Higher order and anisotropic hydrodynamics for Bjorken and Gubser flows

Chattopadhyay, Chandrodoy; Heinz, Ulrich; Pal, Subrata; Vujanovic, Gojko

doi:10.1103/physrevc.97.064909

Title: Higher order and anisotropic hydrodynamics for Bjorken and Gubser flows

Journal Article · 14 June 2018 · Physical Review. C

DOI: https://doi.org/10.1103/physrevc.97.064909 · OSTI ID:1454315

Chattopadhyay, Chandrodoy ^[1]; Heinz, Ulrich ^[2]; Pal, Subrata ^[1]; Vujanovic, Gojko ^[3]

Tata Inst. of Fundamental Research, Mumbai (India). Dept. of Nuclear and Atomic Physics
The Ohio State Univ., Columbus, OH (United States). Dept. of Physics; European Organization for Nuclear Research (CERN), Geneva (Switzerland). Theoretical Physics Dept.
The Ohio State Univ., Columbus, OH (United States). Dept. of Physics

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.

View Journal Article

Cite

Export

Save

Research Organization:: The Ohio State Univ., Columbus, OH (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP); National Science Foundation (NSF)

Grant/Contract Number:: SC0004286; ACI-1550223

OSTI ID:: 1454315

Alternate ID(s):: OSTI ID: 1503828; OSTI ID: 1604328

Journal Information:: Physical Review. C, Vol. 97, Issue 6; ISSN 2469-9985

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 20 works

Citation information provided by
Web of Science

References (53)

Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation Denicol, Gabriel; Heinz, Ulrich; Martinez, Mauricio Physical Review D, Vol. 90, Issue 12 https://doi.org/10.1103/PhysRevD.90.125026	journal	December 2014
Relativistic third-order viscous corrections to the entropy four-current from kinetic theory Chattopadhyay, Chandrodoy; Jaiswal, Amaresh; Pal, Subrata Physical Review C, Vol. 91, Issue 2 https://doi.org/10.1103/PhysRevC.91.024917	journal	February 2015
Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics Kovtun, P. K.; Son, D. T.; Starinets, A. O. Physical Review Letters, Vol. 94, Issue 11 https://doi.org/10.1103/PhysRevLett.94.111601	journal	March 2005
Conformal hydrodynamics in Minkowski and de Sitter spacetimes Gubser, Steven S.; Yarom, Amos Nuclear Physics B, Vol. 846, Issue 3 https://doi.org/10.1016/j.nuclphysb.2011.01.012	journal	May 2011
Analytic Solution of the Boltzmann Equation in an Expanding System Bazow, D.; Denicol, G. S.; Heinz, U. Physical Review Letters, Vol. 116, Issue 2 https://doi.org/10.1103/PhysRevLett.116.022301	journal	January 2016
Boltzmann equation with a nonlocal collision term and the resultant dissipative fluid dynamics Jaiswal, Amaresh; Bhalerao, Rajeev S.; Pal, Subrata Journal of Physics: Conference Series, Vol. 422 https://doi.org/10.1088/1742-6596/422/1/012003	journal	March 2013
A relativistic relaxation-time model for the Boltzmann equation Anderson, J. L.; Witting, H. R. Physica, Vol. 74, Issue 3 https://doi.org/10.1016/0031-8914(74)90355-3	journal	June 1974
Shear Viscosity of Strongly Coupled N = 4 Supersymmetric Yang-Mills Plasma Policastro, G.; Son, D. T.; Starinets, A. O. Physical Review Letters, Vol. 87, Issue 8 https://doi.org/10.1103/PhysRevLett.87.081601	journal	August 2001
Complete relativistic second-order dissipative hydrodynamics from the entropy principle Jaiswal, Amaresh; Bhalerao, Rajeev S.; Pal, Subrata Physical Review C, Vol. 87, Issue 2 https://doi.org/10.1103/PhysRevC.87.021901	journal	February 2013
Relativistic third-order dissipative fluid dynamics from kinetic theory Jaiswal, Amaresh Physical Review C, Vol. 88, Issue 2 https://doi.org/10.1103/PhysRevC.88.021903	journal	August 2013
Projection method and new formulation of leading-order anisotropic hydrodynamics Tinti, Leonardo; Florkowski, Wojciech Physical Review C, Vol. 89, Issue 3 https://doi.org/10.1103/PhysRevC.89.034907	journal	March 2014
Erratum: Derivation of transient relativistic fluid dynamics from the Boltzmann equation [Phys. Rev. D 85 , 114047 (2012)] Denicol, G. S.; Niemi, H.; Molnár, E. Physical Review D, Vol. 91, Issue 3 https://doi.org/10.1103/PhysRevD.91.039902	journal	February 2015
Symmetry constraints on generalizations of Bjorken flow Gubser, Steven S. Physical Review D, Vol. 82, Issue 8 https://doi.org/10.1103/PhysRevD.82.085027	journal	October 2010
Relativistic (lattice) Boltzmann equation with nonideal equation of state Romatschke, Paul Physical Review D, Vol. 85, Issue 6 https://doi.org/10.1103/PhysRevD.85.065012	journal	March 2012
Collective modes of an anisotropic quark-gluon plasma Romatschke, Paul; Strickland, Michael Physical Review D, Vol. 68, Issue 3 https://doi.org/10.1103/PhysRevD.68.036004	journal	August 2003
Second order hydrodynamic coefficients from kinetic theory York, Mark Abraao; Moore, Guy D. Physical Review D, Vol. 79, Issue 5 https://doi.org/10.1103/PhysRevD.79.054011	journal	March 2009
New relativistic dissipative fluid dynamics from kinetic theory Jaiswal, Amaresh; Bhalerao, Rajeev S.; Pal, Subrata Physics Letters B, Vol. 720, Issue 4-5 https://doi.org/10.1016/j.physletb.2013.02.025	journal	March 2013
Transient relativistic thermodynamics and kinetic theory Israel, W.; Stewart, J. M. Annals of Physics, Vol. 118, Issue 2 https://doi.org/10.1016/0003-4916(79)90130-1	journal	April 1979
Dissipative dynamics of highly anisotropic systems Martinez, Mauricio; Strickland, Michael Nuclear Physics A, Vol. 848, Issue 1-2 https://doi.org/10.1016/j.nuclphysa.2010.08.011	journal	December 2010
Anisotropic fluid dynamics for Gubser flow Martinez, M.; McNelis, M.; Heinz, U. Physical Review C, Vol. 95, Issue 5 https://doi.org/10.1103/PhysRevC.95.054907	journal	May 2017
Causal theories of dissipative relativistic fluid dynamics for nuclear collisions Muronga, Azwinndini Physical Review C, Vol. 69, Issue 3 https://doi.org/10.1103/PhysRevC.69.034903	journal	March 2004
Particle production in relativistic heavy-ion collisions: A consistent hydrodynamic approach Bhalerao, Rajeev S.; Jaiswal, Amaresh; Pal, Subrata Physical Review C, Vol. 88, Issue 4 https://doi.org/10.1103/PhysRevC.88.044911	journal	October 2013
Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in AdS 2 ⊗ S 2 Noronha, Jorge; Denicol, Gabriel S. Physical Review D, Vol. 92, Issue 11 https://doi.org/10.1103/PhysRevD.92.114032	journal	December 2015
Anisotropic matching principle for the hydrodynamic expansion Tinti, Leonardo Physical Review C, Vol. 94, Issue 4 https://doi.org/10.1103/PhysRevC.94.044902	journal	October 2016
Anisotropic hydrodynamics for conformal Gubser flow Nopoush, Mohammad; Ryblewski, Radoslaw; Strickland, Michael Physical Review D, Vol. 91, Issue 4 https://doi.org/10.1103/PhysRevD.91.045007	journal	February 2015
Transport coefficients for bulk viscous evolution in the relaxation-time approximation Jaiswal, Amaresh; Ryblewski, Radoslaw; Strickland, Michael Physical Review C, Vol. 90, Issue 4 https://doi.org/10.1103/PhysRevC.90.044908	journal	October 2014
Highly relativistic nucleus-nucleus collisions: The central rapidity region Bjorken, J. D. Physical Review D, Vol. 27, Issue 1 https://doi.org/10.1103/PhysRevD.27.140	journal	January 1983
Collective Flow and Viscosity in Relativistic Heavy-Ion Collisions Heinz, Ulrich; Snellings, Raimond Annual Review of Nuclear and Particle Science, Vol. 63, Issue 1 https://doi.org/10.1146/annurev-nucl-102212-170540	journal	October 2013
Relativistic dissipative hydrodynamics from kinetic theory with relaxation-time approximation Jaiswal, Amaresh Physical Review C, Vol. 87, Issue 5 https://doi.org/10.1103/PhysRevC.87.051901	journal	May 2013
Closing the equations of motion of anisotropic fluid dynamics by a judicious choice of a moment of the Boltzmann equation Molnár, E.; Niemi, H.; Rischke, D. H. Physical Review D, Vol. 94, Issue 12 https://doi.org/10.1103/PhysRevD.94.125003	journal	December 2016
Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime Bazow, D.; Denicol, G. S.; Heinz, U. Physical Review D, Vol. 94, Issue 12 https://doi.org/10.1103/PhysRevD.94.125006	journal	December 2016
On the kinetic theory of rarefied gases Grad, Harold Communications on Pure and Applied Mathematics, Vol. 2, Issue 4 https://doi.org/10.1002/cpa.3160020403	journal	December 1949
Exact solution of the (0+1)-dimensional Boltzmann equation for massive Bose–Einstein and Fermi–Dirac gases Florkowski, Wojciech; Maksymiuk, Ewa Journal of Physics G: Nuclear and Particle Physics, Vol. 42, Issue 4 https://doi.org/10.1088/0954-3899/42/4/045106	journal	February 2015
Generic instabilities in first-order dissipative relativistic fluid theories Hiscock, William A.; Lindblom, Lee Physical Review D, Vol. 31, Issue 4 https://doi.org/10.1103/PhysRevD.31.725	journal	February 1985
Testing different formulations of leading-order anisotropic hydrodynamics Tinti, Leonardo; Ryblewski, Radoslaw; Florkowski, Wojciech Nuclear Physics A, Vol. 946 https://doi.org/10.1016/j.nuclphysa.2015.11.006	journal	February 2016
Stability and causality in dissipative relativistic fluids Hiscock, William A.; Lindblom, Lee Annals of Physics, Vol. 151, Issue 2 https://doi.org/10.1016/0003-4916(83)90288-9	journal	December 1983
Derivation of transient relativistic fluid dynamics from the Boltzmann equation Denicol, G. S.; Niemi, H.; Molnár, E. Physical Review D, Vol. 85, Issue 11 https://doi.org/10.1103/PhysRevD.85.114047	journal	June 2012
Zum Paradoxon der W�rmeleitungstheorie M�ller, Ingo Zeitschrift f�r Physik, Vol. 198, Issue 4 https://doi.org/10.1007/BF01326412	journal	August 1967
New Exact Solution of the Relativistic Boltzmann Equation and its Hydrodynamic Limit Denicol, Gabriel S.; Heinz, Ulrich; Martinez, Mauricio Physical Review Letters, Vol. 113, Issue 20 https://doi.org/10.1103/PhysRevLett.113.202301	journal	November 2014
Relativistic viscous hydrodynamics for heavy-ion collisions: A comparison between the Chapman-Enskog and Grad methods Bhalerao, Rajeev S.; Jaiswal, Amaresh; Pal, Subrata Physical Review C, Vol. 89, Issue 5 https://doi.org/10.1103/PhysRevC.89.054903	journal	May 2014
Second-order ( 2 + 1 ) -dimensional anisotropic hydrodynamics Bazow, Dennis; Heinz, Ulrich; Strickland, Michael Physical Review C, Vol. 90, Issue 5 https://doi.org/10.1103/PhysRevC.90.054910	journal	November 2014
Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation Molnár, Etele; Niemi, Harri; Rischke, Dirk H. Physical Review D, Vol. 93, Issue 11 https://doi.org/10.1103/PhysRevD.93.114025	journal	June 2016
Exact solutions of the Boltzmann equation and optimized hydrodynamic approaches for relativistic heavy-ion collisions Heinz, U.; Bazow, D.; Denicol, G. S. Nuclear and Particle Physics Proceedings, Vol. 276-278 https://doi.org/10.1016/j.nuclphysbps.2016.05.042	journal	July 2016
The Thermodynamics of Irreversible Processes. I. The Simple Fluid Eckart, Carl Physical Review, Vol. 58, Issue 3 https://doi.org/10.1103/PhysRev.58.267	journal	August 1940
Relaxation-time approximation and relativistic third-order viscous hydrodynamics from kinetic theory Jaiswal, Amaresh Nuclear Physics A, Vol. 931 https://doi.org/10.1016/j.nuclphysa.2014.08.035	journal	November 2014
Anisotropic nonequilibrium hydrodynamic attractor Strickland, Michael; Noronha, Jorge; Denicol, Gabriel S. Physical Review D, Vol. 97, Issue 3 https://doi.org/10.1103/PhysRevD.97.036020	journal	February 2018
Testing viscous and anisotropic hydrodynamics in an exactly solvable case Florkowski, Wojciech; Ryblewski, Radoslaw; Strickland, Michael Physical Review C, Vol. 88, Issue 2 https://doi.org/10.1103/PhysRevC.88.024903	journal	August 2013
Thermal equilibration in ultra-relativistic heavy-ion collisions Baym, Gordon Physics Letters B, Vol. 138, Issue 1-3 https://doi.org/10.1016/0370-2693(84)91863-X	journal	April 1984
Exact solution of the ( 0 + 1 )-dimensional Boltzmann equation for a massive gas Florkowski, Wojciech; Maksymiuk, Ewa; Ryblewski, Radoslaw Physical Review C, Vol. 89, Issue 5 https://doi.org/10.1103/PhysRevC.89.054908	journal	May 2014
Hydrodynamization in kinetic theory: Transient modes and the gradient expansion Heller, Michal P.; Kurkela, Aleksi; Spaliński, Michał Physical Review D, Vol. 97, Issue 9 https://doi.org/10.1103/PhysRevD.97.091503	journal	May 2018
Highly anisotropic hydrodynamics in 3 + 1 space-time dimensions Ryblewski, Radoslaw; Florkowski, Wojciech Physical Review C, Vol. 85, Issue 6 https://doi.org/10.1103/PhysRevC.85.064901	journal	June 2012
Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow Behtash, Alireza; Cruz-Camacho, C. N.; Martinez, M. Physical Review D, Vol. 97, Issue 4 https://doi.org/10.1103/PhysRevD.97.044041	journal	February 2018
Wigner function and normal ordering Van Weert, Ch. G. Physica A: Statistical Mechanics and its Applications, Vol. 100, Issue 3 https://doi.org/10.1016/0378-4371(80)90174-0	journal	March 1980

Cited By (2)

Radiative heavy quark energy loss in an expanding viscous QCD plasma Sarkar, Sreemoyee; Chattopadhyay, Chandrodoy; Pal, Subrata Physical Review C, Vol. 97, Issue 6 https://doi.org/10.1103/physrevc.97.064916	journal	June 2018
Exact solutions and attractors of higher-order viscous fluid dynamics for Bjorken flow Jaiswal, Sunil; Chattopadhyay, Chandrodoy; Jaiswal, Amaresh arXiv https://doi.org/10.48550/arxiv.1907.07965	text	January 2019

Similar Records

Thermalization & hydrodynamics in Bjorken & Gubser flows

Journal Article · 2019 · Nuclear Physics. A · OSTI ID:1547837

Chattopadhyay, Chandrodoy; Heinz, Ulrich; Pal, Subrata; +1 more

Hydrodynamic generators in relativistic kinetic theory

Journal Article · 2020 · Physical Review. C · OSTI ID:1617126

McNelis, M.; Heinz, U.

Anisotropic fluid dynamics for Gubser flow

Journal Article · 2017 · Physical Review C · OSTI ID:1604333

Martinez, M.; McNelis, M.; Heinz, Ulrich

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
hydrodynamic models
quark-gluon plasma
relativistic heavy-ion collisions

Title: Higher order and anisotropic hydrodynamics for Bjorken and Gubser flows

Citation Formats

References (53)

Cited By (2)

Similar Records

Related Subjects