Kubo Formulae for Second-Order Hydrodynamic Coefficients

Abstract

At second order in gradients, conformal relativistic hydrodynamics depends on the viscosity eta and on five additional "second-order" hydrodynamical coefficients tauPi, kappa, lambda1, lambda2, and lambda3. We derive Kubo relations for these coefficients, relating them to equilibrium, fully retarded 3-point correlation functions of the stress tensor. We show that the coefficient lambda3 can be evaluated directly by Euclidean means and does not in general vanish.

four pages, no figures. Corrects an error pointed out by Arnold, Vaman, Wu, and Wei; the general technique of the original paper is correct but the specific 2'nd order Kubo relations were wrong and are replaced here by correct versions

References in corpus (20)

• Experimental and Theoretical Challenges in the Search for the Quark Gluon Plasma: The STAR Collaboration's Critical Assessment of the Evidence from RHIC Collisions
• Formation of dense partonic matter in relativistic nucleus-nucleus collisions at RHIC: Experimental evaluation by the PHENIX collaboration
• Quark Gluon Plasma an Color Glass Condensate at RHIC? The perspective from the BRAHMS experiment
• The PHOBOS Perspective on Discoveries at RHIC
• Nonlinear Fluid Dynamics from Gravity
• Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?
• Radial and elliptic flow at RHIC: further predictions
• Conformal Relativistic Viscous Hydrodynamics: Applications to RHIC results at sqrt(s_NN) = 200 GeV
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Flow at the SPS and RHIC as a Quark Gluon Plasma Signature
• Causal viscous hydrodynamics in 2+1 dimensions for relativistic heavy-ion collisions
• Collective flow and two-pion correlations from a relativistic hydrodynamic model with early chemical freeze out
• Simulating elliptic flow with viscous hydrodynamics
• Hydrodynamic Transport Coefficients in Relativistic Scalar Field Theory
• Centrality dependence of multiplicity, transverse energy, and elliptic flow from hydrodynamics
• Transverse flow and hadro-chemistry in Au+Au collisions at \sqrt{s_{NN}}=200 GeV
• Relativistic Viscous Fluid Dynamics and Non-Equilibrium Entropy
• Second order hydrodynamic coefficients from kinetic theory
• Spectral sum rules for the quark-gluon plasma
• A Generalized Fluctuation-Dissipation Theorem for Nonlinear Response Functions

Cited by in corpus (60)

• Lectures on hydrodynamic fluctuations in relativistic theories
• Basics of thermal field theory -- a tutorial on perturbative computations
• The stickiness of sound: An absolute lower limit on viscosity and the breakdown of second order relativistic hydrodynamics
• Parity-Violating Hydrodynamics in 2+1 Dimensions
• Origin of the Relaxation Time in Dissipative Fluid Dynamics
• Constructing higher-order hydrodynamics: The third order
• Anomaly/Transport in an Ideal Weyl gas
• Triangle Anomalies, Thermodynamics, and Hydrodynamics
• Retarded Correlators in Kinetic Theory: Branch Cuts, Poles and Hydrodynamic Onset Transitions
• Second-order transport, quasinormal modes and zero-viscosity limit in the Gauss-Bonnet holographic fluid
• Emergent hydrodynamics in a strongly interacting dipolar spin ensemble
• Chiral conductivities and effective field theory
• Causality and dissipation in relativistic polarizeable fluids
• On the universal identity in second order hydrodynamics
• General equilibrium second-order hydrodynamic coefficients for free quantum fields
• Relativistic Spin Magnetohydrodynamics
• Non-dissipative hydrodynamics: Effective actions versus entropy current
• Aspects of hot Galilean field theory
• Shear viscosity in holography and effective theory of transport without translational symmetry
• Thermodynamical second-order hydrodynamic coefficients
• Hydrodynamic transport coefficients for the non-conformal quark-gluon plasma from holography
• Entropy current and equilibrium partition function in fluid dynamics
• Stochastic hydrodynamics and long time tails of an expanding conformal charged fluid
• Causality of fluid dynamics for high-energy nuclear collisions
• Causal three-point functions and nonlinear second-order hydrodynamic coefficients in AdS/CFT
• Second-Order Hydrodynamics and Universality in Non-Conformal Holographic Fluids
• Holographic perfect fluidity, Cotton energy-momentum duality and transport properties
• Second order hydrodynamic coefficients from 3-point stress tensor correlators via AdS/CFT
• Thermodynamics of strong-interaction matter from Lattice QCD
• Classical and Quantum Computing of Shear Viscosity for $2+1D$ SU(2) Gauge Theory
• Kubo formulae for the shear and bulk viscosity relaxation times and the scalar field theory shear ${\tau }_{\pi }$ calculation
• Shear viscosity from thermal fluctuations in relativistic conformal fluid dynamics
• Kubo formulas for thermodynamic transport coefficients
• Fluid/gravity correspondence: Second order transport coefficients in compactified D4-branes
• Thermodynamic equilibrium of massless fermions with vorticity, chirality and electromagnetic field
• Anti de Sitter black holes and branes in dynamical Chern-Simons gravity: perturbations, stability and the hydrodynamic modes
• Dynamics of the electric current in an ideal electron gas: a sound mode inside the quasi-particles
• Relativistic Dissipative Fluid Dynamics from Non-Equilibrium Statistical Operator
• Conformal symmetry and non-relativistic second order fluid dynamics
• Einstein's Equations in Matter
• Temperature in relativistic fluids
• Nonlinear Fluctuations in Relativistic Causal Fluids
• Transport coefficients in AdS/CFT and quantum gravity corrections due to a functional measure
• Hydrodynamic fluctuations from a weakly coupled scalar field
• Equilibrium thermodynamic susceptibilities for a dense degenerate Dirac field
• Determining Transport Coefficients for a Microscopic Simulation of a Hadron Gas
• Homogeneous Relaxation at Strong Coupling from Gravity
• Second order causal hydrodynamics in Eckart frame: using gradient expansion scheme
• Conserved and non-conserved Noether currents from the quantum effective action
• Superfluid Kubo Formulas from Partition Function
• Reconstruction of spectra and an algorithm based on the theorems of Darboux and Puiseux
• Phenomenological Relativistic Second-Order Hydrodynamics for Multiflavor Fluids
• Gravitational duality, topologically massive gravity and holographic fluids
• On Classical Equivalence Between Noncritical and Einstein Gravity : The AdS/CFT Perspectives
• Shear viscosity in QCD and why it's hard to calculate
• Microscopic Study of Vorticities in Relativistic Chiral Fermions
• The shear and bulk relaxation times from the general correlation functions
• Transport and response coefficients in second-order dissipative relativistic hydrodynamics with quantum corrections: probing the quark-gluon plasma
• Relativistic second-order dissipative hydrodynamics from Zubarev's non-equilibrium statistical operator
• Nonlinear Dynamics of Tensor Modes in Conformal Real Relativistic Fluids