Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation

Physical Review Letters
Michal P Heller, Michał Spaliński

Abstract

Consistent formulations of relativistic viscous hydrodynamics involve short-lived modes, leading to asymptotic rather than convergent gradient expansions. In this Letter we consider the Müller-Israel-Stewart theory applied to a longitudinally expanding quark-gluon plasma system and identify hydrodynamics as a universal attractor without invoking the gradient expansion. We give strong evidence for the existence of this attractor and then show that it can be recovered from the divergent gradient expansion by Borel summation. This requires careful accounting for the short-lived modes which leads to an intricate mathematical structure known from the theory of resurgence.

References

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Sep 4, 2008·Physical Review Letters·Wojciech BroniowskiAdam Kisiel
Sep 26, 2012·Physical Review Letters·Michal P HellerPrzemysław Witaszczyk
Sep 26, 2012·Physical Review Letters·Philip Argyres, Mithat Unsal
Jun 12, 2013·Physical Review Letters·Michal P HellerPrzemysław Witaszczyk
Jan 24, 2015·Physical Review Letters·Michal P HellerPrzemysław Witaszczyk
Jan 1, 2007·Living Reviews in Relativity·Nils Andersson, Gregory L Comer

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Citations

Dec 12, 2017·Reports on Progress in Physics·Wojciech FlorkowskiMichał Spaliński
May 6, 2019·Physical Review Letters·Aleksi Kurkela, Aleksas Mazeliauskas
May 2, 2020·Physical Review Letters·Gabriel S Denicol, Jorge Noronha
Nov 4, 2017·Physical Review Letters·Julian Sonner, Benjamin Withers
Jan 20, 2018·Physical Review Letters·Paul Romatschke
Jul 28, 2019·Physical Review Letters·Sašo GrozdanovPetar Tadić
Nov 10, 2015·Physical Review Letters·Héctor MeraBranislav K Nikolić
Oct 6, 2020·Physical Review Letters·Dekrayat AlmaalolMichael Strickland
Jan 18, 2020·Physical Review Letters·Giuliano GiacaloneSören Schlichting
Mar 29, 2020·Physical Review Letters·Aleksi KurkelaBin Wu
Oct 10, 2020·Physical Review Letters·Michal P HellerViktor Svensson
Feb 20, 2021·Physical Review Letters·Sašo Grozdanov
Jun 22, 2021·Physical Review Letters·Fábio S BemficaMaria Radosz
Aug 7, 2021·Physical Review Letters·Gabriel S RochaJorge Noronha
Jul 16, 2021·Reports on Progress in Physics·Björn Schenke

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