002216104 001__ 2216104
002216104 003__ SzGeCERN
002216104 005__ 20231124081514.0
002216104 0248_ $$aoai:cds.cern.ch:2216104$$pcerncds:CERN$$pcerncds:CERN:FULLTEXT$$pcerncds:FULLTEXT
002216104 0247_ $$2DOI$$a10.1103/PhysRevD.97.091503
002216104 035__ $$9arXiv$$aoai:arXiv.org:1609.04803
002216104 035__ $$9Inspire$$a1486692
002216104 037__ $$9arXiv$$aarXiv:1609.04803$$cnucl-th
002216104 037__ $$aCERN-TH-2016-199
002216104 041__ $$aeng
002216104 100__ $$aHeller, Michal [email protected]$$uPotsdam, Max Planck Inst.$$uPerimeter Inst. Theor. Phys.$$uWarsaw, Inst. Nucl. Studies$$vMax Planck Institute for Gravitational Physics , Potsdam-Golm D-14476, Germany$$vPerimeter Institute for Theoretical Physics , Waterloo, Ontario N2L 2Y5, Canada$$vNational Centre for Nuclear Research , 00-681 Warsaw, Poland
002216104 245__ $$9arXiv$$aHydrodynamic series and hydrodynamization of expanding plasma in kinetic theory
002216104 269__ $$c15 Sep 2016
002216104 260__ $$c2018-06-01
002216104 300__ $$a6 p
002216104 500__ $$aComments: 6 pages, 3 figures, coefficients of the gradient expansion included in the submission
002216104 500__ $$9arXiv$$a6 pages, 2 figures, v2: author added, major rewrite, mysterious off real axis singularities in the Borel plane explained (!), see also arXiv:1802.08225 [nucl-th] by Heller and Svensson; v3: references added, minor improvements in the text, first 426 terms from Eq. (8) included in the submission; v4: title changed, matches published version
002216104 520__ $$9APS$$aWe explore the transition to hydrodynamics in a weakly coupled model of quark-gluon plasma given by kinetic theory in the relaxation-time approximation with conformal symmetry. We demonstrate that the gradient expansion in this model has a vanishing radius of convergence due to the presence of a transient (nonhydrodynamic) mode, in a way similar to results obtained earlier in strongly coupled gauge theories. This suggests that the mechanism by which hydrodynamic behavior emerges is the same, which we further corroborate by a novel comparison between solutions of different weakly and strongly coupled models. However, in contrast with other known cases, we find that not all the singularities of the analytic continuation of the Borel transform of the gradient expansion correspond to transient excitations of the microscopic system; some of them reflect analytic properties of the kinetic equation when the proper time is continued to complex values.
002216104 520__ $$9arXiv$$aWe explore the transition to hydrodynamics in a weakly-coupled model of quark-gluon plasma given by kinetic theory in the relaxation time approximation with conformal symmetry. We demonstrate that the gradient expansion in this model has a vanishing radius of convergence due to the presence of a transient (nonhydrodynamic) mode, in a way similar to results obtained earlier in strongly-coupled gauge theories. This suggests that the mechanism by which hydrodynamic behaviour emerges is the same, which we further corroborate by a novel comparison between solutions of different weakly and strongly coupled models. However, in contrast with other known cases, we find that not all the singularities of the analytic continuation of the Borel transform of the gradient expansion correspond to transient excitations of the microscopic system: some of them reflect analytic properties of the kinetic equation when the proper time is continued to complex values.
002216104 540__ $$aarXiv nonexclusive-distrib. 1.0$$barXiv$$uhttp://arxiv.org/licenses/nonexclusive-distrib/1.0/
002216104 542__ $$3Publication$$dauthors$$g2018
002216104 595__ $$aLANL EDS
002216104 595__ $$aCERN-TH
002216104 65017 $$2arXiv$$aphysics.flu-dyn
002216104 65017 $$2SzGeCERN$$aOther Fields of Physics
002216104 65017 $$2arXiv$$ahep-th
002216104 65017 $$2SzGeCERN$$aParticle Physics - Theory
002216104 65017 $$2arXiv$$ahep-ph
002216104 65017 $$2SzGeCERN$$aParticle Physics - Phenomenology
002216104 65017 $$2arXiv$$anucl-th
002216104 65017 $$2SzGeCERN$$aNuclear Physics - Theory
002216104 695__ $$9LANL EDS$$anucl-th
002216104 695__ $$9LANL EDS$$ahep-ph
002216104 695__ $$9LANL EDS$$ahep-th
002216104 695__ $$9LANL EDS$$aphysics.flu-dyn
002216104 690C_ $$aARTICLE
002216104 690C_ $$aCERN
002216104 700__ $$aKurkela, [email protected]$$uCERN$$uStavanger U.$$vTheoretical Physics Department, CERN , CH-1211 Geneva, Switzerland$$vFaculty of Science and Technology, University of Stavanger , 4036 Stavanger, Norway
002216104 700__ $$aSpaliński, [email protected]$$uBialystok U.$$uWarsaw, Inst. Nucl. Studies$$vNational Centre for Nuclear Research , 00-681 Warsaw, Poland$$vPhysics Department, University of Białystok , 15-245 Białystok, Poland
002216104 700__ $$aSvensson, [email protected]$$uWarsaw, Inst. Nucl. Studies$$uPotsdam, Max Planck Inst.$$vNational Centre for Nuclear Research , 00-681 Warsaw, Poland$$vMax Planck Institute for Gravitational Physics , Potsdam-Golm D-14476, Germany
002216104 773__ $$c091503$$pPhys. Rev. D$$v97$$y2018
002216104 8564_ $$uhttp://arxiv.org/pdf/1609.04803.pdf$$yPreprint
002216104 8564_ $$81449423$$s327790$$uhttp://cds.cern.ch/record/2216104/files/10.1103_PhysRevD.97.091503.pdf$$yFulltext from Publisher
002216104 8564_ $$82226590$$s94528$$uhttp://cds.cern.ch/record/2216104/files/poles3.png$$y00001 Poles in the Pade approximant to the Borel transform of the gradient expansion. Note that although the expression is not Borel-summable due to a singularity on the positive real line, its resummation is expected to give a well-defined answer (up to a choice of initial conditions) due to the phenomenon of resurgence~\cite{Heller:2015dha}.
002216104 8564_ $$82226591$$s609682$$uhttp://cds.cern.ch/record/2216104/files/arXiv:1609.04803.pdf
002216104 8564_ $$82226592$$s127394$$uhttp://cds.cern.ch/record/2216104/files/diverge.png$$y00000 Large order behaviour of the hydrodynamic expansion coefficients.
002216104 8564_ $$82226593$$s115759$$uhttp://cds.cern.ch/record/2216104/files/borel.png$$y00000 Poles of the Pad{\'e} approximant to the Borel transform of the gradient expansion. We have checked that the structure of singularities remains stable as the number of terms kept in the series is varied. We have also checked that the residues of the pictured poles lie well above what was set as the numerical accuracy, i.e. that they are not numerical artefacts. The depicted singularities are discretizations of branch cuts with branch points at values of $\xi$ given in Eqs.~\eqref{eq.leadsing} and~\eqref{eq.omegacomplex}, as well as at $\xi_{0} + \xi_{\pm}$ and $2\, \xi_{\pm}$ (see also Ref.~\cite{Casalderrey-Solana:2017zyh} for a related statement based on a smaller data set from the previous version of the present manuscript).
002216104 8564_ $$82226594$$s228602$$uhttp://cds.cern.ch/record/2216104/files/tilde.png$$y00002 The magenta plot is first order hydrodynamics, the brown dot-dashed line is the holographic result, and the red, dotted line is from EKT. The remaining lines are numerical solutions of the RTA model starting from the same initial distribution, but with different values of $\eta/s$. The blue, dashed curve corresponds to $\eta/s=1/4\pi$, while the green, dotted curve corresponds $\eta/s=0.624$ (matching the data behind the red dotted line).
002216104 8564_ $$82226595$$s111324$$uhttp://cds.cern.ch/record/2216104/files/tilde_v2.png$$y00001 The dashed magenta curve represents first order hydrodynamics, the blue line is the holographic result, and the red, dashed-dotted line is from EKT. The green dotted curve stands for a solution of RTA starting from similar initial distribution as EKT and with the same shear viscosity, $\eta/s=0.624$. Despite differences in microscopic dynamics, one sees significant qualitative and some quantitative similarities between different theories.
002216104 916__ $$sn$$w201637
002216104 960__ $$a13
002216104 980__ $$aARTICLE