Lectures on hydrodynamic fluctuations in relativistic theories

Abstract

These are pedagogical lecture notes on hydrodynamic fluctuations in normal relativistic fluids. The lectures discuss correlation functions of conserved densities in thermal equilibrium, interactions of the hydrodynamic modes, an effective action for viscous fluids, and the breakdown of the derivative expansion in hydrodynamics.

55 pages. Based on lectures given at the Seattle INT Summer School on Applications of String Theory in July 2011

References in corpus (10)

• The electronic properties of graphene
• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Lectures on Holographic Superfluidity and Superconductivity
• Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes
• Gravitational Anomaly and Transport
• Quantum Criticality
• Towards hydrodynamics without an entropy current
• The stickiness of sound: An absolute lower limit on viscosity and the breakdown of second order relativistic hydrodynamics
• Collective cyclotron motion of the relativistic plasma in graphene
• Kubo Formulae for Second-Order Hydrodynamic Coefficients

Cited by in corpus (305)

• Hydrodynamics of electrons in graphene
• Heavy Ion Collisions: Achievements and Challenges
• First-order relativistic hydrodynamics is stable
• Causality and existence of solutions of relativistic viscous fluid dynamics with gravity
• Holographic duality and the resistivity of strange metals
• Momentum relaxation in holographic massive gravity
• Nonlinear causality of general first-order relativistic viscous hydrodynamics
• Fate of spin polarization in a relativistic fluid: An entropy-current analysis
• Dense Nuclear Matter Equation of State from Heavy-Ion Collisions
• Effective kinetic description of event-by-event pre-equilibrium dynamics in high-energy heavy-ion collisions
• Generalized global symmetries and dissipative magnetohydrodynamics
• Black hole scrambling from hydrodynamics
• Viscosity and dissipative hydrodynamics from effective field theory
• The complex life of hydrodynamic modes
• Relativistic magnetohydrodynamics
• Local thermodynamical equilibrium and the beta frame for a quantum relativistic fluid
• On the convergence of the gradient expansion in hydrodynamics
• Covariant Galilean versus Carrollian hydrodynamics from relativistic fluids
• Memory matrix theory of magnetotransport in strange metals
• Holography and hydrodynamics with weakly broken symmetries
• A kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion
• Gapped momentum states
• Diffusive dynamics of critical fluctuations near the QCD critical point
• Constructing higher-order hydrodynamics: The third order
• The dynamics of quantum criticality via Quantum Monte Carlo and holography
• Do nuclear collisions create a locally equilibrated quark-gluon plasma?
• Cavity Spintronics: An Early Review of Recent Progress in the Study of Magnon-Photon Level Repulsion
• Retarded Correlators in Kinetic Theory: Branch Cuts, Poles and Hydrodynamic Onset Transitions
• Horizon constraints on holographic Green's functions
• Theory of diffusive fluctuations
• Holographic Axion Model: a simple gravitational tool for quantum matter
• Thermal transport, geometry, and anomalies
• Reaction rates and transport in neutron stars
• Linear response theory of relativistic hydrodynamics with spin
• Causality and dissipation in relativistic polarizeable fluids
• On thermal fluctuations and the generating functional in relativistic hydrodynamics
• Generalised global symmetries in states with dynamical defects: the case of the transverse sound in field theory and holography
• Hydrodynamic transport in strongly coupled disordered quantum field theories
• Generalised global symmetries in holography: magnetohydrodynamic waves in a strongly interacting plasma
• Complexified quasinormal modes and the pole-skipping in a holographic system at finite chemical potential
• The quasi-normal modes of quantum criticality
• Two-dimensional fluids and their holographic duals
• Superfluids as Higher-form Anomalies
• Pinning of longitudinal phonons in holographic spontaneous helices
• Hydrodynamic attractors in heavy ion collisions: a review
• Shear viscosity in holography and effective theory of transport without translational symmetry
• Heavy Operators and Hydrodynamic Tails
• The Large D Limit of Einstein's Equations
• Non-Boost Invariant Fluid Dynamics
• Bounds on transport from univalence and pole-skipping
• Universal relaxation in a holographic metallic density wave phase
• Bulk viscosity from hydrodynamic fluctuations with relativistic hydro-kinetic theory
• Quasinormal modes in charged fluids at complex momentum
• Theories of Relativistic Dissipative Fluid Dynamics
• Colloquium: Hydrodynamics and holography of charge density wave phases
• New developments in relativistic magnetohydrodynamics
• Universal linear and nonlinear electrodynamics of the Dirac fluid
• Hydrodynamic fluctuations and the minimum shear viscosity of the dilute Fermi gas at unitarity
• Pseudospectra of Holographic Quasinormal Modes
• Stochastic hydrodynamics and long time tails of an expanding conformal charged fluid
• A numerical exploration of first-order relativistic hydrodynamics
• Hydrodynamic fluctuations and dissipation in an integrated dynamical model
• Transient Relativistic Fluid Dynamics in a General Hydrodynamic Frame
• Slow relaxation and diffusion in holographic quantum critical phases
• Losing Forward Momentum Holographically
• Gauges in Three-Dimensional Gravity and Holographic Fluids
• Hydrodynamic gradient expansion in linear response theory
• Pole-skipping and Rarita-Schwinger fields
• Effective theory of two-dimensional chiral superfluids: gauge duality and Newton-Cartan formulation
• Dispersing quasinormal modes in 2+1 dimensional conformal field theories
• Modeling the diffusive dynamics of critical fluctuations near the QCD critical point
• Universal Bounds on Transport in Holographic Systems with Broken Translations
• Critical behavior of the bulk viscosity in QCD
• Fluctuation bounds on charge and heat diffusion
• Hydrodynamic tails and a fluctuation bound on the bulk viscosity
• Second-Order Hydrodynamics and Universality in Non-Conformal Holographic Fluids
• Modeling general-relativistic plasmas with collisionless moments and dissipative two-fluid magnetohydrodynamics
• Pseudo-spontaneous $U(1)$ Symmetry Breaking in Hydrodynamics and Holography
• Fluctuating relativistic dissipative hydrodynamics as a gauge theory
• Sound waves and resonances in electron-hole plasma
• Spontaneously Broken Boosts in CFTs
• Gravity waves generated by sounds from big bang phase transitions
• Unified Extended Irreversible Thermodynamics and the stability of relativistic theories for dissipation
• Conservative finite volume scheme for first-order viscous relativistic hydrodynamics
• Hydrodynamic Modes of Homogeneous and Isotropic Fluids
• Low frequency propagating shear waves in holographic liquids
• Holography and magnetohydrodynamics with dynamical gauge fields
• Hydrodynamic diffusion and its breakdown near AdS${}_2$ quantum critical points
• Progress and Challenges in Small Systems
• Causal first-order hydrodynamics from kinetic theory and holography
• Maxwell interpolation and close similarities between liquids and holographic models
• A Holographic Superfluid Symphony
• Classical and Quantum Computing of Shear Viscosity for $2+1D$ SU(2) Gauge Theory
• Newton-Cartan Submanifolds and Fluid Membranes
• Symmetric-hyperbolic quasi-hydrodynamics
• Effective field theory of stochastic diffusion from gravity
• Kubo formulae for the shear and bulk viscosity relaxation times and the scalar field theory shear ${\tau }_{\pi }$ calculation
• A Lagrangian formulation of relativistic Israel-Stewart hydrodynamics
• First order non-Lorentzian fluids, entropy production and linear instabilities
• Perturbative approaches in relativistic kinetic theory and the emergence of first-order hydrodynamics
• Impact of irrelevant deformations on thermodynamics and transport in holographic quantum critical states
• Dynamical exploring the QCD matter at finite temperatures and densities-a short review
• Implications of hydrodynamic fluctuations on the minimum shear viscosity of the dilute Fermi gas at unitarity
• On the universality of AdS${}_2$ diffusion bounds and the breakdown of linearized hydrodynamics
• Kubo formulas for thermodynamic transport coefficients
• Fluid dynamic propagation of initial baryon number perturbations on a Bjorken flow background
• Quasi-normal modes of dyonic black holes and magneto-hydrodynamics
• Holographic Plasmon Relaxation with and without Broken Translations
• Shear viscosity at the Ising-nematic quantum critical point in two dimensional metals
• Relativistic hydrodynamics with spin in the presence of electromagnetic fields
• 2-group global symmetries, hydrodynamics and holography
• Hydrodynamics without boosts
• Holographic Plasmons
• Relativistic Liquids: GENERIC or EIT?
• Nonlinear Oscillatory Shear Tests in Viscoelastic Holography
• Holographic Interpretation of Acoustic Black Holes
• Bulk viscosity of strongly interacting matter in the relaxation time approximation
• Dissipative hydrodynamics with higher-form symmetry
• Field Theory of Dissipative Systems with Gapped Momentum States
• Hydrodynamic dispersion relations at finite coupling
• Hydrodynamic flows of non-Fermi liquids: magnetotransport and bilayer drag
• Effective Field Theory of Force-Free Electrodynamics
• Approximate higher-form symmetries, topological defects, and dynamical phase transitions
• All order effective action for charge diffusion from Schwinger-Keldysh holography
• An effective description of momentum diffusion in a charged plasma from holography
• Second law of thermodynamics for relativistic fluids formulated with relative entropy
• Hydrodynamics of charged two-dimensional Dirac systems I: thermo-electric transport
• U(1) quasi-hydrodynamics: Schwinger-Keldysh effective field theory and holography
• Effective field theory for non-relativistic hydrodynamics
• Relativistic Bulk Rheology: From Neutron Star Mergers to Viscous Cosmology
• Black Brane Solution in Rastall AdS Massive Gravity and Viscosity Bound
• The Hydrohedron: Bootstrapping Relativistic Hydrodynamics
• Effective holographic models for QCD: Thermodynamics and viscosity coefficients
• Shear flows in far-from-equilibrium strongly coupled fluids
• Conformal Bjorken flow in the general frame and its attractor: Similarities and discrepancies with the Müller-Israel-Stewart formalism
• Breakdown of hydrodynamics from holographic pole collision
• Transport coefficients of quasi-particle models within a new relaxation time approximation of the Boltzmann equation
• Dynamics of the electric current in an ideal electron gas: a sound mode inside the quasi-particles
• Shear Viscosity at Infinite Coupling: A Field Theory Calculation
• T-linear resistivity, optical conductivity and Planckian transport for a holographic local quantum critical metal in a periodic potential
• Universality of anomalous conductivities in theories with higher-derivative holographic duals
• Strongly coupled electron fluids in the Poiseuille regime
• Hydrodynamic effective field theory and the analyticity of hydrostatic correlators
• Non-Gaussian diffusive fluctuations in Dirac fluids
• Causal and stable first-order chiral hydrodynamics
• Einstein-Yang-Mills AdS Black Brane Solution in Massive Gravity and Viscosity Bound
• Metal-Insulator Transition with Charge Fractionalization
• Hydrodynamic Waves in an Anomalous Charged Fluid
• Hydrodynamic effective field theories with discrete rotational symmetry
• Exploring the Redshift-Space Peculiar Velocity Field and its Power Spectrum
• Fluctuating Relativistic hydrodynamics from Crooks theorem
• Hydrodynamic charge and heat transport on inhomogeneous curved spaces
• Thermal chiral vortical and magnetic waves: new excitation modes in chiral fluids
• Anharmonic theory of superconductivity and its applications to emerging quantum materials
• Ginzburg-Landau effective action for a fluctuating holographic superconductor
• Thermalization, Viscosity and the Averaged Null Energy Condition
• Hydrodynamic Gradient Expansion Diverges beyond Bjorken Flow
• Similarity between the kinematic viscosity of quark-gluon plasma and liquids at the viscosity minimum
• From quasinormal modes of rotating black strings to hydrodynamics of a moving CFT plasma
• Hydrodynamics of plastic deformations in electronic crystals
• Cross effects in spin hydrodynamics: A revisit Entropy analysis and statistical operator
• Multiplicative noise and the diffusion of conserved densities
• Holography of Linear Dilaton Spacetimes from the Bottom Up
• Gapless non-hydrodynamic modes in relativistic kinetic theory
• Structure formation during phase transitions in strongly interacting matter
• Revisiting relativistic magnetohydrodynamics from quantum electrodynamics
• On the hydrodynamics of (2 + 1)-dimensional strongly coupled relativistic theories in an external magnetic field
• Collisional corrections to spin polarization from quantum kinetic theory using Chapman-Enskog expansion
• Linear response hydrodynamics of a relativistic dissipative fluid with spin
• Quasinormal modes of a semi-holographic black brane and thermalization
• Gibbons-Hawking-York boundary terms and the generalized geometrical trinity of gravity
• Non-vanishing normal density in cold holographic superfluids
• Aspects of univalence in holographic axion models
• Kinetic theory of electronic transport in random magnetic fields
• Critical behaviour of hydrodynamic series
• Collective Excitations in Hot QCD Plasma
• Non-dissipative electrically driven fluids
• Nonlinear Fluctuations in Relativistic Causal Fluids
• Magneto-vortical Effect in Strong Magnetic Field
• Zero sound and higher-form symmetries in compressible holographic phases
• Holographic phonons by gauge-axion coupling
• Holographic DC Conductivity for Backreacted NLED in Massive Gravity
• On pole-skipping with gauge-invariant variables in holographic axion theories
• Microcausality without Lorentz invariance
• Magneto-Transport in a Chiral Fluid from Kinetic Theory
• Emergent Hydrodynamic Mode on SU(2) Plaquette Chains and Quantum Simulation
• The Loschmidt Spectral Form Factor
• Equilibrium thermodynamic susceptibilities for a dense degenerate Dirac field
• Relaxed hydrodynamic theory of electrically driven non-equilibrium steady states
• AdS Black Brane Solution Surrounded by Quintessence in Massive Gravity and KSS Bound
• Relaxation terms for anomalous hydrodynamic transport in Weyl semimetals from kinetic theory
• A Bound on Thermalization from Diffusive Fluctuations
• Hydrodynamic Excitations from Chiral Kinetic Theory and the Hydrodynamic Frames
• Consistent inclusion of fluctuations in first-order causal and stable relativistic hydrodynamics
• Restoring time-reversal covariance in relaxed hydrodynamics
• Does a Cloud of Strings Affect Shear Viscosity Bound?
• Artificial electric field and electron hydrodynamics
• Anomalous transport model with axial magnetic fields
• Entanglement of scales as a possible mechanism for decoherence and thermalization in relativistic heavy ion collisions
• Second order equilibrium transport in strongly coupled $\mathcal{N}=4$ supersymmetric $SU(N_c)$ Yang-Mills plasma via holography
• A holographic bottom-up description of light nuclide spectroscopy and stability
• Anomalous Hydrodynamics in One Dimensional Electronic Fluid
• Non-abelian Einstein-Born-Infeld AdS black brane and color DC conductivity
• Effective description of non-equilibrium currents in cold magnetized plasma
• Incoherent hydrodynamics of density waves in magnetic fields
• Positive magnetoresistance induced by hydrodynamic fluctuations in chiral media
• Long-time tails in the SYK chain from the effective field theory with a large number of derivatives
• Reconstruction of spectra and an algorithm based on the theorems of Darboux and Puiseux
• Magneto-vortical effect in strongly coupled plasma
• Charge density response and fake plasmons in holographic models with strong translation symmetry breaking
• Leading order magnetic field dependence of conductivities in anomalous hydrodynamics
• Anomalous Hall instability in the Chern-Simons magnetohydrodynamics
• Hydrodynamics of quantum spin liquids
• Transport signatures of plasmon fluctuations in electron hydrodynamics
• Dipole excitation of collective modes in viscous two-dimensional electron systems
• Finite temperature sum rules in the vector channel at finite momentum
• Radiation in Fluid/Gravity and the Flat Limit
• Chiral Anomalous Magnetohydrodynamics in action: effective field theory and holography
• Field Theory Approaches to Relativistic Hydrodynamics
• Characteristic momentum of Hydro+ and a bound on the speed of sound near the QCD critical point
• Spontaneous Symmetry Breaking, Spectral Statistics, and the Ramp
• Conductivities in an anisotropic medium
• Electron Currents from Gradual Heating in Tilted Dirac Cone Materials
• Ringdown in the SYK model
• Holographic Dissipation from the Symplectic Current
• Analogue Stochastic Gravity in Strongly-Interacting Bose-Einstein Condensates
• Correspondence between momentum dependent relaxation time and field redefinition of relativistic hydrodynamic theory
• The effect of three matters on KSS bound
• Collective modes of gluons in an anisotropic thermo-magnetic medium
• Topological modes in relativistic hydrodynamics
• Analytic structure of diffusive correlation functions
• Duality and four-dimensional black holes: gravitational waves, algebraically special solutions, pole skipping, and the spectral duality relation in holographic thermal CFTs
• Strange metal crossover in the doped holographic superconductor
• Hydrodynamics of a relativistic charged fluid in the presence of a periodically modulated chemical potential
• Numerical simulations of divergence-type theories for conformal dissipative fluids
• Microscopic model for relativistic hydrodynamics of ideal plasmas
• Hydrodynamic fluctuations and long-time tails in a fluid on an anisotropic background
• Hydrodynamization in hybrid Bjorken flow attractors
• Mapping GENERIC hydrodynamics into Carter's multifluid theory
• Holographic Aspects of Non-minimal $R{F}_{\mu \alpha }^{(a)}{F}^{(a)\mu \alpha }$ Black Brane
• Beyond Drude transport in hydrodynamic metals
• Thermoelectric transport properties of gapless pinned charge density waves
• Coulomb drag between two strange metals
• Higher-form symmetry and chiral transport in real-time Abelian lattice gauge theory
• The shear viscosity of interacting graphene
• Dissipative electrically driven fluids
• Linear responses of D0-branes via gauge/gravity correspondence
• Kinetic evolution and correlation of fluctuations in an expanding quark gluon plasma
• Using the non-hydrodynamic mode to study the onset of hydrodynamic behavior in ultraperipheral symmetric nuclear collisions
• Simple holographic dual of the Maxwell-Cattaneo model & the fate of KMS symmetry for non-hydrodynamic modes
• Shear viscosity over entropy density ratio with extended quasi-particles
• Drude weight and Mazur-Suzuki bounds in holography
• Effective field theory for hydrodynamics without boosts
• Strongly interacting matter in extreme magnetic fields
• Hydrodynamics in the Carrollian regime
• Role of slow, out-of-equilibrium modes on the dynamic structure factor near the QCD critical point
• Relativistic hydrodynamics with the parity anomaly
• Kinetics of hydrodynamic pions in chiral perturbation theory
• Correlation functions of the Bjorken flow in the holographic Schwinger-Keldysh approach
• Holographic Aspects of Non-minimal $R_{\mu \alpha \nu \beta }{F}^{(a)\mu \alpha }{F}^{(a)\nu \beta }$ AdS Black Brane
• Phase Transitions and Conductivties of Floquet Fluids
• Hydrodynamic fluctuations and topological susceptibility in chiral magnetohydrodynamics
• One-dimensional Carrollian fluids I: Carroll-Galilei duality
• Brane Viscous Cosmology in the Plasma Era
• Stable non-linear evolution in regularised higher derivative effective field theories
• Constraint evolution in first-order viscous relativistic fluids
• First-Order Viscous Relativistic Hydrodynamics on the Two-Sphere
• Transverse Shear Viscosity to Entropy Density for the General Anisotropic Black Brane in Horava-Lifshitz Gravity
• Semi-Classical Spin Hydrodynamics in Flat and Curved Spacetime: Covariance, Linear Waves, and Bjorken Background
• Hysteresis in $\eta /s$ for QFTs dual to spherical black holes
• Causal and Stable Superfluid Hydrodynamics
• Dynamic and Thermodynamic Stability of Charged Perfect Fluid Stars
• AdS black brane coupled to non-abelian logarithmic gauge theory and color DC conductivity
• The Effect of Bulk Dimension in the presence of String Cloud on Viscosity Bound
• Relativistic Fluids, Hydrodynamic Frames and their Galilean versus Carrollian Avatars
• Hydrodynamics of particle-hole symmetric systems: a quantum Monte Carlo study
• Geometrisation of Ohm's reciprocity relation in a holographic plasma
• Non-Abelian Exponential Yang-Mills AdS Black Brane and Transport Coefficients
• Universal thermalization dynamics in (1+1)d QFTs
• Gravitational susceptibility of QGP
• Hydrodynamics of Arcsin AdS Black Brane
• Linear response in a charged gas in curved spacetime and covariant heat equation
• Correspondences between scalar field and fluid fluctuations in curved spacetime
• Cosmology from Strong Interactions
• Chiral transport in curved spacetime via holography
• Dissipative Charged Fluid in a Magnetic Field
• Emergent Viscous Hydrodynamics From a Single Quantum Particle
• The Hamiltonian mechanics of exotic particles
• Soret and Dufour effects in hot and dense QCD matter
• More on Topological Hydrodynamic Modes
• Radial Oscillations of Viscous Stars
• Nonlinear Yang-Mills AdS black brane and DC conductivity
• Conductivity and Shear Viscosity of $arcsin$-Yang-Mills AdS Black Brane
• Thermalization and Hydrodynamics of Two-Dimensional Quantum Field Theories
• Holographic timelike superconductor
• Dynamics of a nonminimally coupled scalar field in asymptotically $Ad{S}_4$ spacetime
• Counterflow and coflow instabilities in miscible binary superfluids
• Relativistic Langevin Equation derived from a particle-bath Lagrangian
• Constitutive relations of a chiral hadronic fluid
• Anomalous transport in second order hydrodynamics
• Theoretical aspects of relativistic spin hydrodynamics coupled with electromagnetic fields
• Holography in Quark-Gluon Plasma and Neutron Stars
• A general relativistic kinetic theory approach to linear transport in generic hydrodynamic frame
• Nonperfect Carrollian Fluids Through Holography
• Holographic Aspects of Non-minimal $R^3{F}^2$ Black Brane in an EFT Framework