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Title: Exact solutions and attractors of higher-order viscous fluid dynamics for Bjorken flow

Journal Article · · Physical Review. C
ORCiD logo [1];  [2];  [3];  [1]; ORCiD logo [4]
  1. Tata Inst. of Fundamental Research, Bombay (India)
  2. The Ohio State Univ., Columbus, OH (United States)
  3. Homi Bhabha National Inst., Odisha (India)
  4. The Ohio State Univ., Columbus, OH (United States); Goethe Univ., Frankfurt (Germany)
+ Show Author Affiliations

We consider causal higher order theories of relativistic viscous hydrodynamics in the limit of one-dimensional boost-invariant expansion and study the associated dynamical attractor. We obtain evolution equations for the inverse Reynolds number as a function of Knudsen number. The solutions of these equations exhibit attractor behavior which we analyze in terms of Lyapunov exponents using several different techniques. We compare the attractors of the second-order Müller-Israel-Stewart (MIS), transient Denicol-Niemi-Molnar-Rischke (DNMR), and third-order theories with the exact solution of the Boltzmann equation in the relaxation-time approximation. It is shown that for Bjorken flow the third-order theory provides a better approximation to the exact kinetic theory attractor than both MIS and DNMR theories. For three different choices of the time dependence of the shear relaxation rate we find analytical solutions for the energy density and shear stress and use these to study the attractors analytically. By studying these analytical solutions at both small and large Knudsen numbers we characterize and uniquely determine the attractors and Lyapunov exponents. While for small Knudsen numbers the approach to the attractor is exponential, strong power-law decay of deviations from the attractor and rapid loss of initial state memory are found even for large Knudsen numbers. Implications for the applicability of hydrodynamics in far-off-equilibrium situations are discussed.

Research Organization:
The Ohio State Univ., Columbus, OH (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Nuclear Physics (NP)
Grant/Contract Number:
SC0004286
OSTI ID:
1604297
Alternate ID(s):
OSTI ID: 1560288; OSTI ID: 1770695
Journal Information:
Physical Review. C, Vol. 100, Issue 3; ISSN 2469-9985
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 47 works
Citation information provided by
Web of Science

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  • 19TH PARTICLES AND NUCLEI INTERNATIONAL CONFERENCE (PANIC11), AIP Conference Proceedings https://doi.org/10.1063/1.3700674
conference January 2012
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Simulating elliptic flow with viscous hydrodynamics text January 2007
Causal viscous hydrodynamics in 2+1 dimensions for relativistic heavy-ion collisions text January 2007
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Dissipative Dynamics of Highly Anisotropic Systems text January 2010
Viscous QCD matter in a hybrid hydrodynamic+Boltzmann approach text January 2010
Hadron spectra and elliptic flow for 200 A GeV Au+Au collisions from viscous hydrodynamics coupled to a Boltzmann cascade text January 2011
Derivation of transient relativistic fluid dynamics from the Boltzmann equation text January 2012
Event-by-event anisotropic flow in heavy-ion collisions from combined Yang-Mills and viscous fluid dynamics text January 2012
Collective flow and viscosity in relativistic heavy-ion collisions text January 2013
Hydrodynamic gradient expansion in gauge theory plasmas text January 2013
Second-order (2+1)-dimensional anisotropic hydrodynamics text January 2013
Exact analytical solutions of second-order conformal hydrodynamics text January 2014
Isotropization and hydrodynamization in weakly coupled heavy-ion collisions text January 2015
Resurgence in Extended Hydrodynamics text January 2015
Relativistic hydrodynamics in heavy-ion collisions: general aspects and recent developments text January 2016
Closing the equations of motion of anisotropic fluid dynamics by a judicious choice of moment of the Boltzmann equation text January 2016
Do nuclear collisions create a locally equilibrated quark-gluon plasma? text January 2016
Hydrodynamization in kinetic theory: Transient modes and the gradient expansion text January 2016
Holography, Hydrodynamization and Heavy-Ion Collisions text January 2016
Onset of hydrodynamics for a quark-gluon plasma from the evolution of moments of distribution functions text January 2017
Anisotropic fluid dynamics for Gubser flow text January 2017
Relativistic Hydrodynamic Attractors with Broken Symmetries: Non-Conformal and Non-Homogeneous text January 2017
Analytical attractor and the divergence of the slow-roll expansion in relativistic hydrodynamics text January 2017
Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow text January 2017
On higher order and anisotropic hydrodynamics for Bjorken and Gubser flows text January 2018
(3+1)-dimensional anisotropic fluid dynamics with a lattice QCD equation of state text January 2018
Hydrodynamic attractor and the fate of perturbative expansions in Gubser flow text January 2018
Resummed hydrodynamic expansion for a plasma of particles interacting with fields text January 2018
The non-equilibrium attractor for kinetic theory in relaxation time approximation text January 2018
Including off-diagonal anisotropies in anisotropic hydrodynamics text January 2019
Hydrodynamic flow in small systems, or: "How the heck is it possible that a system emitting only a dozen particles can be described by fluid dynamics?" text January 2019
Early thermalization at RHIC text January 2001
Dissipative Hydrodynamics and Heavy Ion Collisions text January 2006
Do nuclear collisions create a locally equilibrated quark–gluon plasma? journal January 2017
Collective Flow and Viscosity in Relativistic Heavy-Ion Collisions journal October 2013
Relativistic viscous hydrodynamics, conformal invariance, and holography text January 2007
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Hydrodynamic gradient expansion in gauge theory plasmas text January 2013
Isotropization and hydrodynamization in weakly coupled heavy-ion collisions text January 2015
Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation text January 2016
Closing the equations of motion of anisotropic fluid dynamics by a judicious choice of moment of the Boltzmann equation text January 2016
New theories of relativistic hydrodynamics in the LHC era text January 2017
On the hydrodynamic attractor of Yang-Mills plasma text January 2017
The large proper-time expansion of Yang-Mills plasma as a resurgent transseries text January 2018

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