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

Abstract

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. Implicationsmore » for the applicability of hydrodynamics in far-off-equilibrium situations are discussed.« less

Authors:
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)
Publication Date:
Research Org.:
The Ohio State Univ., Columbus, OH (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP)
OSTI Identifier:
1604297
Alternate Identifier(s):
OSTI ID: 1560288; OSTI ID: 1770695
Grant/Contract Number:  
SC0004286
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review C
Additional Journal Information:
Journal Volume: 100; Journal Issue: 3; Journal ID: ISSN 2469-9985
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Hydrodynamic models; Relativistic heavy-ion collisions

Citation Formats

Jaiswal, Sunil, Chattopadhyay, Chandrodoy, Jaiswal, Amaresh, Pal, Subrata, and Heinz, Ulrich. Exact solutions and attractors of higher-order viscous fluid dynamics for Bjorken flow. United States: N. p., 2019. Web. https://doi.org/10.1103/PhysRevC.100.034901.
Jaiswal, Sunil, Chattopadhyay, Chandrodoy, Jaiswal, Amaresh, Pal, Subrata, & Heinz, Ulrich. Exact solutions and attractors of higher-order viscous fluid dynamics for Bjorken flow. United States. https://doi.org/10.1103/PhysRevC.100.034901
Jaiswal, Sunil, Chattopadhyay, Chandrodoy, Jaiswal, Amaresh, Pal, Subrata, and Heinz, Ulrich. Tue . "Exact solutions and attractors of higher-order viscous fluid dynamics for Bjorken flow". United States. https://doi.org/10.1103/PhysRevC.100.034901. https://www.osti.gov/servlets/purl/1604297.
@article{osti_1604297,
title = {Exact solutions and attractors of higher-order viscous fluid dynamics for Bjorken flow},
author = {Jaiswal, Sunil and Chattopadhyay, Chandrodoy and Jaiswal, Amaresh and Pal, Subrata and Heinz, Ulrich},
abstractNote = {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.},
doi = {10.1103/PhysRevC.100.034901},
journal = {Physical Review C},
number = 3,
volume = 100,
place = {United States},
year = {2019},
month = {9}
}

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Cited by: 6 works
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