Hydrodynamics, resurgence and trans-asymptotics

Abstract

The second-order hydrodynamical description of a homogeneous conformal plasma that undergoes a boost- invariant expansion is given by a single nonlinear ordinary differential equation, whose resurgent asymptotic properties we study, developing further the recent work of Heller and Spalinski [Phys. Rev. Lett. 115, 072501 (2015)]. Resurgence clearly identifies the non-hydrodynamic modes that are exponentially suppressed at late times, analogous to the quasi-normal-modes in gravitational language, organizing these modes in terms of a trans-series expansion. These modes are analogs of instantons in semi-classical expansions, where the damping rate plays the role of the instanton action. We show that this system displays the generic features of resurgence, with explicit quantitative relations between the fluctuations about different orders of these non-hydrodynamic modes. The imaginary part of the trans-series parameter is identified with the Stokes constant, and the real part with the freedom associated with initial conditions.

29 pages, 13 figures

References in corpus (9)

• Nonlinear Fluid Dynamics from Gravity
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation
• Viscous hydrodynamics relaxation time from AdS/CFT
• Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
• Constructing higher-order hydrodynamics: The third order
• A Holographic Dual of Bjorken Flow
• All Order Linearized Hydrodynamics from Fluid/Gravity Correspondence
• Exponential asymptotics, transseries, and generalized Borel summation for analytic rank one systems of ODE's

Cited by in corpus (62)

• New theories of relativistic hydrodynamics in the LHC era
• Causality and existence of solutions of relativistic viscous fluid dynamics with gravity
• QCD thermalization: Ab initio approaches and interdisciplinary connections
• Fluid Dynamics far from Local Equilibrium
• A Primer on Resurgent Transseries and Their Asymptotics
• The complex life of hydrodynamic modes
• Hydrodynamization in kinetic theory: Transient modes and the gradient expansion
• Gapped momentum states
• 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
• On the hydrodynamic attractor of Yang-Mills plasma
• Resurgence in Extended Hydrodynamics
• Analytical attractor and the divergence of the slow-roll expansion in relativistic hydrodynamics
• How does relativistic kinetic theory remember about initial conditions?
• Hydrodynamic attractors in heavy ion collisions: a review
• Exact solutions and attractors of higher-order viscous fluid dynamics for Bjorken flow
• Hydrodynamic attractor and the fate of perturbative expansions in Gubser flow
• Quasinormal modes in charged fluids at complex momentum
• Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow
• Non-perturbative rheological behavior of a far-from-equilibrium expanding plasma
• Gradient expansion for anisotropic hydrodynamics
• Transient Relativistic Fluid Dynamics in a General Hydrodynamic Frame
• The grin of Cheshire cat resurgence from supersymmetric localization
• Hydrodynamic gradient expansion in linear response theory
• Causality of fluid dynamics for high-energy nuclear collisions
• The large proper-time expansion of Yang-Mills plasma as a resurgent transseries
• On attractor and fixed points in Bjorken flows
• Hydrodynamic attractors in phase space
• Remark on the Dunne-Unsal relation in exact semi-classics
• Hydrodynamization in systems with detailed transverse profiles
• Holography, Hydrodynamization and Heavy-Ion Collisions
• Analytical attractor for Bjorken expansion
• Hydrodynamic Attractors in Ultrarelativistic Nuclear Collisions
• A Lagrangian formulation of relativistic Israel-Stewart hydrodynamics
• An Action for and Hydrodynamics from the improved Large D membrane
• Global flow structure and exact formal transseries of the Gubser flow in kinetic theory
• Transasymptotics and hydrodynamization of the Fokker-Planck equation for gluons
• Exponential Approach to the Hydrodynamic Attractor in Yang-Mills Kinetic Theory
• Holographic Bjorken Flow at Large-D
• Conformal Bjorken flow in the general frame and its attractor: Similarities and discrepancies with the Müller-Israel-Stewart formalism
• Bands and gaps in Nekrasov partition function
• Relativistic Hydrodynamics: A Singulant Perspective
• Hydrodynamic Attractor in a Hubble Expansion
• Hydrodynamic Gradient Expansion Diverges beyond Bjorken Flow
• Prescaling relaxation to nonthermal attractors
• Hydrodynamic attractor of a hybrid viscous fluid in Bjorken flow
• Holography as a highly efficient RG flow II: An explicit construction
• Resurgence in Lorentzian quantum cosmology: No-boundary saddles and resummation of quantum gravity corrections around tunneling saddle points
• Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED
• Gradient resummation for nonlinear chiral transport: an insight from holography
• Resurgence and Lefschetz thimble in 3d N=2 supersymmetric Chern-Simons matter theories
• Hydrodynamic attractor in the non-conformal Bjorken flow
• Pseudorapidity dependent hydrodynamic response in heavy-ion collisions
• Understanding the holographic principle via RG flow
• Reconstruction of spectra and an algorithm based on the theorems of Darboux and Puiseux
• Novel features of attractors and transseries in non-conformal Bjorken flows
• Transseries for causal diffusive systems
• The late to early time behaviour of an expanding plasma: hydrodynamisation from exponential asymptotics
• Hydrodynamical attractor and thermal particle production in heavy-ion collision
• Correlation functions of the Bjorken flow in the holographic Schwinger-Keldysh approach
• Resurgence for the non-conformal Bjorken flow with Fermi-Dirac and Bose-Einstein statistics
• Self-Similar acoustic white hole solutions in Bose-Einstein condensates and their Borel analysis