Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime

Bazow, D.; Denicol, G. S.; Heinz, Ulrich; Martinez, M.; Noronha, J.

doi:10.1103/PhysRevD.94.125006

Title: Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime

Journal Article · Thu Dec 08 00:00:00 EST 2016 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.94.125006· OSTI ID:1604346

Bazow, D. ^[1]; Denicol, G. S. ^[2];

^[1]; Martinez, M. ^[1]; Noronha, J. ^[3]

The Ohio State Univ., Columbus, OH (United States)
Fluminense Federal Univ., Niterói, RJ (Brazil); Brookhaven National Lab. (BNL), Upton, NY (United States)
Univ. of São Paulo (Brazil)

The dissipative dynamics of an expanding massless gas with constant cross section in a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe is researched. The mathematical problem of solving the full nonlinear relativistic Boltzmann equation is recast into an infinite set of nonlinear ordinary differential equations for the moments of the one-particle distribution function. Momentum-space resolution is determined by the number of nonhydrodynamic modes included in the moment hierarchy, i.e., by the truncation order. We show that in the FLRW spacetime the nonhydrodynamic modes decouple completely from the hydrodynamic degrees of freedom. This results in the system flowing as an ideal fluid while at the same time producing entropy. The solutions to the nonlinear Boltzmann equation exhibit transient tails of the distribution function with nontrivial momentum dependence. The evolution of this tail is not correctly captured by the relaxation time approximation nor by the linearized Boltzmann equation. Yet, the latter probes additional high-momentum details unresolved by the relaxation time approximation. While the expansion of the FLRW spacetime is slow enough for the system to move towards (and not away from) local thermal equilibrium, it is not sufficiently slow for the system to actually ever reach complete local equilibrium. Equilibration is fastest in the relaxation time approximation, followed, in turn, by kinetic evolution with a linearized and a fully nonlinear Boltzmann collision term.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: The Ohio State Univ., Columbus, OH (United States); Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: SC0004286; SC0012704

OSTI ID:: 1604346

Alternate ID(s):: OSTI ID: 1334854

Journal Information:: Physical Review D, Vol. 94, Issue 12; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 32 works

Citation information provided by
Web of Science

References (102)

Turbulent thermalization process in heavy-ion collisions at ultrarelativistic energies Berges, J.; Boguslavski, K.; Schlichting, S. Physical Review D, Vol. 89, Issue 7 https://doi.org/10.1103/PhysRevD.89.074011	journal	April 2014
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
Relative importance of second-order terms in relativistic dissipative fluid dynamics Molnár, E.; Niemi, H.; Denicol, G. S. Physical Review D, Vol. 89, Issue 7 https://doi.org/10.1103/PhysRevD.89.074010	journal	April 2014
Inhomogeneous Cosmological Models Krasinski, Andrzej https://doi.org/10.1017/CBO9780511721694	book	January 1997
The quark–gluon plasma: collective dynamics and hard thermal loops Blaizot, Jean-Paul; Iancu, Edmond Physics Reports, Vol. 359, Issue 5-6 https://doi.org/10.1016/S0370-1573(01)00061-8	journal	March 2002
Quark-gluon transport theory II. Color response and color correlations in a quark-gluon plasma Heinz, Ulrich Annals of Physics, Vol. 168, Issue 1 https://doi.org/10.1016/0003-4916(86)90114-4	journal	April 1986
Boltzmann hierarchy for interacting neutrinos I: formalism Oldengott, Isabel M.; Rampf, Cornelius; Wong, Yvonne Y. Y. Journal of Cosmology and Astroparticle Physics, Vol. 2015, Issue 04 https://doi.org/10.1088/1475-7516/2015/04/016	journal	April 2015
Microscopic models for ultrarelativistic heavy ion collisions Bass, S. Progress in Particle and Nuclear Physics, Vol. 41 https://doi.org/10.1016/S0146-6410(98)00058-1	journal	January 1998
Asymptotic behaviour of the relativistic Boltzmann equation in the Robertson–Walker spacetime Lee, Ho Journal of Differential Equations, Vol. 255, Issue 11 https://doi.org/10.1016/j.jde.2013.08.006	journal	December 2013
Boltzmann equation in classical and quantum field theory Jeon, Sangyong Physical Review C, Vol. 72, Issue 1 https://doi.org/10.1103/PhysRevC.72.014907	journal	July 2005
Relativistic dynamics of non-ideal fluids: Viscous and heat-conducting fluids. II. Transport properties and microscopic description of relativistic nuclear matter Muronga, Azwinndini Physical Review C, Vol. 76, Issue 1 https://doi.org/10.1103/PhysRevC.76.014910	journal	July 2007
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
Erratum to “Saturation of elliptic flow and the transport opacity of the gluon plasma at RHIC” Molnar, D. Nuclear Physics A, Vol. 703, Issue 3-4 https://doi.org/10.1016/S0375-9474(02)00859-X	journal	June 2002
Formation of Maxwellian Tails Krook, Max; Wu, Tai Tsun Physical Review Letters, Vol. 36, Issue 19 https://doi.org/10.1103/PhysRevLett.36.1107	journal	May 1976
Nonthermal Fixed Points: Effective Weak Coupling for Strongly Correlated Systems Far from Equilibrium Berges, Jürgen; Rothkopf, Alexander; Schmidt, Jonas Physical Review Letters, Vol. 101, Issue 4 https://doi.org/10.1103/PhysRevLett.101.041603	journal	July 2008
Isotropization and Hydrodynamization in Weakly Coupled Heavy-Ion Collisions Kurkela, Aleksi; Zhu, Yan Physical Review Letters, Vol. 115, Issue 18 https://doi.org/10.1103/PhysRevLett.115.182301	journal	October 2015
Finite-Temperature Field Theory Kapusta, Joseph I.; Gale, Charles https://doi.org/10.1017/CBO9780511535130	book	January 2006
Reheating and thermalization in a simple scalar model Son, D. T. Physical Review D, Vol. 54, Issue 6 https://doi.org/10.1103/PhysRevD.54.3745	journal	September 1996
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
General relativistic Boltzmann equation, II: Manifestly covariant treatment Debbasch, F.; van Leeuwen, W. A. Physica A: Statistical Mechanics and its Applications, Vol. 388, Issue 9 https://doi.org/10.1016/j.physa.2009.01.009	journal	May 2009
The Boltzmann equation and its applications Ramos, J. I. Applied Mathematical Modelling, Vol. 14, Issue 11 https://doi.org/10.1016/0307-904x(90)90115-l	journal	November 1990
Saturation of elliptic flow and the transport opacity of the gluon plasma at RHIC Molnár, Dénes; Gyulassy, Miklos Nuclear Physics A, Vol. 697, Issue 1-2 https://doi.org/10.1016/S0375-9474(01)01224-6	journal	January 2002
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
Approach to Equilibrium in Weakly Coupled Non-Abelian Plasmas Kurkela, Aleksi; Lu, Egang Physical Review Letters, Vol. 113, Issue 18 https://doi.org/10.1103/PhysRevLett.113.182301	journal	October 2014
Role of quantum fluctuations in a system with strong fields: Onset of hydrodynamical flow Dusling, Kevin; Epelbaum, Thomas; Gelis, François Nuclear Physics A, Vol. 850, Issue 1 https://doi.org/10.1016/j.nuclphysa.2010.11.009	journal	January 2011
Thermal Field Theory Le Bellac, Michel Cambridge University Press https://doi.org/10.1017/CBO9780511721700	book	January 2010
Solutions of the Boltzmann equation for Maxwell interactions and singular angle-dependent cross sections Cornille, H.; Gervois, A. Journal of Statistical Physics, Vol. 23, Issue 2 https://doi.org/10.1007/BF01012590	journal	August 1980
Universality Far from Equilibrium: From Superfluid Bose Gases to Heavy-Ion Collisions Berges, J.; Boguslavski, K.; Schlichting, S. Physical Review Letters, Vol. 114, Issue 6 https://doi.org/10.1103/PhysRevLett.114.061601	journal	February 2015
Properties of the Boltzmann equation in the classical approximation Epelbaum, Thomas; Gelis, François; Tanji, Naoto Physical Review D, Vol. 90, Issue 12 https://doi.org/10.1103/PhysRevD.90.125032	journal	December 2014
Collisional relaxation in simulations of heavy-ion collisions using Boltzmann-type equations Welke, G.; Malfliet, R.; Grégoire, C. Physical Review C, Vol. 40, Issue 6 https://doi.org/10.1103/PhysRevC.40.2611	journal	December 1989
Nonequilibrium fixed points in longitudinally expanding scalar theories: Infrared cascade, Bose condensation, and a challenge for kinetic theory Berges, J.; Boguslavski, K.; Schlichting, S. Physical Review D, Vol. 92, Issue 9 https://doi.org/10.1103/PhysRevD.92.096006	journal	November 2015
Basin of attraction for turbulent thermalization and the range of validity of classical-statistical simulations Berges, J.; Boguslavski, K.; Schlichting, S. Journal of High Energy Physics, Vol. 2014, Issue 5 https://doi.org/10.1007/JHEP05(2014)054	journal	May 2014
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
Thermalization of gluons in ultrarelativistic heavy ion collisions by including three-body interactions in a parton cascade Xu, Zhe; Greiner, Carsten Physical Review C, Vol. 71, Issue 6 https://doi.org/10.1103/PhysRevC.71.064901	journal	June 2005
General relativistic Boltzmann equation, I: Covariant treatment Debbasch, F.; van Leeuwen, W. A. Physica A: Statistical Mechanics and its Applications, Vol. 388, Issue 7 https://doi.org/10.1016/j.physa.2008.12.023	journal	April 2009
Semiclassicality and decoherence of cosmological perturbations Polarski, David; Starobinsky, Alexei A. Classical and Quantum Gravity, Vol. 13, Issue 3 https://doi.org/10.1088/0264-9381/13/3/006	journal	March 1996
Effective transport equations for non-Abelian plasmas Litim, Daniel F.; Manuel, Cristina Nuclear Physics B, Vol. 562, Issue 1-2 https://doi.org/10.1016/S0550-3213(99)00531-3	journal	November 1999
The Boltzmann equation in classical Yang–Mills theory Mathieu, V.; Mueller, A. H.; Triantafyllopoulos, D. N. The European Physical Journal C, Vol. 74, Issue 5 https://doi.org/10.1140/epjc/s10052-014-2873-8	journal	May 2014
Kinetic theory of a longitudinally expanding system of scalar particles Epelbaum, Thomas; Gelis, François; Jeon, Sangyong Journal of High Energy Physics, Vol. 2015, Issue 9 https://doi.org/10.1007/JHEP09(2015)117	journal	September 2015
A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems Bhatnagar, P. L.; Gross, E. P.; Krook, M. Physical Review, Vol. 94, Issue 3 https://doi.org/10.1103/PhysRev.94.511	journal	May 1954
Theory of core-collapse supernovae Janka, H.; Langanke, K.; Marek, A. Physics Reports, Vol. 442, Issue 1-6 https://doi.org/10.1016/j.physrep.2007.02.002	journal	April 2007
Supernova Simulations with Boltzmann Neutrino Transport: A Comparison of Methods Liebendorfer, M.; Rampp, M.; Janka, H. ‐Th. The Astrophysical Journal, Vol. 620, Issue 2 https://doi.org/10.1086/427203	journal	February 2005
Reheating in Inflationary Cosmology: Theory and Applications Allahverdi, Rouzbeh; Brandenberger, Robert; Cyr-Racine, Francis-Yan Annual Review of Nuclear and Particle Science, Vol. 60, Issue 1 https://doi.org/10.1146/annurev.nucl.012809.104511	journal	November 2010
Bulk viscosity of high-temperature QCD Arnold, Peter; Doğan, Çağlar; Moore, Guy D. Physical Review D, Vol. 74, Issue 8 https://doi.org/10.1103/PhysRevD.74.085021	journal	October 2006
Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in ${AdS}_{2} \otimes S_{2}$ Noronha, Jorge; Denicol, Gabriel S. Physical Review D, Vol. 92, Issue 11 https://doi.org/10.1103/PhysRevD.92.114032	journal	December 2015
Anisotropic 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
DEFROST: a new code for simulating preheating after inflation Frolov, Andrei V. Journal of Cosmology and Astroparticle Physics, Vol. 2008, Issue 11 https://doi.org/10.1088/1475-7516/2008/11/009	journal	November 2008
Classical Decay of the Inflaton Khlebnikov, S. Yu.; Tkachev, I. I. Physical Review Letters, Vol. 77, Issue 2 https://doi.org/10.1103/PhysRevLett.77.219	journal	July 1996
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
Relativistic Turbulence: A Long Way from Preheating to Equilibrium Micha, Raphael; Tkachev, Igor I. Physical Review Letters, Vol. 90, Issue 12 https://doi.org/10.1103/PhysRevLett.90.121301	journal	March 2003
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
On the equivalence between the Boltzmann equation and classical field theory at large occupation numbers Mueller, A. H.; Son, D. T. Physics Letters B, Vol. 582, Issue 3-4 https://doi.org/10.1016/j.physletb.2003.12.047	journal	March 2004
Pressure Isotropization in High Energy Heavy Ion Collisions Epelbaum, Thomas; Gelis, François Physical Review Letters, Vol. 111, Issue 23 https://doi.org/10.1103/PhysRevLett.111.232301	journal	December 2013
“Bottom-up” thermalization in heavy ion collisions Baier, R.; Mueller, A. H.; Schiff, D. Physics Letters B, Vol. 502, Issue 1-4 https://doi.org/10.1016/S0370-2693(01)00191-5	journal	March 2001
Analytic solutions of the relativistic Boltzmann equation Hatta, Yoshitaka; Martinez, Mauricio; Xiao, Bo-Wen Physical Review D, Vol. 91, Issue 8 https://doi.org/10.1103/PhysRevD.91.085024	journal	April 2015
Nonlinear model-Boltzmann equations and exact solutions Ernst, M. H. Physics Reports, Vol. 78, Issue 1 https://doi.org/10.1016/0370-1573(81)90002-8	journal	November 1981
Finite-temperature field theory Kapusta, J. I.; Landshoff, P. V. Journal of Physics G: Nuclear and Particle Physics, Vol. 15, Issue 3 https://doi.org/10.1088/0954-3899/15/3/005	journal	March 1989
Universal attractor in a highly occupied non-Abelian plasma Berges, J.; Boguslavski, K.; Schlichting, S. Physical Review D, Vol. 89, Issue 11 https://doi.org/10.1103/PhysRevD.89.114007	journal	June 2014
Entropy Generation and the Survival of Protogalaxies in an Expanding Universe Weinberg, Steven The Astrophysical Journal, Vol. 168 https://doi.org/10.1086/151073	journal	September 1971
Exact solutions of the Boltzmann equation Krook, Max; Wu, Tai Tsun Physics of Fluids, Vol. 20, Issue 10 https://doi.org/10.1063/1.861780	journal	January 1977
Cosmological Perturbation Theory in the Synchronous and Conformal Newtonian Gauges Ma, Chung-Pei; Bertschinger, Edmund The Astrophysical Journal, Vol. 455 https://doi.org/10.1086/176550	journal	December 1995
Kinetic Theory for Plasmas with Non-Abelian Interactions Heinz, Ulrich Physical Review Letters, Vol. 51, Issue 5 https://doi.org/10.1103/PhysRevLett.51.351	journal	August 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
How particles emerge from decaying classical fields in heavy ion collisions: Towards a kinetic description of the Glasma Gelis, François; Jeon, Sangyong; Venugopalan, Raju Nuclear Physics A, Vol. 817, Issue 1-4 https://doi.org/10.1016/j.nuclphysa.2008.11.011	journal	February 2009
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
From quantum field theory to hydrodynamics: Transport coefficients and effective kinetic theory Jeon, Sangyong; Yaffe, Laurence G. Physical Review D, Vol. 53, Issue 10 https://doi.org/10.1103/PhysRevD.53.5799	journal	May 1996
Quark-Gluon transport theory Elze, Hans-Thomas; Heinz, Ulrich Physics Reports, Vol. 183, Issue 3 https://doi.org/10.1016/0370-1573(89)90059-8	journal	November 1989
Origin of the relaxation time in dissipative fluid dynamics Denicol, Gabriel S.; Noronha, Jorge; Niemi, Harri Physical Review D, Vol. 83, Issue 7 https://doi.org/10.1103/PhysRevD.83.074019	journal	April 2011
A Boltzmann equation for the QCD plasma Blaizot, Jean-Paul; Iancu, Edmond Nuclear Physics B, Vol. 557, Issue 1-2 https://doi.org/10.1016/S0550-3213(99)00341-7	journal	September 1999
Semi-classical transport theory for non-Abelian plasmas Litim, Daniel F.; Manuel, Cristina Physics Reports, Vol. 364, Issue 6 https://doi.org/10.1016/S0370-1573(02)00015-7	journal	July 2002
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
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
Solutions of conformal Israel-Stewart relativistic viscous fluid dynamics Marrochio, Hugo; Noronha, Jorge; Denicol, Gabriel S. Physical Review C, Vol. 91, Issue 1 https://doi.org/10.1103/PhysRevC.91.014903	journal	January 2015
Investigating the domain of validity of the Gubser solution to the Boltzmann equation Heinz, Ulrich; Martinez, Mauricio Nuclear Physics A, Vol. 943 https://doi.org/10.1016/j.nuclphysa.2015.08.009	journal	November 2015
Anisotropic hydrodynamics for conformal Gubser flow Strickland, Michael; Nopoush, Mohammad; Ryblewski, Radoslaw Nuclear Physics A, Vol. 956 https://doi.org/10.1016/j.nuclphysa.2016.02.014	journal	December 2016
Inhomogeneous Cosmological Models: Proceedings of the Spanish Relativity Meeting Molina, A.; Senovilla, M. M. https://doi.org/10.1142/2825	conference	June 1995
Lattice study of classical inflaton decay Prokopec, Tomislav; Roos, Thomas G. Physical Review D, Vol. 55, Issue 6 https://doi.org/10.1103/PhysRevD.55.3768	journal	March 1997
Turbulent thermalization Micha, Raphael; Tkachev, Igor I. Physical Review D, Vol. 70, Issue 4 https://doi.org/10.1103/PhysRevD.70.043538	journal	August 2004
Non-thermal Fixed Points: Effective Weak-coupling for Strongly Correlated Systems far from Equilibrium. Berges, Juergen; Rothkopf, Alexander.; Schmidt, Jonas Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/phppubdb-7455	text	January 2008
DEFROST: A New Code for Simulating Preheating after Inflation Frolov, Andrei V. arXiv https://doi.org/10.48550/arxiv.0809.4904	text	January 2008
Role of quantum fluctuations in a system with strong fields: Onset of hydrodynamical flow Dusling, K.; Epelbaum, T.; Gelis, F. arXiv https://doi.org/10.48550/arxiv.1009.4363	text	January 2010
Origin of the Relaxation Time in Dissipative Fluid Dynamics Denicol, G. S.; Noronha, J.; Niemi, H. arXiv https://doi.org/10.48550/arxiv.1102.4780	text	January 2011
Derivation of transient relativistic fluid dynamics from the Boltzmann equation Denicol, G. S.; Niemi, H.; Molnar, E. arXiv https://doi.org/10.48550/arxiv.1202.4551	text	January 2012
Turbulent thermalization process in heavy-ion collisions at ultrarelativistic energies Berges, J.; Boguslavski, K.; Schlichting, S. arXiv https://doi.org/10.48550/arxiv.1303.5650	text	January 2013
On the relative importance of second-order terms in relativistic dissipative fluid dynamics Molnár, E.; Niemi, H.; Denicol, G. S. arXiv https://doi.org/10.48550/arxiv.1308.0785	text	January 2013
Universal attractor in a highly occupied non-Abelian plasma Berges, Juergen; Boguslavski, Kirill; Schlichting, Soeren arXiv https://doi.org/10.48550/arxiv.1311.3005	text	January 2013
The Boltzmann Equation in Classical Yang-Mills Theory Mathieu, V.; Mueller, A. H.; Triantafyllopoulos, D. N. arXiv https://doi.org/10.48550/arxiv.1403.1184	text	January 2014
Approach to equilibrium in weakly coupled nonabelian plasmas Kurkela, Aleksi; Lu, Egang arXiv https://doi.org/10.48550/arxiv.1405.6318	text	January 2014
Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation Denicol, Gabriel S.; Heinz, Ulrich W.; Martinez, Mauricio arXiv https://doi.org/10.48550/arxiv.1408.7048	text	January 2014
Kinetic theory of a longitudinally expanding system of scalar particles Epelbaum, Thomas; Gelis, Francois; Jeon, Sangyong arXiv https://doi.org/10.48550/arxiv.1506.05580	text	January 2015
Isotropization and hydrodynamization in weakly coupled heavy-ion collisions Kurkela, Aleksi; Zhu, Yan arXiv https://doi.org/10.48550/arxiv.1506.06647	text	January 2015
Investigating the domain of validity of the Gubser solution to the Boltzmann equation Heinz, Ulrich W.; Martinez, Mauricio arXiv https://doi.org/10.48550/arxiv.1506.07500	text	January 2015
Semiclassicality and Decoherence of Cosmological Perturbations Polarski, David; Starobinsky, Alexei A. arXiv https://doi.org/10.48550/arxiv.gr-qc/9504030	text	January 1995
The Quark-Gluon Plasma: Collective Dynamics and Hard Thermal Loops Blaizot, Jean-Paul; Iancu, Edmond arXiv https://doi.org/10.48550/arxiv.hep-ph/0101103	text	January 2001
Semi-classical transport theory for non-Abelian plasmas Litim, Daniel F.; Manuel, Cristina arXiv https://doi.org/10.48550/arxiv.hep-ph/0110104	text	January 2001
Relativistic Turbulence: A Long Way from Preheating to Equilibrium Micha, R.; Tkachev, I. I. arXiv https://doi.org/10.48550/arxiv.hep-ph/0210202	text	January 2002
Turbulent Thermalization Micha, Raphael; Tkachev, Igor I. arXiv https://doi.org/10.48550/arxiv.hep-ph/0403101	text	January 2004
Thermalization of gluons in ultrarelativistic heavy ion collisions by including three-body interactions in a parton cascade Xu, Zhe; Greiner, Carsten arXiv https://doi.org/10.48550/arxiv.hep-ph/0406278	text	January 2004
Reheating and thermalization in a simple scalar model Son, D. T. arXiv https://doi.org/10.48550/arxiv.hep-ph/9604340	text	January 1996
Lattice study of classical inflaton decay Prokopec, Tomislav; Roos, Thomas G. arXiv https://doi.org/10.48550/arxiv.hep-ph/9610400	text	January 1996
Effective Transport Equations for non-Abelian Plasmas Litim, Daniel F.; Manuel, Cristina arXiv https://doi.org/10.48550/arxiv.hep-ph/9906210	text	January 1999

Cited By (3)

Interacting neutrinos in cosmology: exact description and constraints Oldengott, Isabel M.; Tram, Thomas; Rampf, Cornelius Journal of Cosmology and Astroparticle Physics, Vol. 2017, Issue 11 https://doi.org/10.1088/1475-7516/2017/11/027	journal	November 2017
Causality and existence of solutions of relativistic viscous fluid dynamics with gravity Bemfica, Fabio S.; Disconzi, Marcelo M.; Noronha, Jorge arXiv https://doi.org/10.48550/arxiv.1708.06255	text	January 2017
Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow Behtash, Alireza; Cruz-Camacho, C. N.; Martinez, M. arXiv https://doi.org/10.48550/arxiv.1711.01745	text	January 2017

Similar Records

The lapse function in Friedmann—Lemaître–Robertson–Walker cosmologies

Journal Article · Sun Dec 15 00:00:00 EST 2019 · Annals of Physics · OSTI ID:1604346

Scalar field dynamics in Friedmann-Robertson-Walker spacetimes

Journal Article · Fri Aug 01 00:00:00 EDT 1997 · Physical Review, D · OSTI ID:1604346

Boyanovsky, D; Cormier, D; Holman, R; +3 more

Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime

Journal Article · Thu Dec 01 00:00:00 EST 2016 · Physical Review D · OSTI ID:1604346

Bazow, D.; Denicol, G. S.; Heinz, U.; +2 more

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
79 ASTRONOMY AND ASTROPHYSICS

Title: Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime

Citation Formats

References (102)

Cited By (3)

Similar Records

Related Subjects