Higher order and anisotropic hydrodynamics for Bjorken and Gubser flows
Abstract
We study the evolution of hydrodynamic and nonhydrodynamic moments of the distribution function using anisotropic and third-order Chapman-Enskog hydrodynamics for systems undergoing Bjorken and Gubser flows. The hydrodynamic results are compared with the exact solution of the Boltzmann equation with a collision term in relaxation time approximation. While the evolution of the hydrodynamic moments of the distribution function (i.e., of the energy momentum tensor) can be described with high accuracy by both hydrodynamic approximation schemes, their description of the evolution of the entropy of the system is much less precise. We attribute this to large contributions from nonhydrodynamic modes coupling into the entropy evolution, which are not well captured by the hydrodynamic approximations. The differences between the exact solution and the hydrodynamic approximations are larger for the third-order Chapman-Enskog hydrodynamics than for anisotropic hydrodynamics, which effectively resums some of the dissipative effects from anisotropic expansion to all orders in the anisotropy, and are larger for Gubser flow than for Bjorken flow. Overall, anisotropic hydrodynamics provides the most precise macroscopic description for these highly anisotropically expanding systems.
- Authors:
- Publication Date:
- Research Org.:
- The Ohio State Univ., Columbus, OH (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP); National Science Foundation (NSF)
- OSTI Identifier:
- 1454315
- Alternate Identifier(s):
- OSTI ID: 1503828; OSTI ID: 1604328
- Grant/Contract Number:
- SC0004286; ACI-1550223
- Resource Type:
- Published Article
- Journal Name:
- Physical Review C
- Additional Journal Information:
- Journal Name: Physical Review C Journal Volume: 97 Journal Issue: 6; 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; quark-gluon plasma; relativistic heavy-ion collisions
Citation Formats
Chattopadhyay, Chandrodoy, Heinz, Ulrich, Pal, Subrata, and Vujanovic, Gojko. Higher order and anisotropic hydrodynamics for Bjorken and Gubser flows. United States: N. p., 2018.
Web. doi:10.1103/PhysRevC.97.064909.
Chattopadhyay, Chandrodoy, Heinz, Ulrich, Pal, Subrata, & Vujanovic, Gojko. Higher order and anisotropic hydrodynamics for Bjorken and Gubser flows. United States. https://doi.org/10.1103/PhysRevC.97.064909
Chattopadhyay, Chandrodoy, Heinz, Ulrich, Pal, Subrata, and Vujanovic, Gojko. Thu .
"Higher order and anisotropic hydrodynamics for Bjorken and Gubser flows". United States. https://doi.org/10.1103/PhysRevC.97.064909.
@article{osti_1454315,
title = {Higher order and anisotropic hydrodynamics for Bjorken and Gubser flows},
author = {Chattopadhyay, Chandrodoy and Heinz, Ulrich and Pal, Subrata and Vujanovic, Gojko},
abstractNote = {We study the evolution of hydrodynamic and nonhydrodynamic moments of the distribution function using anisotropic and third-order Chapman-Enskog hydrodynamics for systems undergoing Bjorken and Gubser flows. The hydrodynamic results are compared with the exact solution of the Boltzmann equation with a collision term in relaxation time approximation. While the evolution of the hydrodynamic moments of the distribution function (i.e., of the energy momentum tensor) can be described with high accuracy by both hydrodynamic approximation schemes, their description of the evolution of the entropy of the system is much less precise. We attribute this to large contributions from nonhydrodynamic modes coupling into the entropy evolution, which are not well captured by the hydrodynamic approximations. The differences between the exact solution and the hydrodynamic approximations are larger for the third-order Chapman-Enskog hydrodynamics than for anisotropic hydrodynamics, which effectively resums some of the dissipative effects from anisotropic expansion to all orders in the anisotropy, and are larger for Gubser flow than for Bjorken flow. Overall, anisotropic hydrodynamics provides the most precise macroscopic description for these highly anisotropically expanding systems.},
doi = {10.1103/PhysRevC.97.064909},
journal = {Physical Review C},
number = 6,
volume = 97,
place = {United States},
year = {2018},
month = {6}
}
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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
Relativistic third-order viscous corrections to the entropy four-current from kinetic theory
journal, February 2015
- Chattopadhyay, Chandrodoy; Jaiswal, Amaresh; Pal, Subrata
- Physical Review C, Vol. 91, Issue 2
Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
journal, March 2005
- Kovtun, P. K.; Son, D. T.; Starinets, A. O.
- Physical Review Letters, Vol. 94, Issue 11
Conformal hydrodynamics in Minkowski and de Sitter spacetimes
journal, May 2011
- Gubser, Steven S.; Yarom, Amos
- Nuclear Physics B, Vol. 846, Issue 3
Analytic Solution of the Boltzmann Equation in an Expanding System
journal, January 2016
- Bazow, D.; Denicol, G. S.; Heinz, U.
- Physical Review Letters, Vol. 116, Issue 2
Boltzmann equation with a nonlocal collision term and the resultant dissipative fluid dynamics
journal, March 2013
- Jaiswal, Amaresh; Bhalerao, Rajeev S.; Pal, Subrata
- Journal of Physics: Conference Series, Vol. 422
A relativistic relaxation-time model for the Boltzmann equation
journal, June 1974
- Anderson, J. L.; Witting, H. R.
- Physica, Vol. 74, Issue 3
Shear Viscosity of Strongly Coupled Supersymmetric Yang-Mills Plasma
journal, August 2001
- Policastro, G.; Son, D. T.; Starinets, A. O.
- Physical Review Letters, Vol. 87, Issue 8
Complete relativistic second-order dissipative hydrodynamics from the entropy principle
journal, February 2013
- Jaiswal, Amaresh; Bhalerao, Rajeev S.; Pal, Subrata
- Physical Review C, Vol. 87, Issue 2
Relativistic third-order dissipative fluid dynamics from kinetic theory
journal, August 2013
- Jaiswal, Amaresh
- Physical Review C, Vol. 88, Issue 2
Projection method and new formulation of leading-order anisotropic hydrodynamics
journal, March 2014
- Tinti, Leonardo; Florkowski, Wojciech
- Physical Review C, Vol. 89, Issue 3
Erratum: Derivation of transient relativistic fluid dynamics from the Boltzmann equation [Phys. Rev. D 85 , 114047 (2012)]
journal, February 2015
- Denicol, G. S.; Niemi, H.; Molnár, E.
- Physical Review D, Vol. 91, Issue 3
Symmetry constraints on generalizations of Bjorken flow
journal, October 2010
- Gubser, Steven S.
- Physical Review D, Vol. 82, Issue 8
Relativistic (lattice) Boltzmann equation with nonideal equation of state
journal, March 2012
- Romatschke, Paul
- Physical Review D, Vol. 85, Issue 6
Collective modes of an anisotropic quark-gluon plasma
journal, August 2003
- Romatschke, Paul; Strickland, Michael
- Physical Review D, Vol. 68, Issue 3
Second order hydrodynamic coefficients from kinetic theory
journal, March 2009
- York, Mark Abraao; Moore, Guy D.
- Physical Review D, Vol. 79, Issue 5
New relativistic dissipative fluid dynamics from kinetic theory
journal, March 2013
- Jaiswal, Amaresh; Bhalerao, Rajeev S.; Pal, Subrata
- Physics Letters B, Vol. 720, Issue 4-5
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
Anisotropic fluid dynamics for Gubser flow
journal, May 2017
- Martinez, M.; McNelis, M.; Heinz, U.
- Physical Review C, Vol. 95, Issue 5
Causal theories of dissipative relativistic fluid dynamics for nuclear collisions
journal, March 2004
- Muronga, Azwinndini
- Physical Review C, Vol. 69, Issue 3
Particle production in relativistic heavy-ion collisions: A consistent hydrodynamic approach
journal, October 2013
- Bhalerao, Rajeev S.; Jaiswal, Amaresh; Pal, Subrata
- Physical Review C, Vol. 88, Issue 4
Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in
journal, December 2015
- Noronha, Jorge; Denicol, Gabriel S.
- Physical Review D, Vol. 92, Issue 11
Anisotropic matching principle for the hydrodynamic expansion
journal, October 2016
- Tinti, Leonardo
- Physical Review C, Vol. 94, Issue 4
Anisotropic hydrodynamics for conformal Gubser flow
journal, February 2015
- Nopoush, Mohammad; Ryblewski, Radoslaw; Strickland, Michael
- Physical Review D, Vol. 91, Issue 4
Transport coefficients for bulk viscous evolution in the relaxation-time approximation
journal, October 2014
- Jaiswal, Amaresh; Ryblewski, Radoslaw; Strickland, Michael
- Physical Review C, Vol. 90, Issue 4
Highly relativistic nucleus-nucleus collisions: The central rapidity region
journal, January 1983
- Bjorken, J. D.
- Physical Review D, Vol. 27, Issue 1
Collective Flow and Viscosity in Relativistic Heavy-Ion Collisions
journal, October 2013
- Heinz, Ulrich; Snellings, Raimond
- Annual Review of Nuclear and Particle Science, Vol. 63, Issue 1
Relativistic dissipative hydrodynamics from kinetic theory with relaxation-time approximation
journal, May 2013
- Jaiswal, Amaresh
- Physical Review C, Vol. 87, Issue 5
Closing the equations of motion of anisotropic fluid dynamics by a judicious choice of a moment of the Boltzmann equation
journal, December 2016
- Molnár, E.; Niemi, H.; Rischke, D. H.
- Physical Review D, Vol. 94, Issue 12
Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime
journal, December 2016
- Bazow, D.; Denicol, G. S.; Heinz, U.
- Physical Review D, Vol. 94, Issue 12
On the kinetic theory of rarefied gases
journal, December 1949
- Grad, Harold
- Communications on Pure and Applied Mathematics, Vol. 2, Issue 4
Exact solution of the (0+1)-dimensional Boltzmann equation for massive Bose–Einstein and Fermi–Dirac gases
journal, February 2015
- Florkowski, Wojciech; Maksymiuk, Ewa
- Journal of Physics G: Nuclear and Particle Physics, Vol. 42, Issue 4
Generic instabilities in first-order dissipative relativistic fluid theories
journal, February 1985
- Hiscock, William A.; Lindblom, Lee
- Physical Review D, Vol. 31, Issue 4
Testing different formulations of leading-order anisotropic hydrodynamics
journal, February 2016
- Tinti, Leonardo; Ryblewski, Radoslaw; Florkowski, Wojciech
- Nuclear Physics A, Vol. 946
Stability and causality in dissipative relativistic fluids
journal, December 1983
- Hiscock, William A.; Lindblom, Lee
- Annals of Physics, Vol. 151, Issue 2
Derivation of transient relativistic fluid dynamics from the Boltzmann equation
journal, June 2012
- Denicol, G. S.; Niemi, H.; Molnár, E.
- Physical Review D, Vol. 85, Issue 11
Zum Paradoxon der W�rmeleitungstheorie
journal, August 1967
- M�ller, Ingo
- Zeitschrift f�r Physik, Vol. 198, Issue 4
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
Relativistic viscous hydrodynamics for heavy-ion collisions: A comparison between the Chapman-Enskog and Grad methods
journal, May 2014
- Bhalerao, Rajeev S.; Jaiswal, Amaresh; Pal, Subrata
- Physical Review C, Vol. 89, Issue 5
Second-order -dimensional anisotropic hydrodynamics
journal, November 2014
- Bazow, Dennis; Heinz, Ulrich; Strickland, Michael
- Physical Review C, Vol. 90, Issue 5
Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation
journal, June 2016
- Molnár, Etele; Niemi, Harri; Rischke, Dirk H.
- Physical Review D, Vol. 93, Issue 11
Exact solutions of the Boltzmann equation and optimized hydrodynamic approaches for relativistic heavy-ion collisions
journal, July 2016
- Heinz, U.; Bazow, D.; Denicol, G. S.
- Nuclear and Particle Physics Proceedings, Vol. 276-278
The Thermodynamics of Irreversible Processes. I. The Simple Fluid
journal, August 1940
- Eckart, Carl
- Physical Review, Vol. 58, Issue 3
Relaxation-time approximation and relativistic third-order viscous hydrodynamics from kinetic theory
journal, November 2014
- Jaiswal, Amaresh
- Nuclear Physics A, Vol. 931
Anisotropic nonequilibrium hydrodynamic attractor
journal, February 2018
- Strickland, Michael; Noronha, Jorge; Denicol, Gabriel S.
- Physical Review D, Vol. 97, Issue 3
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
Thermal equilibration in ultra-relativistic heavy-ion collisions
journal, April 1984
- Baym, Gordon
- Physics Letters B, Vol. 138, Issue 1-3
Exact solution of the ( )-dimensional Boltzmann equation for a massive gas
journal, May 2014
- Florkowski, Wojciech; Maksymiuk, Ewa; Ryblewski, Radoslaw
- Physical Review C, Vol. 89, Issue 5
Hydrodynamization in kinetic theory: Transient modes and the gradient expansion
journal, May 2018
- Heller, Michal P.; Kurkela, Aleksi; Spaliński, Michał
- Physical Review D, Vol. 97, Issue 9
Highly anisotropic hydrodynamics in space-time dimensions
journal, June 2012
- Ryblewski, Radoslaw; Florkowski, Wojciech
- Physical Review C, Vol. 85, Issue 6
Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow
journal, February 2018
- Behtash, Alireza; Cruz-Camacho, C. N.; Martinez, M.
- Physical Review D, Vol. 97, Issue 4