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Title: Anisotropic hydrodynamics with a scalar collisional kernel

Abstract

Prior studies of nonequilibrium dynamics using anisotropic hydrodynamics have used the relativistic Anderson-Witting scattering kernel or some variant thereof. In this paper, we make the first study of the impact of using a more realistic scattering kernel. For this purpose, we consider a conformal system undergoing transversally homogenous and boost-invariant Bjorken expansion and take the collisional kernel to be given by the leading order $$2{\leftrightarrow}2$$ scattering kernel in scalar $${\lambda}{{\phi}}^{4}$$. We consider both classical and quantum statistics to assess the impact of Bose enhancement on the dynamics. We also determine the anisotropic nonequilibrium attractor of a system subject to this collisional kernel. We find that, when the near-equilibrium relaxation-times in the Anderson-Witting and scalar collisional kernels are matched, the scalar kernel results in a higher degree of momentum-space anisotropy during the system's evolution, given the same initial conditions. Additionally, we find that taking into account Bose enhancement further increases the dynamically generated momentum-space anisotropy.

Authors:
;
Publication Date:
Research Org.:
Kent State Univ., Kent, OH (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
OSTI Identifier:
1434185
Alternate Identifier(s):
OSTI ID: 1503825
Grant/Contract Number:  
[SC0013470]
Resource Type:
Published Article
Journal Name:
Physical Review C
Additional Journal Information:
[Journal Name: Physical Review C Journal Volume: 97 Journal Issue: 4]; Journal ID: ISSN 2469-9985
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; collective flow; hydrodynamic models; quark-gluon plasma; relativistic heavy-ion collisions; relativistic hydrodynamics

Citation Formats

Almaalol, Dekrayat, and Strickland, Michael. Anisotropic hydrodynamics with a scalar collisional kernel. United States: N. p., 2018. Web. doi:10.1103/PhysRevC.97.044911.
Almaalol, Dekrayat, & Strickland, Michael. Anisotropic hydrodynamics with a scalar collisional kernel. United States. doi:10.1103/PhysRevC.97.044911.
Almaalol, Dekrayat, and Strickland, Michael. Fri . "Anisotropic hydrodynamics with a scalar collisional kernel". United States. doi:10.1103/PhysRevC.97.044911.
@article{osti_1434185,
title = {Anisotropic hydrodynamics with a scalar collisional kernel},
author = {Almaalol, Dekrayat and Strickland, Michael},
abstractNote = {Prior studies of nonequilibrium dynamics using anisotropic hydrodynamics have used the relativistic Anderson-Witting scattering kernel or some variant thereof. In this paper, we make the first study of the impact of using a more realistic scattering kernel. For this purpose, we consider a conformal system undergoing transversally homogenous and boost-invariant Bjorken expansion and take the collisional kernel to be given by the leading order $2{\leftrightarrow}2$ scattering kernel in scalar ${\lambda}{{\phi}}^{4}$. We consider both classical and quantum statistics to assess the impact of Bose enhancement on the dynamics. We also determine the anisotropic nonequilibrium attractor of a system subject to this collisional kernel. We find that, when the near-equilibrium relaxation-times in the Anderson-Witting and scalar collisional kernels are matched, the scalar kernel results in a higher degree of momentum-space anisotropy during the system's evolution, given the same initial conditions. Additionally, we find that taking into account Bose enhancement further increases the dynamically generated momentum-space anisotropy.},
doi = {10.1103/PhysRevC.97.044911},
journal = {Physical Review C},
number = [4],
volume = [97],
place = {United States},
year = {2018},
month = {4}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevC.97.044911

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Cited by: 4 works
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Figures / Tables:

FIG. 1 FIG. 1: Generic two-to-two scattering diagram.

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Works referenced in this record:

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margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#5C7B2D;"> Florkowski, Wojciech; Ryblewski, Radoslaw; Strickland, Michael</span> </li> <li> Nuclear Physics A, Vol. 916</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1016/j.nuclphysa.2013.08.004" class="text-muted" target="_blank" rel="noopener noreferrer">10.1016/j.nuclphysa.2013.08.004<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div><div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1103/PhysRevLett.119.042301" target="_blank" rel="noopener noreferrer" class="name"><math display="inline"> <mrow> <mo stretchy="false">(</mo> <mrow> <mn>3</mn> <mo>+</mo> <mn>1</mn> </mrow> <mo stretchy="false">)</mo> <mi mathvariant="normal">D</mi> </mrow> </math> Quasiparticle Anisotropic Hydrodynamics for Ultrarelativistic Heavy-Ion Collisions<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2017-07-01">July 2017</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#5C7B2D;"> Alqahtani, Mubarak; Nopoush, Mohammad; Ryblewski, Radoslaw</span> </li> <li> Physical Review Letters, Vol. 119, Issue 4</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1103/PhysRevLett.119.042301" class="text-muted" target="_blank" rel="noopener noreferrer">10.1103/PhysRevLett.119.042301<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div><div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1126/science.1215901" target="_blank" rel="noopener noreferrer" class="name">The Exploration of Hot Nuclear Matter<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2012-07-19">July 2012</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#5C7B2D;"> Jacak, B. V.; Muller, B.</span> </li> <li> Science, Vol. 337, Issue 6092</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1126/science.1215901" class="text-muted" target="_blank" rel="noopener noreferrer">10.1126/science.1215901<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div><div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1103/PhysRevC.88.024903" target="_blank" rel="noopener noreferrer" class="name">Testing viscous and anisotropic hydrodynamics in an exactly solvable case<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2013-08-01">August 2013</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#5C7B2D;"> Florkowski, Wojciech; Ryblewski, Radoslaw; Strickland, Michael</span> </li> <li> Physical Review C, Vol. 88, Issue 2</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1103/PhysRevC.88.024903" class="text-muted" target="_blank" rel="noopener noreferrer">10.1103/PhysRevC.88.024903<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div><div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1007/JHEP09(2013)026" target="_blank" rel="noopener noreferrer" class="name">Holographic isotropization linearized<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2013-09-01">September 2013</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#5C7B2D;"> Heller, Michal P.; Mateos, David; van der Schee, Wilke</span> </li> <li> Journal of High Energy Physics, Vol. 2013, Issue 9</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1007/JHEP09(2013)026" class="text-muted" target="_blank" rel="noopener noreferrer">10.1007/JHEP09(2013)026<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div><div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1016/j.nuclphysa.2016.02.014" target="_blank" rel="noopener noreferrer" class="name">Anisotropic hydrodynamics for conformal Gubser flow<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2016-12-01">December 2016</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#5C7B2D;"> Strickland, Michael; Nopoush, Mohammad; Ryblewski, Radoslaw</span> </li> <li> Nuclear Physics A, Vol. 956</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1016/j.nuclphysa.2016.02.014" class="text-muted" target="_blank" rel="noopener noreferrer">10.1016/j.nuclphysa.2016.02.014<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div><div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1103/PhysRevA.92.043602" target="_blank" rel="noopener noreferrer" class="name">Dissipative fluid dynamics for the dilute Fermi gas at unitarity: Anisotropic fluid dynamics<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2015-10-01">October 2015</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#5C7B2D;"> Bluhm, M.; Schäfer, T.</span> </li> <li> Physical Review A, Vol. 92, Issue 4</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1103/PhysRevA.92.043602" class="text-muted" target="_blank" rel="noopener noreferrer">10.1103/PhysRevA.92.043602<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div><div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1103/PhysRevC.96.044910" target="_blank" rel="noopener noreferrer" class="name">Anisotropic hydrodynamic modeling of 2.76 TeV Pb-Pb collisions<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2017-10-01">October 2017</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#5C7B2D;"> Alqahtani, Mubarak; Nopoush, Mohammad; Ryblewski, Radoslaw</span> </li> <li> Physical Review C, Vol. 96, Issue 4</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1103/PhysRevC.96.044910" class="text-muted" target="_blank" rel="noopener noreferrer">10.1103/PhysRevC.96.044910<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div><div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1103/PhysRevC.85.064901" target="_blank" rel="noopener noreferrer" class="name">Highly anisotropic hydrodynamics in <math display="inline"> <mrow> <mn mathvariant="bold">3</mn> <mo>+</mo> <mn mathvariant="bold">1</mn> </mrow> </math> space-time dimensions<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2012-06-01">June 2012</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#5C7B2D;"> Ryblewski, Radoslaw; Florkowski, Wojciech</span> </li> <li> Physical Review C, Vol. 85, Issue 6</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1103/PhysRevC.85.064901" class="text-muted" target="_blank" rel="noopener noreferrer">10.1103/PhysRevC.85.064901<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div><div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1103/PhysRevLett.111.181601" target="_blank" rel="noopener noreferrer" class="name">From Full Stopping to Transparency in a Holographic Model of Heavy Ion Collisions<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2013-10-01">October 2013</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#5C7B2D;"> Casalderrey-Solana, Jorge; Heller, Michal P.; Mateos, David</span> </li> <li> Physical Review Letters, Vol. 111, Issue 18</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1103/PhysRevLett.111.181601" class="text-muted" target="_blank" rel="noopener noreferrer">10.1103/PhysRevLett.111.181601<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div><div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1103/PhysRevD.97.044041" target="_blank" rel="noopener noreferrer" class="name">Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2018-02-01">February 2018</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#5C7B2D;"> Behtash, Alireza; Cruz-Camacho, C. N.; Martinez, M.</span> </li> <li> Physical Review D, Vol. 97, Issue 4</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1103/PhysRevD.97.044041" class="text-muted" target="_blank" rel="noopener noreferrer">10.1103/PhysRevD.97.044041<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div><div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1007/JHEP01(2017)026" target="_blank" rel="noopener noreferrer" class="name">Holographic collisions in non-conformal theories<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2017-01-01">January 2017</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#5C7B2D;"> Attems, Maximilian; Casalderrey-Solana, Jorge; Mateos, David</span> </li> <li> Journal of High Energy Physics, Vol. 2017, Issue 1</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1007/JHEP01(2017)026" class="text-muted" target="_blank" rel="noopener noreferrer">10.1007/JHEP01(2017)026<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div></div> <div class="pagination-container small"> <a class="pure-button prev page" href="#" rel="prev"><span class="fa fa-angle-left"></span></a><ul class="pagination d-inline-block" style="padding-left:.2em;"></ul><a class="pure-button next page" href="#" rel="next"><span class="fa fa-angle-right"></span></a> </div> </div> </div> <div class="col-sm-3 order-sm-3"> <ul class="nav nav-stacked"> <li class="active"><a href="" class="reference-type-filter tab-nav" data-tab="biblio-references" data-filter="type" data-pattern="*"><span class="fa fa-angle-right"></span> All References</a></li> <li class="small" style="margin-left:.75em; 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float:none;">[ × clear filter / sort ]</a> </div> </form> </div> </div> </div> </section> <section id="biblio-images" class="tab-content tab-content-sec osti-curated" data-tab="biblio"> <div class="row"> <div class="col-sm-9 order-sm-9"> <div class="padding"> <p class="lead text-muted" style="font-size: 18px; margin-top:0px;"><span id="image-type-label">Figures / Tables</span> found in this record:</p> <div class="list clearfix"> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 2" data-order="1" data-imgid="1434185-img51428" data-imgsrc="/biblio/1434185/image/000/739/0007396/2/0051428.png" data-title="FIG. 1" data-desc="Generic two-to-two scattering diagram." data-ostiid="1434185" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1434185-img51428" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1434185-img51428"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">FIG. 1<small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 2)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1434185/image/000/739/0007396/2/t0051428.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 4" data-order="2" data-imgid="1434185-img51433" data-imgsrc="/biblio/1434185/image/000/739/0007396/2/0051433.png" data-title="FIG. 2" data-desc="Comparison of the LO scalar scattering kernel moments for both the classical and quantum cases with those obtained in RTA as a function of ξ . Panel (a) shows Czz/Λ6 and panel (b) shows Cxx/Λ6. For the purposes of this figure, we took η̄ = 0.2." data-ostiid="1434185" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1434185-img51433" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1434185-img51433"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">FIG. 2<small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 4)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1434185/image/000/739/0007396/2/t0051433.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 5" data-order="3" data-imgid="1434185-img51436" data-imgsrc="/biblio/1434185/image/000/739/0007396/2/0051436.png" data-title="FIG. 3" data-desc="Ratio of the moments of the LO scalar collisional kernel in the classical and quantum and quantum cases as a function of ξ . Panel (a) shows C$^{zz}_{classical}$/C$^{zz}_{quantum}$ and panel (b) shows C$^{xx}_{classical}$/C$^{xx}_{quantum}$. The red points show the ratio of the two Monte-Carlo results and the solid black line is a fifth-order polynomial fit to the numerical data." data-ostiid="1434185" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1434185-img51436" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1434185-img51436"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">FIG. 3<small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 5)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1434185/image/000/739/0007396/2/t0051436.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 6" data-order="4" data-imgid="1434185-img51427" data-imgsrc="/biblio/1434185/image/000/739/0007396/2/0051427.png" data-title="FIG. 4" data-desc="Comparison of W using the LO scalar and RTA kernels. Panels (a) and (b) in the top row show the classical case (a = 0) while (c) and (d) from the bottom row show the quantum case (a = 1). The left column shows the result for small values of ξ and the right column shows the result for a larger range of values of ξ ." data-ostiid="1434185" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1434185-img51427" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1434185-img51427"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">FIG. 4<small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 6)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1434185/image/000/739/0007396/2/t0051427.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 7" data-order="5" data-imgid="1434185-img51429" data-imgsrc="/biblio/1434185/image/000/739/0007396/2/0051429.png" data-title="FIG. 5" data-desc="Comparison of the evolution of the scaled temperature (a) and pressure anisotropy (b) for an isotropic initial condition. The RTA results are indicated by a solid black line, the LO classical scalar results by a short-dashed red line, and the LO quantum scalar results by a long-dashed blue line." data-ostiid="1434185" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1434185-img51429" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1434185-img51429"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">FIG. 5<small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 7)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1434185/image/000/739/0007396/2/t0051429.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 7" data-order="6" data-imgid="1434185-img51430" data-imgsrc="/biblio/1434185/image/000/739/0007396/2/0051430.png" data-title="Table I" data-desc="Polynomial fit coefficients for the classical and quantum LO scalar W(ξ) function defined in Eq. (51). The fit was made assuming W(ξ) = ∑n cnξn using 101 moment evaluations in the range −0.68 ≤ ξ ≤ 99." data-ostiid="1434185" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1434185-img51430" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1434185-img51430"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">Table I<small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 7)</small><span class="d-none type">table</span></small> <div style=" background-image:url('/biblio/1434185/image/000/739/0007396/2/t0051430.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 8" data-order="7" data-imgid="1434185-img51432" data-imgsrc="/biblio/1434185/image/000/739/0007396/2/0051432.png" data-title="FIG. 6" data-desc="Comparison of the evolution of the scaled temperature (a) and pressure anisotropy (b) for a highly oblate initial condition. Line styles are the same is in Fig. 5." data-ostiid="1434185" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1434185-img51432" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1434185-img51432"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">FIG. 6<small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 8)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1434185/image/000/739/0007396/2/t0051432.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 9" data-order="8" data-imgid="1434185-img51435" data-imgsrc="/biblio/1434185/image/000/739/0007396/2/0051435.png" data-title="FIG. 7" data-desc="Panel (a) shows the attractor amplitude ϕ as a function of $\bar{w}$ and panel (b) shows the pressure anisotropy PL/PT as a function of $\bar{w}$. In both panels, the scalar quantum result is indicated by a solid black line, the scalar classical result is indicated by a red short-dashed line, and the RTA result is indicated by a blue long-dashed line. In panel (a), we additionally show the Navier-Stokes (NS) result as a green dot-dashed line and the asymptotic bounds ϕ = 2/3 and ϕ = 3/4 as gray and orange dotted lines, respectively." data-ostiid="1434185" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1434185-img51435" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1434185-img51435"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">FIG. 7<small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 9)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1434185/image/000/739/0007396/2/t0051435.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 9" data-order="9" data-imgid="1434185-img51434" data-imgsrc="/biblio/1434185/image/000/739/0007396/2/0051434.png" data-title="FIG. 8" data-desc="Comparison of the classical LO scalar attractor with a set of numerical solutions to the equations of motion for a variety of initial conditions. Panel (a) shows ϕ and panel (b) shows the resulting pressure anisotropy." data-ostiid="1434185" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1434185-img51434" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1434185-img51434"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">FIG. 8<small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 9)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1434185/image/000/739/0007396/2/t0051434.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 10" data-order="10" data-imgid="1434185-img51431" data-imgsrc="/biblio/1434185/image/000/739/0007396/2/0051431.png" data-title="FIG. 9" data-desc="Comparison of the quantum LO scalar attractor with a set of numerical solutions to the equations of motion for a variety of initial conditions. Panel (a) shows ϕ and panel (b) shows the resulting pressure anisotropy." data-ostiid="1434185" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1434185-img51431" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1434185-img51431"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">FIG. 9<small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 10)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1434185/image/000/739/0007396/2/t0051431.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> </div> <div class="pagination-container small"> <a class="pure-button prev page" href="#" rel="prev"><span class="fa fa-angle-left"></span></a><ul class="pagination d-inline-block" style="padding-left:.2em;"></ul><a class="pure-button next page" href="#" rel="next"><span class="fa fa-angle-right"></span></a> </div> </div> </div> <div class="col-sm-3 order-sm-3"> <ul class="nav nav-stacked"> <li class="active"><a href="" class="reference-type-filter tab-nav" data-tab="biblio-images" data-filter="type" data-pattern="*"><span class="fa fa-angle-right"></span> All Images</a></li> <li class="small" style="margin-left:.75em; text-transform:capitalize;"><a href="" class="reference-type-filter tab-nav ga-click-event" data-tab="biblio-images" data-filter="type" data-pattern="figure" data-category="Extracted Images" data-label="biblio: image filter - figure"><span class="fa fa-angle-right"></span> figures<small class="text-muted"> (9)</small></a></li> <li class="small" style="margin-left:.75em; text-transform:capitalize;"><a href="" class="reference-type-filter tab-nav ga-click-event" data-tab="biblio-images" data-filter="type" data-pattern="table" data-category="Extracted Images" data-label="biblio: image filter - table"><span class="fa fa-angle-right"></span> tables<small class="text-muted"> (1)</small></a></li> </ul> <div style="margin-top:2em;"> <form class="pure-form small text-muted image-search"> <label for="image-search-text" class="sr-only">Search</label> <input class="search form-control pure-input-1" id="image-search-text" placeholder="Search" style="margin-bottom:10px;" /> <fieldset> <div style="margin-left:1em; font-weight:normal; line-height: 1.6em;"><input type="radio" class="sort ga-click-event" name="images-sort" data-sort="name" style="position:relative;top:2px;" id="image-search-sort-name" data-category="Extracted Images" data-label="biblio: image sort - name"><label for="image-search-sort-name" style="margin-left: .3em;">Sort by figure / table title</label></div> <div style="margin-left:1em; font-weight:normal; line-height: 1.6em;"><input type="radio" class="sort ga-click-event" name="images-sort" data-sort="order" style="position:relative;top:2px;" id="image-search-sort-date" data-category="Extracted Images" data-label="biblio: image sort - order"><label for="image-search-sort-date" style="margin-left: .3em;">Sort by page order</label></div> </fieldset> <div class="text-left" style="margin-top:1.5em;margin-left:1em;"> <a href="" class="filter-clear clearfix" title="Clear filter / sort" style="font-weight:normal; float:none;">[ × clear filter / sort ]</a> </div> </form> </div> <div class="text-muted small" style="margin-top:2em; padding:1em;"> <em>Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.</em> </div> </div> </div> </section> <section id="biblio-related" class="tab-content tab-content-sec " data-tab="biblio"> <div class="row"> <div class="col-sm-9 order-sm-9"> <section id="biblio-similar" class="tab-content tab-content-sec active" data-tab="related"> <div class="padding"> <p class="lead text-muted" style="font-size: 18px; margin-top:0px;">Similar Records in DOE PAGES and OSTI.GOV collections:</p> <aside> <ul class="item-list" itemscope itemtype="http://schema.org/ItemList" style="padding-left:0; list-style-type: none;"> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="2" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/pages/biblio/1422657-far-from-equilibrium-attractors-nonlinear-dynamical-systems-approach-gubser-flow" itemprop="url">Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Behtash, Alireza</span> ; <span class="author">Cruz-Camacho, C. N.</span> ; <span class="author">Martinez, M.</span> <span class="text-muted pubdata"> - Physical Review D</span> </span> </div> <div class="abstract">The nonequilibrium attractors of systems undergoing Gubser flow within relativistic kinetic theory are studied. In doing so we employ well-established methods of nonlinear dynamical systems which rely on finding the fixed points, investigating the structure of the flow diagrams of the evolution equations, and characterizing the basin of attraction using a Lyapunov function near the stable fixed points. We obtain the attractors of anisotropic hydrodynamics, Israel-Stewart (IS) and transient fluid (DNMR) theories and show that they are indeed nonplanar and the basin of attraction is essentially three dimensional. The attractors of each hydrodynamical model are compared with the one obtained<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> from the exact Gubser solution of the Boltzmann equation within the relaxation time approximation. We observe that the anisotropic hydrodynamics is able to match up to high numerical accuracy the attractor of the exact solution while the second-order hydrodynamical theories fail to describe it. We show that the IS and DNMR asymptotic series expansions diverge and use resurgence techniques to perform the resummation of these divergences. We also comment on a possible link between the manifold of steepest descent paths in path integrals and the basin of attraction for the attractors via Lyapunov functions that opens a new horizon toward an effective field theory description of hydrodynamics. Our findings indicate that the reorganization of the expansion series carried out by anisotropic hydrodynamics resums the Knudsen and inverse Reynolds numbers to all orders and thus, it can be understood as an effective theory for the far-from-equilibrium fluid dynamics</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <span class="fa fa-book text-muted" aria-hidden="true"></span> Cited by 14<div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink">DOI: <a class="misc doi-link " href="https://doi.org/10.1103/PhysRevD.97.044041" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1422657" data-product-type="Journal Article" data-product-subtype="PA" >10.1103/PhysRevD.97.044041</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="3" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/pages/biblio/1393904-generalized-multiband-typical-medium-dynamical-cluster-approximation-application-ga-mn" itemprop="url">Generalized multiband typical medium dynamical cluster approximation: Application to (Ga,Mn)N</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Zhang, Yi</span> ; <span class="author">Nelson, R.</span> ; <span class="author">Siddiqui, Elisha</span> ; <span class="author">...</span> <span class="text-muted pubdata"> - Physical Review B</span> </span> </div> <div class="abstract">We generalize the multiband typical medium dynamical cluster approximation and the formalism introduced by Blackman, Esterling, and Berk so that it can deal with localization in multiband disordered systems with both diagonal and off-diagonal disorder with complicated potentials. We also introduce an ansatz for the momentum-resolved typical density of states that greatly improves the numerical stability of the method while preserving the independence of scattering events at different frequencies. Starting from the first-principles effective Hamiltonian, we apply this method to the diluted magnetic semiconductor Ga <sub>1 - x</sub> Mn <sub>x</sub> N , and find the impurity band is completely localized<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> for Mn concentrations x < 0.03 , while for 0.03 < x < 0.10 the impurity band has delocalized states but the chemical potential resides at or above the mobility edge. So, the system is always insulating within the experimental compositional limit ( x ≈ 0.10 ) due to Anderson localization. But, for 0.03 < x < 0.10 hole doping could make the system metallic, allowing double-exchange mediated, or enhanced, ferromagnetism. Finally, this developed method is expected to have a large impact on first-principles studies of Anderson localization.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <span class="fa fa-book text-muted" aria-hidden="true"></span> Cited by 4<div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink">DOI: <a class="misc doi-link " href="https://doi.org/10.1103/PhysRevB.94.224208" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1393904" data-product-type="Journal Article" data-product-subtype="AM" >10.1103/PhysRevB.94.224208</a></span></li> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc fulltext-link " href="/pages/servlets/purl/1393904" title="Link to document media" target="_blank" rel="noopener" data-ostiid="1393904" data-product-type="Journal Article" data-product-subtype="AM" >Full Text Available</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="5" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/pages/biblio/1240595-study-multiband-disordered-systems-using-typical-medium-dynamical-cluster-approximation" itemprop="url">Study of multiband disordered systems using the typical medium dynamical cluster approximation</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Zhang, Yi</span> ; <span class="author">Terletska, Hanna</span> ; <span class="author">Moore, C.</span> ; <span class="author">...</span> <span class="text-muted pubdata"> - Physical Review. B, Condensed Matter and Materials Physics</span> </span> </div> <div class="abstract">We generalize the typical medium dynamical cluster approximation to multiband disordered systems. Using our extended formalism, we perform a systematic study of the nonlocal correlation effects induced by disorder on the density of states and the mobility edge of the three-dimensional two-band Anderson model. We include interband and intraband hopping and an intraband disorder potential. Our results are consistent with those obtained by the transfer matrix and the kernel polynomial methods. We also apply the method to K <sub>x</sub>Fe <sub>2-y</sub>Se <sub>2</sub> with Fe vacancies. Despite the strong vacancy disorder and anisotropy, we find the material is not an Anderson insulator.<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> Moreover our results demonstrate the application of the typical medium dynamical cluster approximation method to study Anderson localization in real materials.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink">DOI: <a class="misc doi-link " href="https://doi.org/10.1103/PhysRevB.92.205111" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1240595" data-product-type="Journal Article" data-product-subtype="AM" >10.1103/PhysRevB.92.205111</a></span></li> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc fulltext-link " href="/pages/servlets/purl/1240595" title="Link to document media" target="_blank" rel="noopener" data-ostiid="1240595" data-product-type="Journal Article" data-product-subtype="AM" >Full Text Available</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="6" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/pages/biblio/1419751-quantum-thermodynamics-from-nonequilibrium-dynamics-open-systems-energy-heat-capacity-third-law" itemprop="url">Quantum thermodynamics from the nonequilibrium dynamics of open systems: Energy, heat capacity, and the third law</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Hsiang, Jen -Tsung</span> ; <span class="author">Chou, Chung Hsien</span> ; <span class="author">Subasi, Yigit</span> ; <span class="author">...</span> <span class="text-muted pubdata"> - Physical Review E</span> </span> </div> <div class="abstract">In a series of papers, we intend to take the perspective of open quantum systems and examine from their nonequilibrium dynamics the conditions when the physical quantities, their relations, and the laws of thermodynamics become well defined and viable for quantum many-body systems. We first describe how an open-system nonequilibrium dynamics (ONEq) approach is different from the closed combined system + environment in a global thermal state (CGTs) setup. Only after the open system equilibrates will it be amenable to conventional thermodynamics descriptions, thus quantum thermodynamics (QTD) comes at the end rather than assumed in the beginning. The linkage between<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> the two comes from the reduced density matrix of ONEq in that stage having the same form as that of the system in the CGTs. We see the open-system approach having the advantage of dealing with nonequilibrium processes as many experiments in the near future will call for. Because it spells out the conditions of QTD's existence, it can also aid us in addressing the basic issues in quantum thermodynamics from first principles in a systematic way. We then study one broad class of open quantum systems where the full nonequilibrium dynamics can be solved exactly, that of the quantum Brownian motion of <em>N</em> strongly coupled harmonic oscillators, interacting strongly with a scalar-field environment. In this paper, we focus on the internal energy, heat capacity, and the third law. We show for this class of physical models, amongst other findings, the extensive property of the internal energy, the positivity of the heat capacity, and the validity of the third law from the perspective of the behavior of the heat capacity toward zero temperature. These conclusions obtained from exact solutions and quantitative analysis clearly disprove claims of negative specific heat in such systems and dispel allegations that in such systems the validity of the third law of thermodynamics relies on quantum entanglement. They are conceptually and factually unrelated issues. As a result, entropy and entanglement will be the main theme of our second paper on this subject matter.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <span class="fa fa-book text-muted" aria-hidden="true"></span> Cited by 4<div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink">DOI: <a class="misc doi-link " href="https://doi.org/10.1103/PhysRevE.97.012135" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1419751" data-product-type="Journal Article" data-product-subtype="AM" >10.1103/PhysRevE.97.012135</a></span></li> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc fulltext-link " href="/pages/servlets/purl/1419751" title="Link to document media" target="_blank" rel="noopener" data-ostiid="1419751" data-product-type="Journal Article" data-product-subtype="AM" >Full Text Available</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="7" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/pages/biblio/1454315-higher-order-anisotropic-hydrodynamics-bjorken-gubser-flows" itemprop="url">Higher order and anisotropic hydrodynamics for Bjorken and Gubser flows</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Chattopadhyay, Chandrodoy</span> ; <span class="author">Heinz, Ulrich</span> ; <span class="author">Pal, Subrata</span> ; <span class="author">...</span> <span class="text-muted pubdata"> - Physical Review C</span> </span> </div> <div class="abstract">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<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> into the entropy evolution, which are not well captured by the hydrodynamic approximations. The differences between the exact solution and the hydrodynamic approximations are larger for the third-order Chapman-Enskog hydrodynamics than for anisotropic hydrodynamics, which effectively resums some of the dissipative effects from anisotropic expansion to all orders in the anisotropy, and are larger for Gubser flow than for Bjorken flow. Overall, anisotropic hydrodynamics provides the most precise macroscopic description for these highly anisotropically expanding systems.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <span class="fa fa-book text-muted" aria-hidden="true"></span> Cited by 4<div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink">DOI: <a class="misc doi-link " href="https://doi.org/10.1103/PhysRevC.97.064909" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1454315" data-product-type="Journal Article" data-product-subtype="PA" >10.1103/PhysRevC.97.064909</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> </ul> </aside> </div> </section> </div> <div class="col-sm-3 order-sm-3"> <ul class="nav nav-stacked"> <li class="active"><a class="tab-nav disabled" data-tab="related" style="color: #636c72 !important; opacity: 1;"><span class="fa fa-angle-right"></span> Similar Records</a></li> </ul> </div> </div> </section> </div></div> </div> </div> </section> <footer class="" style="background-color:#f9f9f9; /* padding-top: 0.5rem; */"> <div class="footer-minor"> <div class="container"> <hr class="footer-separator" /> <div class="text-center" style="margin-top:1.25rem;"> <div class="pure-menu pure-menu-horizontal"> <ul class="pure-menu-list" id="footer-org-menu"> <li class="pure-menu-item"> <a href="https://energy.gov" target="_blank" rel="noopener noreferrer"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-us-doe-min" alt="U.S. Department of Energy" /> </a> </li> <li class="pure-menu-item"> <a href="https://www.energy.gov/science/office-science" target="_blank" rel="noopener noreferrer"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-office-of-science-min" alt="Office of Science" /> </a> </li> <li class="pure-menu-item"> <a href="/"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-osti-min" alt="Office of Scientific and Technical Information" /> </a> </li> </ul> </div> </div> <div class="text-center small" style="margin-top:0.5em;margin-bottom:2.0rem;"> <div class="pure-menu pure-menu-horizontal"> <ul class="pure-menu-list"> <li class="pure-menu-item"><a href="/disclaim" class="pure-menu-link"><span class="fa fa-institution"></span> Website Policies <span class="hidden-xs">/ Important Links</span></a></li> <li class="pure-menu-item"><a href="/pages/contact" class="pure-menu-link"><span class="fa fa-comments-o"></span> Contact Us</a></li> <li class="d-block d-md-none"></li> <li class="pure-menu-item"><a href="https://www.facebook.com/ostigov" target="_blank" rel="noopener noreferrer" class="pure-menu-link social"><span class="fa fa-facebook" style=""></span></a></li> <li class="pure-menu-item"><a href="https://twitter.com/OSTIgov" target="_blank" rel="noopener noreferrer" class="pure-menu-link social"><span class="fa fa-twitter" style=""></span></a></li> <li class="pure-menu-item"><a href="https://www.youtube.com/user/ostigov" target="_blank" rel="noopener noreferrer" class="pure-menu-link social"><span class="fa fa-youtube-play" style=""></span></a></li> </ul> </div> </div> </div> </div> </footer> <link href="/pages/css/pages.fonts.200319.1244.css" rel="stylesheet"> <script src="/pages/js/pages.200319.1244.js"></script><noscript></noscript> <script src='https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.4/MathJax.js?config=TeX-MML-AM_CHTML' async> MathJax.Hub.Config({ tex2jax: {displayMath: [], inlineMath: [['$$','$$'], ['\\(','\\)']]}, asciimath2jax: {delimiters: []}, skipStartupTypeset: true, webFont: null, CommonHTML: { scale: 84, // mathjx wants to scale everything to 119% by default? mtextFontInherit: true } }); MathJax.Hub.Queue(["Typeset",MathJax.Hub,"item-list"]); MathJax.Hub.Queue(["Typeset",MathJax.Hub,"citation-pagetitle"]); MathJax.Hub.Queue(["Typeset",MathJax.Hub,"citation-abstract"]); </script><noscript></noscript><script defer src="/pages/js/pages.biblio.200319.1244.js"></script><noscript></noscript> <script defer src="/pages/js/lity.js"></script><noscript></noscript><script async type="text/javascript" src="/pages/js/Universal-Federated-Analytics-Min.js?agency=DOE" id="_fed_an_ua_tag"></script><noscript></noscript></body> <!-- DOE PAGES v.200319.1244 --> </html>