Transient oscillations in a macroscopic effective theory of the Boltzmann equation

Bazow, Dennis; Martinez, Mauricio; Heinz, Ulrich

doi:10.1103/PhysRevD.93.034002

Title: Transient oscillations in a macroscopic effective theory of the Boltzmann equation

Abstract

A new transient effective theory of the relativistic Boltzmann equation is derived for locally momentum-anisotropic systems. In the expansion of the distribution function around a local “quasi-equilibrium” state, a nonhydrodynamic dynamical degree of freedom is introduced at leading order that breaks local momentum isotropy. By replacing the deviation of the distribution function from this quasi-equilibrium state in terms of moments of the leading-order distribution and applying a systematic power-counting scheme that orders the nonhydrodynamic modes by their microscopic time scales, a closed set of equations for the dynamical degrees of freedom is obtained. Truncating this set at the level of the slowest nonhydroynamic mode, we find that it exhibits transient oscillatory behavior—a phenomenon previously found only in strongly coupled theories, where it appears to be generic. In weakly coupled systems described by the Boltzmann equation, these transient oscillations depend on the breaking of local momentum isotropy being treated nonperturbatively at leading order in the expansion of the distribution function.

Authors:

Bazow, Dennis ^[1]; Martinez, Mauricio ^[1];

^[1]

The Ohio State Univ., Columbus, OH (United States). Dept. of Physics

Publication Date:: Mon Feb 01 00:00:00 EST 2016

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

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

OSTI Identifier:: 1604418

Alternate Identifier(s):: OSTI ID: 1236544

Grant/Contract Number:: SC0004286

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review D

Additional Journal Information:: Journal Volume: 93; Journal Issue: 3; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats


                    Bazow, Dennis, Martinez, Mauricio, and Heinz, Ulrich. Transient oscillations in a macroscopic effective theory of the Boltzmann equation.  United States: N. p., 2016. 
Web.  doi:10.1103/PhysRevD.93.034002.

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                    Bazow, Dennis, Martinez, Mauricio, & Heinz, Ulrich. Transient oscillations in a macroscopic effective theory of the Boltzmann equation.  United States.  https://doi.org/10.1103/PhysRevD.93.034002

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                    Bazow, Dennis, Martinez, Mauricio, and Heinz, Ulrich. Mon .  
"Transient oscillations in a macroscopic effective theory of the Boltzmann equation".  United States.  https://doi.org/10.1103/PhysRevD.93.034002.  https://www.osti.gov/servlets/purl/1604418.

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@article{osti_1604418,

  title        = {Transient oscillations in a macroscopic effective theory of the Boltzmann equation},

  author       = {Bazow, Dennis and Martinez, Mauricio and Heinz, Ulrich},

  abstractNote = {A new transient effective theory of the relativistic Boltzmann equation is derived for locally momentum-anisotropic systems. In the expansion of the distribution function around a local “quasi-equilibrium” state, a nonhydrodynamic dynamical degree of freedom is introduced at leading order that breaks local momentum isotropy. By replacing the deviation of the distribution function from this quasi-equilibrium state in terms of moments of the leading-order distribution and applying a systematic power-counting scheme that orders the nonhydrodynamic modes by their microscopic time scales, a closed set of equations for the dynamical degrees of freedom is obtained. Truncating this set at the level of the slowest nonhydroynamic mode, we find that it exhibits transient oscillatory behavior—a phenomenon previously found only in strongly coupled theories, where it appears to be generic. In weakly coupled systems described by the Boltzmann equation, these transient oscillations depend on the breaking of local momentum isotropy being treated nonperturbatively at leading order in the expansion of the distribution function.},

  doi          = {10.1103/PhysRevD.93.034002},

  journal      = {Physical Review D},

  number       = 3,

  volume       = 93,

  place        = {United States},

  year         = {Mon Feb 01 00:00:00 EST 2016},

  month        = {Mon Feb 01 00:00:00 EST 2016}

}

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Works referenced in this record:

Collective modes of an anisotropic quark-gluon plasma
journal, August 2003

Romatschke, Paul; Strickland, Michael
Physical Review D, Vol. 68, Issue 3
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Coupling Hydrodynamics to Nonequilibrium Degrees of Freedom in Strongly Interacting Quark-Gluon Plasma
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Heller, Michal P.; Janik, Romuald A.; Spaliński, Michał
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Viscous hydrodynamics for strongly anisotropic expansion
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Heinz, Ulrich; Bazow, Dennis; Strickland, Michael
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Second-order $(2 + 1)$ -dimensional anisotropic hydrodynamics
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Bazow, Dennis; Heinz, Ulrich; Strickland, Michael
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Denicol, G. S.; Niemi, H.; Bouras, I.
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Numerical solution of gravitational dynamics in asymptotically anti-de Sitter spacetimes
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Chesler, Paul M.; Yaffe, Laurence G.
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Denicol, G. S.; Koide, T.; Rischke, D. H.
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Physical Review Letters, Vol. 102, Issue 21
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Relativistic causal hydrodynamics derived from Boltzmann equation: A novel reduction theoretical approach
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Works referencing / citing this record:

New theories of relativistic hydrodynamics in the LHC era
journal, February 2018

Florkowski, Wojciech; Heller, Michal P.; Spaliński, Michał
Reports on Progress in Physics, Vol. 81, Issue 4
DOI: 10.1088/1361-6633/aaa091

Hydrodynamization in kinetic theory: Transient modes and the gradient expansion
text, January 2016

Heller, Michal P.; Kurkela, Aleksi; Spalinski, Michal
arXiv
DOI: 10.48550/arxiv.1609.04803

Including off-diagonal anisotropies in anisotropic hydrodynamics
text, January 2019

Nopoush, Mohammad; Strickland, Michael
arXiv
DOI: 10.48550/arxiv.1902.03303

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Title: Transient oscillations in a macroscopic effective theory of the Boltzmann equation

Abstract

Citation Formats

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