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

Abstract

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 themore »« less

Authors:

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)

Publication Date:: Thu Dec 08 00:00:00 EST 2016

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

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

OSTI Identifier:: 1604346

Alternate Identifier(s):: OSTI ID: 1334854

Grant/Contract Number:: SC0004286; SC0012704

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review D

Additional Journal Information:: Journal Volume: 94; Journal Issue: 12; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 79 ASTRONOMY AND ASTROPHYSICS

Citation Formats


                    Bazow, D., Denicol, G. S., Heinz, Ulrich, Martinez, M., and Noronha, J. Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime.  United States: N. p., 2016. 
Web.  doi:10.1103/PhysRevD.94.125006.

Copy to clipboard


                    Bazow, D., Denicol, G. S., Heinz, Ulrich, Martinez, M., & Noronha, J. Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime.  United States.  https://doi.org/10.1103/PhysRevD.94.125006

Copy to clipboard


                    Bazow, D., Denicol, G. S., Heinz, Ulrich, Martinez, M., and Noronha, J. Thu .  
"Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime".  United States.  https://doi.org/10.1103/PhysRevD.94.125006.  https://www.osti.gov/servlets/purl/1604346.

Copy to clipboard


                    
@article{osti_1604346,

  title        = {Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime},

  author       = {Bazow, D. and Denicol, G. S. and Heinz, Ulrich and Martinez, M. and Noronha, J.},

  abstractNote = {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.},

  doi          = {10.1103/PhysRevD.94.125006},

  journal      = {Physical Review D},

  number       = 12,

  volume       = 94,

  place        = {United States},

  year         = {Thu Dec 08 00:00:00 EST 2016},

  month        = {Thu Dec 08 00:00:00 EST 2016}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (Publisher)

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1103/PhysRevD.94.125006

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 32 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Turbulent thermalization process in heavy-ion collisions at ultrarelativistic energies
journal, April 2014

Berges, J.; Boguslavski, K.; Schlichting, S.
Physical Review D, Vol. 89, Issue 7
DOI: 10.1103/PhysRevD.89.074011

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
DOI: 10.1103/PhysRevD.90.125026

Relative importance of second-order terms in relativistic dissipative fluid dynamics
journal, April 2014

Molnár, E.; Niemi, H.; Denicol, G. S.
Physical Review D, Vol. 89, Issue 7
DOI: 10.1103/PhysRevD.89.074010

Inhomogeneous Cosmological Models
book, January 1997

Krasinski, Andrzej
DOI: 10.1017/CBO9780511721694

The quark–gluon plasma: collective dynamics and hard thermal loops
journal, March 2002

Blaizot, Jean-Paul; Iancu, Edmond
Physics Reports, Vol. 359, Issue 5-6
DOI: 10.1016/S0370-1573(01)00061-8

Quark-gluon transport theory II. Color response and color correlations in a quark-gluon plasma
journal, April 1986

Heinz, Ulrich
Annals of Physics, Vol. 168, Issue 1
DOI: 10.1016/0003-4916(86)90114-4

Boltzmann hierarchy for interacting neutrinos I: formalism
journal, April 2015

Oldengott, Isabel M.; Rampf, Cornelius; Wong, Yvonne Y. Y.
Journal of Cosmology and Astroparticle Physics, Vol. 2015, Issue 04
DOI: 10.1088/1475-7516/2015/04/016

Microscopic models for ultrarelativistic heavy ion collisions
journal, January 1998

Bass, S.
Progress in Particle and Nuclear Physics, Vol. 41
DOI: 10.1016/S0146-6410(98)00058-1

Asymptotic behaviour of the relativistic Boltzmann equation in the Robertson–Walker spacetime
journal, December 2013

Lee, Ho
Journal of Differential Equations, Vol. 255, Issue 11
DOI: 10.1016/j.jde.2013.08.006

Boltzmann equation in classical and quantum field theory
journal, July 2005

Jeon, Sangyong
Physical Review C, Vol. 72, Issue 1
DOI: 10.1103/PhysRevC.72.014907

Relativistic dynamics of non-ideal fluids: Viscous and heat-conducting fluids. II. Transport properties and microscopic description of relativistic nuclear matter
journal, July 2007

Muronga, Azwinndini
Physical Review C, Vol. 76, Issue 1
DOI: 10.1103/PhysRevC.76.014910

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
DOI: 10.1103/PhysRevLett.116.022301

Erratum to “Saturation of elliptic flow and the transport opacity of the gluon plasma at RHIC”
journal, June 2002

Molnar, D.
Nuclear Physics A, Vol. 703, Issue 3-4
DOI: 10.1016/S0375-9474(02)00859-X

Formation of Maxwellian Tails
journal, May 1976

Krook, Max; Wu, Tai Tsun
Physical Review Letters, Vol. 36, Issue 19
DOI: 10.1103/PhysRevLett.36.1107

Nonthermal Fixed Points: Effective Weak Coupling for Strongly Correlated Systems Far from Equilibrium
journal, July 2008

Berges, Jürgen; Rothkopf, Alexander; Schmidt, Jonas
Physical Review Letters, Vol. 101, Issue 4
DOI: 10.1103/PhysRevLett.101.041603

Isotropization and Hydrodynamization in Weakly Coupled Heavy-Ion Collisions
journal, October 2015

Kurkela, Aleksi; Zhu, Yan
Physical Review Letters, Vol. 115, Issue 18
DOI: 10.1103/PhysRevLett.115.182301

Finite-Temperature Field Theory
book, January 2006

Kapusta, Joseph I.; Gale, Charles
DOI: 10.1017/CBO9780511535130

Reheating and thermalization in a simple scalar model
journal, September 1996

Son, D. T.
Physical Review D, Vol. 54, Issue 6
DOI: 10.1103/PhysRevD.54.3745

A relativistic relaxation-time model for the Boltzmann equation
journal, June 1974

Anderson, J. L.; Witting, H. R.
Physica, Vol. 74, Issue 3
DOI: 10.1016/0031-8914(74)90355-3

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
DOI: 10.1016/j.physa.2009.01.009

The Boltzmann equation and its applications
journal, November 1990

Ramos, J. I.
Applied Mathematical Modelling, Vol. 14, Issue 11
DOI: 10.1016/0307-904x(90)90115-l

Saturation of elliptic flow and the transport opacity of the gluon plasma at RHIC
journal, January 2002

Molnár, Dénes; Gyulassy, Miklos
Nuclear Physics A, Vol. 697, Issue 1-2
DOI: 10.1016/S0375-9474(01)01224-6

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
DOI: 10.1103/PhysRevD.91.039902

Symmetry constraints on generalizations of Bjorken flow
journal, October 2010

Gubser, Steven S.
Physical Review D, Vol. 82, Issue 8
DOI: 10.1103/PhysRevD.82.085027

Approach to Equilibrium in Weakly Coupled Non-Abelian Plasmas
journal, October 2014

Kurkela, Aleksi; Lu, Egang
Physical Review Letters, Vol. 113, Issue 18
DOI: 10.1103/PhysRevLett.113.182301

Role of quantum fluctuations in a system with strong fields: Onset of hydrodynamical flow
journal, January 2011

Dusling, Kevin; Epelbaum, Thomas; Gelis, François
Nuclear Physics A, Vol. 850, Issue 1
DOI: 10.1016/j.nuclphysa.2010.11.009

Thermal Field Theory
book, January 2010

Le Bellac, Michel
Cambridge University Press
DOI: 10.1017/CBO9780511721700

Solutions of the Boltzmann equation for Maxwell interactions and singular angle-dependent cross sections
journal, August 1980

Cornille, H.; Gervois, A.
Journal of Statistical Physics, Vol. 23, Issue 2
DOI: 10.1007/BF01012590

Universality Far from Equilibrium: From Superfluid Bose Gases to Heavy-Ion Collisions
journal, February 2015

Berges, J.; Boguslavski, K.; Schlichting, S.
Physical Review Letters, Vol. 114, Issue 6
DOI: 10.1103/PhysRevLett.114.061601

Properties of the Boltzmann equation in the classical approximation
journal, December 2014

Epelbaum, Thomas; Gelis, François; Tanji, Naoto
Physical Review D, Vol. 90, Issue 12
DOI: 10.1103/PhysRevD.90.125032

Collisional relaxation in simulations of heavy-ion collisions using Boltzmann-type equations
journal, December 1989

Welke, G.; Malfliet, R.; Grégoire, C.
Physical Review C, Vol. 40, Issue 6
DOI: 10.1103/PhysRevC.40.2611

Nonequilibrium fixed points in longitudinally expanding scalar theories: Infrared cascade, Bose condensation, and a challenge for kinetic theory
journal, November 2015

Berges, J.; Boguslavski, K.; Schlichting, S.
Physical Review D, Vol. 92, Issue 9
DOI: 10.1103/PhysRevD.92.096006

Basin of attraction for turbulent thermalization and the range of validity of classical-statistical simulations
journal, May 2014

Berges, J.; Boguslavski, K.; Schlichting, S.
Journal of High Energy Physics, Vol. 2014, Issue 5
DOI: 10.1007/JHEP05(2014)054

Transient relativistic thermodynamics and kinetic theory
journal, April 1979

Israel, W.; Stewart, J. M.
Annals of Physics, Vol. 118, Issue 2
DOI: 10.1016/0003-4916(79)90130-1

Thermalization of gluons in ultrarelativistic heavy ion collisions by including three-body interactions in a parton cascade
journal, June 2005

Xu, Zhe; Greiner, Carsten
Physical Review C, Vol. 71, Issue 6
DOI: 10.1103/PhysRevC.71.064901

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
DOI: 10.1016/j.physa.2008.12.023

Semiclassicality and decoherence of cosmological perturbations
journal, March 1996

Polarski, David; Starobinsky, Alexei A.
Classical and Quantum Gravity, Vol. 13, Issue 3
DOI: 10.1088/0264-9381/13/3/006

Effective transport equations for non-Abelian plasmas
journal, November 1999

Litim, Daniel F.; Manuel, Cristina
Nuclear Physics B, Vol. 562, Issue 1-2
DOI: 10.1016/S0550-3213(99)00531-3

The Boltzmann equation in classical Yang–Mills theory
journal, May 2014

Mathieu, V.; Mueller, A. H.; Triantafyllopoulos, D. N.
The European Physical Journal C, Vol. 74, Issue 5
DOI: 10.1140/epjc/s10052-014-2873-8

Kinetic theory of a longitudinally expanding system of scalar particles
journal, September 2015

Epelbaum, Thomas; Gelis, François; Jeon, Sangyong
Journal of High Energy Physics, Vol. 2015, Issue 9
DOI: 10.1007/JHEP09(2015)117

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
DOI: 10.1103/PhysRev.94.511

Theory of core-collapse supernovae
journal, April 2007

Janka, H.; Langanke, K.; Marek, A.
Physics Reports, Vol. 442, Issue 1-6
DOI: 10.1016/j.physrep.2007.02.002

Supernova Simulations with Boltzmann Neutrino Transport: A Comparison of Methods
journal, February 2005

Liebendorfer, M.; Rampp, M.; Janka, H. ‐Th.
The Astrophysical Journal, Vol. 620, Issue 2
DOI: 10.1086/427203

Reheating in Inflationary Cosmology: Theory and Applications
journal, November 2010

Allahverdi, Rouzbeh; Brandenberger, Robert; Cyr-Racine, Francis-Yan
Annual Review of Nuclear and Particle Science, Vol. 60, Issue 1
DOI: 10.1146/annurev.nucl.012809.104511

Bulk viscosity of high-temperature QCD
journal, October 2006

Arnold, Peter; Doğan, Çağlar; Moore, Guy D.
Physical Review D, Vol. 74, Issue 8
DOI: 10.1103/PhysRevD.74.085021

Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in ${AdS}_{2} \otimes S_{2}$
journal, December 2015

Noronha, Jorge; Denicol, Gabriel S.
Physical Review D, Vol. 92, Issue 11
DOI: 10.1103/PhysRevD.92.114032

Anisotropic hydrodynamics for conformal Gubser flow
journal, February 2015

Nopoush, Mohammad; Ryblewski, Radoslaw; Strickland, Michael
Physical Review D, Vol. 91, Issue 4
DOI: 10.1103/PhysRevD.91.045007

DEFROST: a new code for simulating preheating after inflation
journal, November 2008

Frolov, Andrei V.
Journal of Cosmology and Astroparticle Physics, Vol. 2008, Issue 11
DOI: 10.1088/1475-7516/2008/11/009

Classical Decay of the Inflaton
journal, July 1996

Khlebnikov, S. Yu.; Tkachev, I. I.
Physical Review Letters, Vol. 77, Issue 2
DOI: 10.1103/PhysRevLett.77.219

Highly relativistic nucleus-nucleus collisions: The central rapidity region
journal, January 1983

Bjorken, J. D.
Physical Review D, Vol. 27, Issue 1
DOI: 10.1103/PhysRevD.27.140

Relativistic Turbulence: A Long Way from Preheating to Equilibrium
journal, March 2003

Micha, Raphael; Tkachev, Igor I.
Physical Review Letters, Vol. 90, Issue 12
DOI: 10.1103/PhysRevLett.90.121301

On the kinetic theory of rarefied gases
journal, December 1949

Grad, Harold
Communications on Pure and Applied Mathematics, Vol. 2, Issue 4
DOI: 10.1002/cpa.3160020403

On the equivalence between the Boltzmann equation and classical field theory at large occupation numbers
journal, March 2004

Mueller, A. H.; Son, D. T.
Physics Letters B, Vol. 582, Issue 3-4
DOI: 10.1016/j.physletb.2003.12.047

Pressure Isotropization in High Energy Heavy Ion Collisions
journal, December 2013

Epelbaum, Thomas; Gelis, François
Physical Review Letters, Vol. 111, Issue 23
DOI: 10.1103/PhysRevLett.111.232301

“Bottom-up” thermalization in heavy ion collisions
journal, March 2001

Baier, R.; Mueller, A. H.; Schiff, D.
Physics Letters B, Vol. 502, Issue 1-4
DOI: 10.1016/S0370-2693(01)00191-5

Analytic solutions of the relativistic Boltzmann equation
journal, April 2015

Hatta, Yoshitaka; Martinez, Mauricio; Xiao, Bo-Wen
Physical Review D, Vol. 91, Issue 8
DOI: 10.1103/PhysRevD.91.085024

Nonlinear model-Boltzmann equations and exact solutions
journal, November 1981

Ernst, M. H.
Physics Reports, Vol. 78, Issue 1
DOI: 10.1016/0370-1573(81)90002-8

Finite-temperature field theory
journal, March 1989

Kapusta, J. I.; Landshoff, P. V.
Journal of Physics G: Nuclear and Particle Physics, Vol. 15, Issue 3
DOI: 10.1088/0954-3899/15/3/005

Universal attractor in a highly occupied non-Abelian plasma
journal, June 2014

Berges, J.; Boguslavski, K.; Schlichting, S.
Physical Review D, Vol. 89, Issue 11
DOI: 10.1103/PhysRevD.89.114007

Entropy Generation and the Survival of Protogalaxies in an Expanding Universe
journal, September 1971

Weinberg, Steven
The Astrophysical Journal, Vol. 168
DOI: 10.1086/151073

Exact solutions of the Boltzmann equation
journal, January 1977

Krook, Max; Wu, Tai Tsun
Physics of Fluids, Vol. 20, Issue 10
DOI: 10.1063/1.861780

Cosmological Perturbation Theory in the Synchronous and Conformal Newtonian Gauges
journal, December 1995

Ma, Chung-Pei; Bertschinger, Edmund
The Astrophysical Journal, Vol. 455
DOI: 10.1086/176550

Kinetic Theory for Plasmas with Non-Abelian Interactions
journal, August 1983

Heinz, Ulrich
Physical Review Letters, Vol. 51, Issue 5
DOI: 10.1103/PhysRevLett.51.351

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
DOI: 10.1103/PhysRevD.85.114047

How particles emerge from decaying classical fields in heavy ion collisions: Towards a kinetic description of the Glasma
journal, February 2009

Gelis, François; Jeon, Sangyong; Venugopalan, Raju
Nuclear Physics A, Vol. 817, Issue 1-4
DOI: 10.1016/j.nuclphysa.2008.11.011

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
DOI: 10.1103/PhysRevLett.113.202301

From quantum field theory to hydrodynamics: Transport coefficients and effective kinetic theory
journal, May 1996

Jeon, Sangyong; Yaffe, Laurence G.
Physical Review D, Vol. 53, Issue 10
DOI: 10.1103/PhysRevD.53.5799

Quark-Gluon transport theory
journal, November 1989

Elze, Hans-Thomas; Heinz, Ulrich
Physics Reports, Vol. 183, Issue 3
DOI: 10.1016/0370-1573(89)90059-8

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
DOI: 10.1103/PhysRevD.83.074019

A Boltzmann equation for the QCD plasma
journal, September 1999

Blaizot, Jean-Paul; Iancu, Edmond
Nuclear Physics B, Vol. 557, Issue 1-2
DOI: 10.1016/S0550-3213(99)00341-7

Semi-classical transport theory for non-Abelian plasmas
journal, July 2002

Litim, Daniel F.; Manuel, Cristina
Physics Reports, Vol. 364, Issue 6
DOI: 10.1016/S0370-1573(02)00015-7

Thermal equilibration in ultra-relativistic heavy-ion collisions
journal, April 1984

Baym, Gordon
Physics Letters B, Vol. 138, Issue 1-3
DOI: 10.1016/0370-2693(84)91863-X

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
DOI: 10.1103/PhysRevC.88.024903

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
DOI: 10.1103/PhysRevC.91.014903

Investigating the domain of validity of the Gubser solution to the Boltzmann equation
journal, November 2015

Heinz, Ulrich; Martinez, Mauricio
Nuclear Physics A, Vol. 943
DOI: 10.1016/j.nuclphysa.2015.08.009

Anisotropic hydrodynamics for conformal Gubser flow
journal, December 2016

Strickland, Michael; Nopoush, Mohammad; Ryblewski, Radoslaw
Nuclear Physics A, Vol. 956
DOI: 10.1016/j.nuclphysa.2016.02.014

Inhomogeneous Cosmological Models: Proceedings of the Spanish Relativity Meeting
conference, June 1995

Molina, A.; Senovilla, M. M.
DOI: 10.1142/2825

Lattice study of classical inflaton decay
journal, March 1997

Prokopec, Tomislav; Roos, Thomas G.
Physical Review D, Vol. 55, Issue 6
DOI: 10.1103/PhysRevD.55.3768

Turbulent thermalization
journal, August 2004

Micha, Raphael; Tkachev, Igor I.
Physical Review D, Vol. 70, Issue 4
DOI: 10.1103/PhysRevD.70.043538

Non-thermal Fixed Points: Effective Weak-coupling for Strongly Correlated Systems far from Equilibrium.
text, January 2008

Berges, Juergen; Rothkopf, Alexander.; Schmidt, Jonas
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/phppubdb-7455

DEFROST: A New Code for Simulating Preheating after Inflation
text, January 2008

Frolov, Andrei V.
arXiv
DOI: 10.48550/arxiv.0809.4904

Role of quantum fluctuations in a system with strong fields: Onset of hydrodynamical flow
text, January 2010

Dusling, K.; Epelbaum, T.; Gelis, F.
arXiv
DOI: 10.48550/arxiv.1009.4363

Origin of the Relaxation Time in Dissipative Fluid Dynamics
text, January 2011

Denicol, G. S.; Noronha, J.; Niemi, H.
arXiv
DOI: 10.48550/arxiv.1102.4780

Derivation of transient relativistic fluid dynamics from the Boltzmann equation
text, January 2012

Denicol, G. S.; Niemi, H.; Molnar, E.
arXiv
DOI: 10.48550/arxiv.1202.4551

Turbulent thermalization process in heavy-ion collisions at ultrarelativistic energies
text, January 2013

Berges, J.; Boguslavski, K.; Schlichting, S.
arXiv
DOI: 10.48550/arxiv.1303.5650

On the relative importance of second-order terms in relativistic dissipative fluid dynamics
text, January 2013

Molnár, E.; Niemi, H.; Denicol, G. S.
arXiv
DOI: 10.48550/arxiv.1308.0785

Universal attractor in a highly occupied non-Abelian plasma
text, January 2013

Berges, Juergen; Boguslavski, Kirill; Schlichting, Soeren
arXiv
DOI: 10.48550/arxiv.1311.3005

The Boltzmann Equation in Classical Yang-Mills Theory
text, January 2014

Mathieu, V.; Mueller, A. H.; Triantafyllopoulos, D. N.
arXiv
DOI: 10.48550/arxiv.1403.1184

Approach to equilibrium in weakly coupled nonabelian plasmas
text, January 2014

Kurkela, Aleksi; Lu, Egang
arXiv
DOI: 10.48550/arxiv.1405.6318

Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation
text, January 2014

Denicol, Gabriel S.; Heinz, Ulrich W.; Martinez, Mauricio
arXiv
DOI: 10.48550/arxiv.1408.7048

Kinetic theory of a longitudinally expanding system of scalar particles
text, January 2015

Epelbaum, Thomas; Gelis, Francois; Jeon, Sangyong
arXiv
DOI: 10.48550/arxiv.1506.05580

Isotropization and hydrodynamization in weakly coupled heavy-ion collisions
text, January 2015

Kurkela, Aleksi; Zhu, Yan
arXiv
DOI: 10.48550/arxiv.1506.06647

Investigating the domain of validity of the Gubser solution to the Boltzmann equation
text, January 2015

Heinz, Ulrich W.; Martinez, Mauricio
arXiv
DOI: 10.48550/arxiv.1506.07500

Semiclassicality and Decoherence of Cosmological Perturbations
text, January 1995

Polarski, David; Starobinsky, Alexei A.
arXiv
DOI: 10.48550/arxiv.gr-qc/9504030

The Quark-Gluon Plasma: Collective Dynamics and Hard Thermal Loops
text, January 2001

Blaizot, Jean-Paul; Iancu, Edmond
arXiv
DOI: 10.48550/arxiv.hep-ph/0101103

Semi-classical transport theory for non-Abelian plasmas
text, January 2001

Litim, Daniel F.; Manuel, Cristina
arXiv
DOI: 10.48550/arxiv.hep-ph/0110104

Relativistic Turbulence: A Long Way from Preheating to Equilibrium
text, January 2002

Micha, R.; Tkachev, I. I.
arXiv
DOI: 10.48550/arxiv.hep-ph/0210202

Turbulent Thermalization
text, January 2004

Micha, Raphael; Tkachev, Igor I.
arXiv
DOI: 10.48550/arxiv.hep-ph/0403101

Thermalization of gluons in ultrarelativistic heavy ion collisions by including three-body interactions in a parton cascade
text, January 2004

Xu, Zhe; Greiner, Carsten
arXiv
DOI: 10.48550/arxiv.hep-ph/0406278

Reheating and thermalization in a simple scalar model
text, January 1996

Son, D. T.
arXiv
DOI: 10.48550/arxiv.hep-ph/9604340

Lattice study of classical inflaton decay
text, January 1996

Prokopec, Tomislav; Roos, Thomas G.
arXiv
DOI: 10.48550/arxiv.hep-ph/9610400

Effective Transport Equations for non-Abelian Plasmas
text, January 1999

Litim, Daniel F.; Manuel, Cristina
arXiv
DOI: 10.48550/arxiv.hep-ph/9906210

Works referencing / citing this record:

Interacting neutrinos in cosmology: exact description and constraints
journal, November 2017

Oldengott, Isabel M.; Tram, Thomas; Rampf, Cornelius
Journal of Cosmology and Astroparticle Physics, Vol. 2017, Issue 11
DOI: 10.1088/1475-7516/2017/11/027

Causality and existence of solutions of relativistic viscous fluid dynamics with gravity
text, January 2017

Bemfica, Fabio S.; Disconzi, Marcelo M.; Noronha, Jorge
arXiv
DOI: 10.48550/arxiv.1708.06255

Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow
text, January 2017

Behtash, Alireza; Cruz-Camacho, C. N.; Martinez, M.
arXiv
DOI: 10.48550/arxiv.1711.01745

Similar Records in DOE PAGES and OSTI.GOV collections:

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

Journal Article Melia, F., E-mail: fmelia@email.arizona.edu - Annals of Physics

Highlights: • The Hubble flow is non-inertial for all cosmic equations-of-state other than p=−ρ∕3. • The Local Flatness Theorem is therefore violated when the lapse function is set equal to a constant. • Thus, the symmetries in the FLRW metric appear to be valid only when ρ+3p=0, producing an expansion factor a(t) t. - Abstract: The Friedmann–Lemaître–Robertson–Walker (FLRW) metric, the backbone of modern cosmology, is founded on the cosmological principle, which assumes homogeneity and isotropy throughout the cosmos. One of its simplifications is the choice of lapse function g{sub tt}=1, regardless of which stress–energy tensor T{sup μν} is used inmore »« less
https://doi.org/10.1016/J.AOP.2019.167997
Scalar field dynamics in Friedmann-Robertson-Walker spacetimes

Journal Article Boyanovsky, D ; Cormier, D ; Holman, R ; ... - Physical Review, D

We study the nonlinear dynamics of quantum fields in matter- and radiation-dominated universes, using the nonequilibrium field theory approach combined with the nonperturbative Hartree and the large N approximations. We examine the phenomenon of explosive particle production due to spinodal instabilities and parametric amplification in expanding universes with and without symmetry breaking. For a variety of initial conditions, we compute the evolution of the inflaton, its quantum fluctuations, and the equation of state. We find explosive growth of quantum fluctuations, although particle production is somewhat sensitive to the expansion of the universe. In the large N limit for symmetry-breaking scenarios,more »« less
https://doi.org/10.1103/PhysRevD.56.1939
Anisotropic evolution of 5D Friedmann-Robertson-Walker spacetime

Journal Article Middleton, Chad A ; Stanley, Ethan - Physical Review. D, Particles Fields

We examine the time evolution of the five-dimensional Einstein field equations subjected to a flat, anisotropic Robertson-Walker metric, where the 3D and higher-dimensional scale factors are allowed to dynamically evolve at different rates. By adopting equations of state relating the 3D and higher-dimensional pressures to the density, we obtain an exact expression relating the higher-dimensional scale factor to a function of the 3D scale factor. This relation allows us to write the Friedmann-Robertson-Walker field equations exclusively in terms of the 3D scale factor, thus yielding a set of 4D effective Friedmann-Robertson-Walker field equations. We examine the effective field equations inmore »« less
https://doi.org/10.1103/PHYSREVD.84.085013
Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime

Journal Article Bazow, D. ; Denicol, G. S. ; Heinz, U. ; ... - Physical Review D

Not provided.
https://doi.org/10.1103/physrevd.94.125006
Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in AdS₂ Ⓧ S₂

Journal Article Noronha, Jorge ; Denicol, Gabriel S. - Physical Review. D, Particles, Fields, Gravitation and Cosmology

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 matchmore »« less
Cited by 10
https://doi.org/10.1103/PhysRevD.92.114032

Full Text Available

Similar Records

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

Abstract

Citation Formats

Turbulent thermalization process in heavy-ion collisions at ultrarelativistic energies journal, April 2014

Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation journal, December 2014

Relative importance of second-order terms in relativistic dissipative fluid dynamics journal, April 2014

Inhomogeneous Cosmological Models book, January 1997

The quark–gluon plasma: collective dynamics and hard thermal loops journal, March 2002

Quark-gluon transport theory II. Color response and color correlations in a quark-gluon plasma journal, April 1986

Boltzmann hierarchy for interacting neutrinos I: formalism journal, April 2015

Microscopic models for ultrarelativistic heavy ion collisions journal, January 1998

Asymptotic behaviour of the relativistic Boltzmann equation in the Robertson–Walker spacetime journal, December 2013

Boltzmann equation in classical and quantum field theory journal, July 2005

Relativistic dynamics of non-ideal fluids: Viscous and heat-conducting fluids. II. Transport properties and microscopic description of relativistic nuclear matter journal, July 2007

Analytic Solution of the Boltzmann Equation in an Expanding System journal, January 2016

Erratum to “Saturation of elliptic flow and the transport opacity of the gluon plasma at RHIC” journal, June 2002

Formation of Maxwellian Tails journal, May 1976

Nonthermal Fixed Points: Effective Weak Coupling for Strongly Correlated Systems Far from Equilibrium journal, July 2008

Isotropization and Hydrodynamization in Weakly Coupled Heavy-Ion Collisions journal, October 2015

Finite-Temperature Field Theory book, January 2006

Reheating and thermalization in a simple scalar model journal, September 1996

A relativistic relaxation-time model for the Boltzmann equation journal, June 1974

General relativistic Boltzmann equation, II: Manifestly covariant treatment journal, May 2009

The Boltzmann equation and its applications journal, November 1990

Saturation of elliptic flow and the transport opacity of the gluon plasma at RHIC journal, January 2002

Erratum: Derivation of transient relativistic fluid dynamics from the Boltzmann equation [Phys. Rev. D 85 , 114047 (2012)] journal, February 2015

Symmetry constraints on generalizations of Bjorken flow journal, October 2010

Approach to Equilibrium in Weakly Coupled Non-Abelian Plasmas journal, October 2014

Role of quantum fluctuations in a system with strong fields: Onset of hydrodynamical flow journal, January 2011

Thermal Field Theory book, January 2010

Solutions of the Boltzmann equation for Maxwell interactions and singular angle-dependent cross sections journal, August 1980

Universality Far from Equilibrium: From Superfluid Bose Gases to Heavy-Ion Collisions journal, February 2015

Properties of the Boltzmann equation in the classical approximation journal, December 2014

Collisional relaxation in simulations of heavy-ion collisions using Boltzmann-type equations journal, December 1989

Nonequilibrium fixed points in longitudinally expanding scalar theories: Infrared cascade, Bose condensation, and a challenge for kinetic theory journal, November 2015

Basin of attraction for turbulent thermalization and the range of validity of classical-statistical simulations journal, May 2014

Transient relativistic thermodynamics and kinetic theory journal, April 1979

Thermalization of gluons in ultrarelativistic heavy ion collisions by including three-body interactions in a parton cascade journal, June 2005

General relativistic Boltzmann equation, I: Covariant treatment journal, April 2009

Semiclassicality and decoherence of cosmological perturbations journal, March 1996

Effective transport equations for non-Abelian plasmas journal, November 1999

The Boltzmann equation in classical Yang–Mills theory journal, May 2014

Kinetic theory of a longitudinally expanding system of scalar particles journal, September 2015

A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems journal, May 1954

Theory of core-collapse supernovae journal, April 2007

Supernova Simulations with Boltzmann Neutrino Transport: A Comparison of Methods journal, February 2005

Reheating in Inflationary Cosmology: Theory and Applications journal, November 2010

Bulk viscosity of high-temperature QCD journal, October 2006

Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in AdS 2 ⊗ S 2 journal, December 2015

Anisotropic hydrodynamics for conformal Gubser flow journal, February 2015

DEFROST: a new code for simulating preheating after inflation journal, November 2008

Classical Decay of the Inflaton journal, July 1996

Highly relativistic nucleus-nucleus collisions: The central rapidity region journal, January 1983

Relativistic Turbulence: A Long Way from Preheating to Equilibrium journal, March 2003

On the kinetic theory of rarefied gases journal, December 1949

On the equivalence between the Boltzmann equation and classical field theory at large occupation numbers journal, March 2004

Pressure Isotropization in High Energy Heavy Ion Collisions journal, December 2013

“Bottom-up” thermalization in heavy ion collisions journal, March 2001

Analytic solutions of the relativistic Boltzmann equation journal, April 2015

Nonlinear model-Boltzmann equations and exact solutions journal, November 1981

Finite-temperature field theory journal, March 1989

Universal attractor in a highly occupied non-Abelian plasma journal, June 2014

Entropy Generation and the Survival of Protogalaxies in an Expanding Universe journal, September 1971

Exact solutions of the Boltzmann equation journal, January 1977

Cosmological Perturbation Theory in the Synchronous and Conformal Newtonian Gauges journal, December 1995

Kinetic Theory for Plasmas with Non-Abelian Interactions journal, August 1983

Derivation of transient relativistic fluid dynamics from the Boltzmann equation journal, June 2012

How particles emerge from decaying classical fields in heavy ion collisions: Towards a kinetic description of the Glasma journal, February 2009

New Exact Solution of the Relativistic Boltzmann Equation and its Hydrodynamic Limit journal, November 2014

From quantum field theory to hydrodynamics: Transport coefficients and effective kinetic theory journal, May 1996

Quark-Gluon transport theory journal, November 1989

Origin of the relaxation time in dissipative fluid dynamics journal, April 2011

A Boltzmann equation for the QCD plasma journal, September 1999

Semi-classical transport theory for non-Abelian plasmas journal, July 2002

Thermal equilibration in ultra-relativistic heavy-ion collisions journal, April 1984

Testing viscous and anisotropic hydrodynamics in an exactly solvable case journal, August 2013

Solutions of conformal Israel-Stewart relativistic viscous fluid dynamics journal, January 2015

Investigating the domain of validity of the Gubser solution to the Boltzmann equation journal, November 2015

Anisotropic hydrodynamics for conformal Gubser flow journal, December 2016

Inhomogeneous Cosmological Models: Proceedings of the Spanish Relativity Meeting conference, June 1995

Turbulent thermalization process in heavy-ion collisions at ultrarelativistic energies
journal, April 2014

Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation
journal, December 2014

Relative importance of second-order terms in relativistic dissipative fluid dynamics
journal, April 2014

Inhomogeneous Cosmological Models
book, January 1997

The quark–gluon plasma: collective dynamics and hard thermal loops
journal, March 2002

Quark-gluon transport theory II. Color response and color correlations in a quark-gluon plasma
journal, April 1986

Boltzmann hierarchy for interacting neutrinos I: formalism
journal, April 2015

Microscopic models for ultrarelativistic heavy ion collisions
journal, January 1998

Asymptotic behaviour of the relativistic Boltzmann equation in the Robertson–Walker spacetime
journal, December 2013

Boltzmann equation in classical and quantum field theory
journal, July 2005

Relativistic dynamics of non-ideal fluids: Viscous and heat-conducting fluids. II. Transport properties and microscopic description of relativistic nuclear matter
journal, July 2007

Analytic Solution of the Boltzmann Equation in an Expanding System
journal, January 2016

Erratum to “Saturation of elliptic flow and the transport opacity of the gluon plasma at RHIC”
journal, June 2002

Formation of Maxwellian Tails
journal, May 1976

Nonthermal Fixed Points: Effective Weak Coupling for Strongly Correlated Systems Far from Equilibrium
journal, July 2008

Isotropization and Hydrodynamization in Weakly Coupled Heavy-Ion Collisions
journal, October 2015

Finite-Temperature Field Theory
book, January 2006

Reheating and thermalization in a simple scalar model
journal, September 1996

A relativistic relaxation-time model for the Boltzmann equation
journal, June 1974

General relativistic Boltzmann equation, II: Manifestly covariant treatment
journal, May 2009

The Boltzmann equation and its applications
journal, November 1990

Saturation of elliptic flow and the transport opacity of the gluon plasma at RHIC
journal, January 2002

Erratum: Derivation of transient relativistic fluid dynamics from the Boltzmann equation [Phys. Rev. D 85 , 114047 (2012)]
journal, February 2015

Symmetry constraints on generalizations of Bjorken flow
journal, October 2010

Approach to Equilibrium in Weakly Coupled Non-Abelian Plasmas
journal, October 2014

Role of quantum fluctuations in a system with strong fields: Onset of hydrodynamical flow
journal, January 2011

Thermal Field Theory
book, January 2010

Solutions of the Boltzmann equation for Maxwell interactions and singular angle-dependent cross sections
journal, August 1980

Universality Far from Equilibrium: From Superfluid Bose Gases to Heavy-Ion Collisions
journal, February 2015

Properties of the Boltzmann equation in the classical approximation
journal, December 2014

Collisional relaxation in simulations of heavy-ion collisions using Boltzmann-type equations
journal, December 1989

Nonequilibrium fixed points in longitudinally expanding scalar theories: Infrared cascade, Bose condensation, and a challenge for kinetic theory
journal, November 2015

Basin of attraction for turbulent thermalization and the range of validity of classical-statistical simulations
journal, May 2014

Transient relativistic thermodynamics and kinetic theory
journal, April 1979

Thermalization of gluons in ultrarelativistic heavy ion collisions by including three-body interactions in a parton cascade
journal, June 2005

General relativistic Boltzmann equation, I: Covariant treatment
journal, April 2009

Semiclassicality and decoherence of cosmological perturbations
journal, March 1996

Effective transport equations for non-Abelian plasmas
journal, November 1999

The Boltzmann equation in classical Yang–Mills theory
journal, May 2014

Kinetic theory of a longitudinally expanding system of scalar particles
journal, September 2015

A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems
journal, May 1954

Theory of core-collapse supernovae
journal, April 2007

Supernova Simulations with Boltzmann Neutrino Transport: A Comparison of Methods
journal, February 2005

Reheating in Inflationary Cosmology: Theory and Applications
journal, November 2010

Bulk viscosity of high-temperature QCD
journal, October 2006

Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in ${AdS}_{2} \otimes S_{2}$
journal, December 2015

Anisotropic hydrodynamics for conformal Gubser flow
journal, February 2015

DEFROST: a new code for simulating preheating after inflation
journal, November 2008

Classical Decay of the Inflaton
journal, July 1996

Highly relativistic nucleus-nucleus collisions: The central rapidity region
journal, January 1983

Relativistic Turbulence: A Long Way from Preheating to Equilibrium
journal, March 2003

On the kinetic theory of rarefied gases
journal, December 1949

On the equivalence between the Boltzmann equation and classical field theory at large occupation numbers
journal, March 2004

Pressure Isotropization in High Energy Heavy Ion Collisions
journal, December 2013

“Bottom-up” thermalization in heavy ion collisions
journal, March 2001

Analytic solutions of the relativistic Boltzmann equation
journal, April 2015

Nonlinear model-Boltzmann equations and exact solutions
journal, November 1981

Finite-temperature field theory
journal, March 1989

Universal attractor in a highly occupied non-Abelian plasma
journal, June 2014

Entropy Generation and the Survival of Protogalaxies in an Expanding Universe
journal, September 1971

Exact solutions of the Boltzmann equation
journal, January 1977

Cosmological Perturbation Theory in the Synchronous and Conformal Newtonian Gauges
journal, December 1995

Kinetic Theory for Plasmas with Non-Abelian Interactions
journal, August 1983

Derivation of transient relativistic fluid dynamics from the Boltzmann equation
journal, June 2012

How particles emerge from decaying classical fields in heavy ion collisions: Towards a kinetic description of the Glasma
journal, February 2009

New Exact Solution of the Relativistic Boltzmann Equation and its Hydrodynamic Limit
journal, November 2014

From quantum field theory to hydrodynamics: Transport coefficients and effective kinetic theory
journal, May 1996

Quark-Gluon transport theory
journal, November 1989

Origin of the relaxation time in dissipative fluid dynamics
journal, April 2011

A Boltzmann equation for the QCD plasma
journal, September 1999

Semi-classical transport theory for non-Abelian plasmas
journal, July 2002

Thermal equilibration in ultra-relativistic heavy-ion collisions
journal, April 1984

Testing viscous and anisotropic hydrodynamics in an exactly solvable case
journal, August 2013

Solutions of conformal Israel-Stewart relativistic viscous fluid dynamics
journal, January 2015

Investigating the domain of validity of the Gubser solution to the Boltzmann equation
journal, November 2015

Anisotropic hydrodynamics for conformal Gubser flow
journal, December 2016

Inhomogeneous Cosmological Models: Proceedings of the Spanish Relativity Meeting
conference, June 1995

Lattice study of classical inflaton decay
journal, March 1997

Turbulent thermalization
journal, August 2004

Non-thermal Fixed Points: Effective Weak-coupling for Strongly Correlated Systems far from Equilibrium.
text, January 2008