Nonlinear Fluctuations in Relativistic Causal Fluids

Abstract

In the Second Order Theories (SOT) of real relativistic fluids, the non-ideal properties of the flows are described by a new set of dynamical tensor variables. In this work we explore the non-linear dynamics of those variables in a conformal fluid. Among all possible SOTs, we choose to work with the Divergence Type Theories (DTT) formalism, which ensures that the second law of thermodynamics is fulfilled non-perturbatively. The tensor modes include two divergence-free modes which have no analog in theories based on covariant generalizations of the Navier-Stokes equation, and that are particularly relevant because they couple linearly to a gravitational field. To study the dynamics of this irreducible tensor sector, we observe that in causal theories such as DTTs, thermal fluctuations induce a stochastic stirring force, which excites the tensor modes while preserving energy momentum conservation. From fluctuation-dissipation considerations it follows that the random force is Gaussian with a white spectrum. The irreducible tensor modes in turn excite vector modes, which back-react on the tensor sector, thus producing a consistent non-linear, second order description of the divergence-free tensor dynamics. Using the Martin-Siggia-Rose (MSR) formalism plus the Two-Particle Irreducible Effective Action (2PIEA) formalism, we obtain the one-loop corrected equations for the relevant two-point correlation functions of the model: the retarded propagator and the Hadamard function. The overall result of the self-consistent dynamics of the irreducible tensor modes at this order is a depletion of the spectrum in the UV sector, which suggests that tensor modes could sustain an inverse entropy cascade.

arXiv comment41 pages, no figures. References updated. This arXiv file replaces former arXiv:1812.01003 because we addressed the studied problem with a more consistent and powerful formalism. In view of these major changes, the former arXiv file was withdrawn and replaced with the present manuscript. Published in JHEP

References in corpus (49)

• Shear viscosity of strongly coupled N=4 supersymmetric Yang-Mills plasma
• Cosmological Backgrounds of Gravitational Waves
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Hydrodynamic Modeling of Heavy-Ion Collisions
• Derivation of transient relativistic fluid dynamics from the Boltzmann equation
• Lectures on hydrodynamic fluctuations in relativistic theories
• Relativistic Fluid Dynamics: Physics for Many Different Scales
• Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation
• Causal Theories of Dissipative Relativistic Fluid Dynamics for Nuclear Collisions
• First-order relativistic hydrodynamics is stable
• Rotating Stars in Relativity
• Relativistic Theory of Hydrodynamic Fluctuations with Applications to Heavy Ion Collisions
• Matching the Nonequilibrium Initial Stage of Heavy Ion Collisions to Hydrodynamics with QCD Kinetic Theory
• Effective kinetic description of event-by-event pre-equilibrium dynamics in high-energy heavy-ion collisions
• Entropy Current in Conformal Hydrodynamics
• The stickiness of sound: An absolute lower limit on viscosity and the breakdown of second order relativistic hydrodynamics
• The anisotropic non-equilibrium hydrodynamic attractor
• Viscosity and dissipative hydrodynamics from effective field theory
• Hydrodynamic Fluctuations, Long-time Tails, and Supersymmetry
• Anisotropic Hydrodynamics: Three lectures
• A kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion
• Causality of the Einstein-Israel-Stewart Theory with Bulk Viscosity
• Dissipative hydrodynamics in superspace
• Gravitational Waves produced by Compressible MHD Turbulence from Cosmological Phase Transitions
• Relativistic Hydrodynamic Attractors with Broken Symmetries: Non-Conformal and Non-Homogeneous
• Kubo Formulae for Second-Order Hydrodynamic Coefficients
• Towards an effective action for relativistic dissipative hydrodynamics
• First order and stable relativistic dissipative hydrodynamics
• On thermal fluctuations and the generating functional in relativistic hydrodynamics
• Relativistic fluctuating hydrodynamics
• Divergence-type nonlinear conformal hydrodynamics
• Effective Action for Relativistic Hydrodynamics: Fluctuations, Dissipation, and Entropy Inflow
• Exact hydrodynamic attractor of an ultrarelativistic gas of hard spheres
• Divergence-type 2+1 dissipative hydrodynamics applied to heavy-ion collisions
• Cosmological Magnetic Fields from Gauge-Mediated Supersymmetry-Breaking Models
• Stochastic hydrodynamics and long time tails of an expanding conformal charged fluid
• Dissipation, noise and vacuum decay in quantum field theory
• Self consistent estimates of magnetic fields from reheating
• A hyperbolic theory of relativistic conformal dissipative fluids
• Shear viscosity from thermal fluctuations in relativistic conformal fluid dynamics
• Why hyperbolic theories of dissipation cannot be ignored: Comments on a paper by Kostadt and Liu
• Noise induced transitions in semiclassical cosmology
• A hydrodynamic approach to boost invariant free streaming
• Equivalence between first-order causal and stable hydrodynamics and Israel-Stewart theory for boost-invariant systems with a constant relaxation time
• Renormalization group and nonequilibrium action in stochastic field theory
• Primordial gravitational waves amplification from causal fluids
• Causal hydrodynamic fluctuations in non-static and inhomogeneous backgrounds
• A Hydrodynamic Approach to the Study of Anisotropic Instabilities in Dissipative Relativistic Plasmas
• Generic instabilities in the relativistic Chapman-Enskog heat conduction law

Cited by in corpus (8)

• Fluctuating relativistic dissipative hydrodynamics as a gauge theory
• Fully developed relativistic turbulence
• Relativistic viscous effects on the primordial gravitational waves spectrum
• Linearized dispersion relations in viscous relativistic hydrodynamics
• Modelling stochastic fluctuations in relativistic kinetic theory
• Field Theory Approaches to Relativistic Hydrodynamics
• Steady asymptotic equilibria in conformal relativistic fluids
• Cumulants of conserved charges in hydrodynamic simulations