Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in AdS2 Ⓧ S2
Abstract
In this paper we obtain an analytical solution of the relativistic Boltzmann equation under the relaxation time approximation that describes the out-of-equilibrium dynamics of a radially expanding massless gas. This solution is found by mapping this expanding system in flat spacetime to a static flow in the curved spacetime AdS2 Ⓧ S2. We further derive explicit analytic expressions for the momentum dependence of the single-particle distribution function as well as for the spatial dependence of its moments. We find that this dissipative system has the ability to flow as a perfect fluid even though its entropy density does not match the equilibrium form. The nonequilibrium contribution to the entropy density is shown to be due to higher-order scalar moments (which possess no hydrodynamical interpretation) of the Boltzmann equation that can remain out of equilibrium but do not couple to the energy-momentum tensor of the system. Furthermore, in this system the slowly moving hydrodynamic degrees of freedom can exhibit true perfect fluidity while being totally decoupled from the fast moving, nonhydrodynamical microscopic degrees of freedom that lead to entropy production.
- Authors:
-
- Columbia Univ., New York, NY (United States); Univ. de Sao Paulo, Sao Paulo (Brazil)
- McGill Univ., Montreal, QC (Canada); Brookhaven National Lab. (BNL), Upton, NY (United States)
- Publication Date:
- Research Org.:
- Brookhaven National Lab. (BNL), Upton, NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP)
- OSTI Identifier:
- 1295202
- Alternate Identifier(s):
- OSTI ID: 1234100
- Report Number(s):
- BNL-112210-2016-JA
Journal ID: ISSN 1550-7998; R&D Project: KB0301020; KB0301020
- Grant/Contract Number:
- SC00112704; SC0012704
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. D, Particles, Fields, Gravitation and Cosmology
- Additional Journal Information:
- Journal Volume: 92; Journal Issue: 11; Journal ID: ISSN 1550-7998
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Citation Formats
Noronha, Jorge, and Denicol, Gabriel S. Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in AdS2 Ⓧ S2. United States: N. p., 2015.
Web. doi:10.1103/PhysRevD.92.114032.
Noronha, Jorge, & Denicol, Gabriel S. Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in AdS2 Ⓧ S2. United States. https://doi.org/10.1103/PhysRevD.92.114032
Noronha, Jorge, and Denicol, Gabriel S. Wed .
"Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in AdS2 Ⓧ S2". United States. https://doi.org/10.1103/PhysRevD.92.114032. https://www.osti.gov/servlets/purl/1295202.
@article{osti_1295202,
title = {Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in AdS2 Ⓧ S2},
author = {Noronha, Jorge and Denicol, Gabriel S.},
abstractNote = {In this paper we obtain an analytical solution of the relativistic Boltzmann equation under the relaxation time approximation that describes the out-of-equilibrium dynamics of a radially expanding massless gas. This solution is found by mapping this expanding system in flat spacetime to a static flow in the curved spacetime AdS2 Ⓧ S2. We further derive explicit analytic expressions for the momentum dependence of the single-particle distribution function as well as for the spatial dependence of its moments. We find that this dissipative system has the ability to flow as a perfect fluid even though its entropy density does not match the equilibrium form. The nonequilibrium contribution to the entropy density is shown to be due to higher-order scalar moments (which possess no hydrodynamical interpretation) of the Boltzmann equation that can remain out of equilibrium but do not couple to the energy-momentum tensor of the system. Furthermore, in this system the slowly moving hydrodynamic degrees of freedom can exhibit true perfect fluidity while being totally decoupled from the fast moving, nonhydrodynamical microscopic degrees of freedom that lead to entropy production.},
doi = {10.1103/PhysRevD.92.114032},
journal = {Physical Review. D, Particles, Fields, Gravitation and Cosmology},
number = 11,
volume = 92,
place = {United States},
year = {2015},
month = {12}
}
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Works referenced in this record:
Microscopic models for ultrarelativistic heavy ion collisions
journal, January 1998
- Bass, S.
- Progress in Particle and Nuclear Physics, Vol. 41
Anisotropic flow in transport + hydrodynamics hybrid approaches
journal, November 2014
- Petersen, Hannah
- Journal of Physics G: Nuclear and Particle Physics, Vol. 41, Issue 12
A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems
journal, May 1954
- Bhatnagar, P. L.; Gross, E. P.; Krook, M.
- Physical Review, Vol. 94, Issue 3
A relativistic relaxation-time model for the Boltzmann equation
journal, June 1974
- Anderson, J. L.; Witting, H. R.
- Physica, Vol. 74, 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
Shear-bulk coupling in nonconformal hydrodynamics
journal, October 2014
- Denicol, Gabriel S.; Florkowski, Wojciech; Ryblewski, Radoslaw
- Physical Review C, Vol. 90, 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
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
Anisotropic hydrodynamics for conformal Gubser flow
journal, February 2015
- Nopoush, Mohammad; Ryblewski, Radoslaw; Strickland, Michael
- Physical Review D, Vol. 91, Issue 4
Symmetry constraints on generalizations of Bjorken flow
journal, October 2010
- Gubser, Steven S.
- Physical Review D, Vol. 82, Issue 8
Conformal hydrodynamics in Minkowski and de Sitter spacetimes
journal, May 2011
- Gubser, Steven S.; Yarom, Amos
- Nuclear Physics B, Vol. 846, Issue 3
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
Exact analytical solutions of second order conformal hydrodynamics
journal, March 2014
- Hatta, Yoshitaka; Noronha, Jorge; Xiao, Bo-Wen
- Physical Review D, Vol. 89, Issue 5
Systematic study of exact solutions in second-order conformal hydrodynamics
journal, June 2014
- Hatta, Yoshitaka; Noronha, Jorge; Xiao, Bo-Wen
- Physical Review D, Vol. 89, Issue 11
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
Transient relativistic thermodynamics and kinetic theory
journal, April 1979
- Israel, W.; Stewart, J. M.
- Annals of Physics, Vol. 118, Issue 2
Relativistic viscous hydrodynamics, conformal invariance, and holography
journal, April 2008
- Baier, Rudolf; Romatschke, Paul; Son, Dam Thanh
- Journal of High Energy Physics, Vol. 2008, Issue 04
Expanding plasmas and quasinormal modes of anti-de Sitter black holes
journal, April 2007
- Friess, Joshua J.; Gubser, Steven S.; Michalogiorgakis, Georgios
- Journal of High Energy Physics, Vol. 2007, Issue 04
The large $N$ limit of superconformal field theories and supergravity
journal, January 1998
- Maldacena, Juan
- Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 2
Dissipative Relativistic Fluid Dynamics: A New Way to Derive the Equations of Motion from Kinetic Theory
journal, October 2010
- Denicol, G. S.; Koide, T.; Rischke, D. H.
- Physical Review Letters, Vol. 105, Issue 16
General relativistic Boltzmann equation, I: Covariant treatment
journal, April 2009
- Debbasch, F.; van Leeuwen, W. A.
- Physica A: Statistical Mechanics and its Applications, Vol. 388, Issue 7
General relativistic Boltzmann equation, II: Manifestly covariant treatment
journal, May 2009
- Debbasch, F.; van Leeuwen, W. A.
- Physica A: Statistical Mechanics and its Applications, Vol. 388, Issue 9
Origin of the relaxation time in dissipative fluid dynamics
journal, April 2011
- Denicol, Gabriel S.; Noronha, Jorge; Niemi, Harri
- Physical Review D, Vol. 83, Issue 7
New simple explicit solutions of perfect-fluid hydrodynamics and phase-space evolution
journal, May 2011
- Nagy, M. I.
- Physical Review C, Vol. 83, Issue 5
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
Works referencing / citing this record:
Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime
text, January 2016
- Bazow, D.; Denicol, G. S.; Heinz, U.
- arXiv
Causality and existence of solutions of relativistic viscous fluid dynamics with gravity
text, January 2017
- Bemfica, Fabio S.; Disconzi, Marcelo M.; Noronha, Jorge
- arXiv