Spaliński, Michał
- Physics Letters B, Vol. 784
One-dimensional dynamical systems and Benford’s law
journal, April 2004
- Berger, Arno; Bunimovich, Leonid A.; Hill, Theodore P.
- Transactions of the American Mathematical Society, Vol. 357, Issue 1
Boost-invariant early time dynamics from AdS/CFT
journal, October 2009
- Beuf, Guillaume; Heller, Michal P.; Janik, Romuald A.
- Journal of High Energy Physics, Vol. 2009, Issue 10
Collective flow from AA, pA to pp collisions – Toward a unified paradigm
journal, November 2017
- Li, Wei
- Nuclear Physics A, Vol. 967
Exact solution for the non-equilibrium attractor in number-conserving relaxation time approximation
journal, October 2019
- Strickland, Michael; Tantary, Ubaid
- Journal of High Energy Physics, Vol. 2019, Issue 10
Relativistic Fluid Dynamics Far From Local Equilibrium
journal, January 2018
- Romatschke, Paul
- Physical Review Letters, Vol. 120, Issue 1
Retarded correlators in kinetic theory: branch cuts, poles and hydrodynamic onset transitions
journal, June 2016
- Romatschke, Paul
- The European Physical Journal C, Vol. 76, Issue 6
Existence of global attractor for a nonautonomous state-dependent delay differential equation of neuronal type
journal, November 2019
- Elia, Cinzia; Maroto, Ismael; Núñez, Carmen
- Communications in Nonlinear Science and Numerical Simulation, Vol. 78
The non-equilibrium attractor for kinetic theory in relaxation time approximation
journal, December 2018
- Strickland, M.
- Journal of High Energy Physics, Vol. 2018, Issue 12
Holographic thermalization with radial flow
journal, March 2013
- van der Schee, Wilke
- Physical Review D, Vol. 87, Issue 6
A generalization of Hartman's linearization theorem
journal, March 1973
- Palmer, Kenneth J.
- Journal of Mathematical Analysis and Applications, Vol. 41, Issue 3
Exact solutions and attractors of higher-order viscous fluid dynamics for Bjorken flow
journal, September 2019
- Jaiswal, Sunil; Chattopadhyay, Chandrodoy; Jaiswal, Amaresh
- Physical Review C, Vol. 100, Issue 3
How does relativistic kinetic theory remember about initial conditions?
journal, September 2018
- Heller, Michal P.; Svensson, Viktor
- Physical Review D, Vol. 98, Issue 5
Novel collective phenomena in high-energy proton–proton and proton–nucleus collisions
journal, January 2016
- Dusling, Kevin; Li, Wei; Schenke, Björn
- International Journal of Modern Physics E, Vol. 25, Issue 01
New Exact Solution of the Relativistic Boltzmann Equation and its Hydrodynamic Limit
journal, November 2014
- Denicol, Gabriel S.; Heinz, Ulrich; Martinez, Mauricio
- Physical Review Letters, Vol. 113, Issue 20
Hydrodynamic attractor and the fate of perturbative expansions in Gubser flow
journal, June 2019
- Denicol, Gabriel S.; Noronha, Jorge
- Physical Review D, Vol. 99, Issue 11
Emergence of hydrodynamical behavior in expanding ultra-relativistic plasmas
journal, January 2020
- Blaizot, Jean-Paul; Yan, Li
- Annals of Physics, Vol. 412
Fluid dynamics of out of equilibrium boost invariant plasmas
journal, May 2018
- Blaizot, Jean-Paul; Yan, Li
- Physics Letters B, Vol. 780
Anisotropic nonequilibrium hydrodynamic attractor
journal, February 2018
- Strickland, Michael; Noronha, Jorge; Denicol, Gabriel S.
- Physical Review D, Vol. 97, Issue 3
Anisotropic hydrodynamics for rapidly expanding systems
journal, October 2013
- Florkowski, Wojciech; Ryblewski, Radoslaw; Strickland, Michael
- Nuclear Physics A, Vol. 916
Testing viscous and anisotropic hydrodynamics in an exactly solvable case
journal, August 2013
- Florkowski, Wojciech; Ryblewski, Radoslaw; Strickland, Michael
- Physical Review C, Vol. 88, Issue 2
Short-lived modes from hydrodynamic dispersion relations
journal, June 2018
- Withers, Benjamin
- Journal of High Energy Physics, Vol. 2018, Issue 6
Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow
journal, June 2019
- Behtash, Alireza; Kamata, Syo; Martinez, Mauricio
- Physical Review D, Vol. 99, Issue 11
Solutions of conformal Israel-Stewart relativistic viscous fluid dynamics
journal, January 2015
- Marrochio, Hugo; Noronha, Jorge; Denicol, Gabriel S.
- Physical Review C, Vol. 91, Issue 1
Laguerre functions and representations of su(1,1)
journal, December 2003
- Groenevelt, Wolter
- Indagationes Mathematicae, Vol. 14, Issue 3-4
Hydrodynamics, resurgence, and transasymptotics
journal, December 2015
- Başar, Gökçe; Dunne, Gerald V.
- Physical Review D, Vol. 92, Issue 12
Resurgence and hydrodynamic attractors in Gauss-Bonnet holography
journal, April 2018
- Casalderrey-Solana, Jorge; Gushterov, Nikola I.; Meiring, Ben
- Journal of High Energy Physics, Vol. 2018, Issue 4
Universal behaviour, transients and attractors in supersymmetric Yang–Mills plasma
journal, September 2018
- Spaliński, Michał
- Physics Letters B, Vol. 784
Anisotropic hydrodynamics with number-conserving kernels
text, January 2018
- Almaalol, D.; Alqahtani, M.; Strickland, M.
- arXiv
Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow
text, January 2019
- Behtash, Alireza; Kamata, Syo; Martinez, M.
- arXiv
Exact solution for the non-equilibrium attractor in number-conserving relaxation time approximation
text, January 2019
- Strickland, Michael; Tantary, Ubaid
- arXiv