Hydrodynamic Gradient Expansion Diverges beyond Bjorken Flow

Abstract

The gradient expansion is the fundamental organising principle underlying relativistic hydrodynamics, yet understanding its convergence properties for general nonlinear flows has posed a major challenge. We introduce a simple method to address this question in a class of fluids modelled by Israel-Stewart--type relaxation equations. We apply it to (1+1)-dimensional flows and provide numerical evidence for factorially divergent gradient expansions. This generalises results previously only obtained for (0+1)-dimensional comoving flows, notably Bjorken flow. We also demonstrate that the only known nontrivial case of a convergent hydrodynamic gradient expansion at the nonlinear level relies on Bjorken flow symmetries and becomes factorially divergent as soon as these are relaxed. Finally, we show that factorial divergence can be removed using a momentum space cutoff, which generalises a result obtained earlier in the context of linear response.

arXiv commentv1: 9 pages, 4 figures; v2: minor clarifications added, version published in PRL

References in corpus (38)

• Collective flow and viscosity in relativistic heavy-ion collisions
• Heavy Ion Collisions: The Big Picture, and the Big Questions
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Derivation of transient relativistic fluid dynamics from the Boltzmann equation
• Lectures on hydrodynamic fluctuations in relativistic theories
• New theories of relativistic hydrodynamics in the LHC era
• The characteristics of thermalization of boost-invariant plasma from holography
• Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation
• Symmetry constraints on generalizations of Bjorken flow
• On the importance of viscous dissipation and heat conduction in binary neutron-star mergers
• Hydrodynamic gradient expansion in gauge theory plasmas
• Fluidity Onset in Graphene
• Conformal hydrodynamics in Minkowski and de Sitter spacetimes
• Entropy Current in Conformal Hydrodynamics
• Relativistic third-order dissipative fluid dynamics from kinetic theory
• Hydrodynamization in kinetic theory: Transient modes and the gradient expansion
• General relativistic viscous hydrodynamics of differentially rotating neutron stars
• Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow
• Entropy Production, Hydrodynamics, and Resurgence in the Primordial Quark-Gluon Plasma from Holography
• Causality of the Einstein-Israel-Stewart Theory with Bulk Viscosity
• Resurgence in Extended Hydrodynamics
• Coupling hydrodynamics to nonequilibrium degrees of freedom in strongly interacting quark-gluon plasma
• Hydrodynamics, resurgence and trans-asymptotics
• Analytical attractor and the divergence of the slow-roll expansion in relativistic hydrodynamics
• How does relativistic kinetic theory remember about initial conditions?
• Short-lived modes from hydrodynamic dispersion relations
• Exact hydrodynamic attractor of an ultrarelativistic gas of hard spheres
• Hydrodynamic attractor and the fate of perturbative expansions in Gubser flow
• Resurgence and Hydrodynamic Attractors in Gauss-Bonnet Holography
• Emergence of hydrodynamical behavior in expanding quark-gluon plasmas
• Gradient expansion for anisotropic hydrodynamics
• Hydrodynamic gradient expansion in linear response theory
• The large proper-time expansion of Yang-Mills plasma as a resurgent transseries
• Global flow structure and exact formal transseries of the Gubser flow in kinetic theory
• Holographic Viscoelastic Hydrodynamics
• Non-boost-invariant dissipative hydrodynamics
• Hydrodynamic Attractor in a Hubble Expansion
• Non-conformal holographic Gauss-Bonnet hydrodynamics

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