Dissipative Dynamics of Highly Anisotropic Systems

Abstract

In this paper we present a method to improve the description of 0+1 dimensional boost invariant dissipative dynamics in the presence of large momentum-space anisotropies. We do this by reorganizing the canonical hydrodynamic expansion of the distribution function around a momentum-space anisotropic ansatz rather than an isotropic equilibrium one. At leading order the result obtained is two coupled ordinary differential equations for the momentum-space anisotropy and typical momentum of the degrees of freedom. We show that this framework can reproduce both the ideal hydrodynamic and free streaming limits. Additionally, we demonstrate that when linearized the differential equations reduce to 2nd order Israel-Stewart viscous hydrodynamics. Finally, we make quantitative comparisons of the evolution of the pressure anisotropy within our approach and 2nd order viscous hydrodynamics in both the strong and weak coupling limits.

17 pages, 5 figures; Published version

References in corpus (27)

• Radial and elliptic flow at RHIC: further predictions
• Conformal Relativistic Viscous Hydrodynamics: Applications to RHIC results at sqrt(s_NN) = 200 GeV
• Collective flow and two-pion correlations from a relativistic hydrodynamic model with early chemical freeze out
• Collective Modes of an Anisotropic Quark-Gluon Plasma
• Simulating elliptic flow with viscous hydrodynamics
• Causal Theories of Dissipative Relativistic Fluid Dynamics for Nuclear Collisions
• Highly-anisotropic and strongly-dissipative hydrodynamics for early stages of relativistic heavy-ion collisions
• Second Order Dissipative Fluid Dynamics for Ultra-Relativistic Nuclear Collisions
• Collective modes of an Anisotropic Quark-Gluon Plasma II
• Dissipative relativistic fluid dynamics: a new way to derive the equations of motion from kinetic theory
• Recent results in relativistic heavy ion collisions: from ``a new state of matter'' to "the perfect fluid"
• Third-order relativistic dissipative hydrodynamics
• The heavy-quark potential in an anisotropic plasma
• Pre-equilibrium dilepton production from an anisotropic quark-gluon plasma
• The imaginary part of the static gluon propagator in an anisotropic (viscous) QCD plasma
• Quarkonium states in an anisotropic QCD plasma
• Photon production from an anisotropic quark-gluon plasma
• Anomalous Transport Processes in Anisotropically Expanding Quark-Gluon Plasmas
• Early collective expansion: Relativistic hydrodynamics and the transport properties of QCD matter
• Divergence-type nonlinear conformal hydrodynamics
• Divergence-type 2+1 dissipative hydrodynamics applied to heavy-ion collisions
• Constraining relativistic viscous hydrodynamical evolution
• Measuring Quark-Gluon-Plasma Thermalization Time with Dileptons
• Suppression of forward dilepton production from an anisotropic quark-gluon plasma
• Matching pre-equilibrium dynamics and viscous hydrodynamics
• A relativistic dissipative hydrodynamic description for systems including particle number changing processes
• Dynamics of anisotropic plasma at the early stages of relativistic heavy-ion collisions

Cited by in corpus (226)

• Collective flow and viscosity in relativistic heavy-ion collisions
• Hydrodynamic Modeling of Heavy-Ion Collisions
• Heavy-flavour and quarkonium production in the LHC era: from proton-proton to heavy-ion collisions
• New theories of relativistic hydrodynamics in the LHC era
• Properties of hot and dense matter from relativistic heavy ion collisions
• Highly-anisotropic and strongly-dissipative hydrodynamics for early stages of relativistic heavy-ion collisions
• Causality and existence of solutions of relativistic viscous fluid dynamics with gravity
• Violation of the Holographic Viscosity Bound in a Strongly Coupled Anisotropic Plasma
• Thermodynamics and Instabilities of a Strongly Coupled Anisotropic Plasma
• Relativistic hydrodynamics for spin-polarized fluids
• Nonlinear causality of general first-order relativistic viscous hydrodynamics
• The anisotropic N=4 super Yang-Mills plasma and its instabilities
• Heavy ions and string theory
• Flow and interferometry in 3+1 dimensional viscous hydrodynamics
• Thermal Bottomonium Suppression at RHIC and LHC
• Testing viscous and anisotropic hydrodynamics in an exactly solvable case
• Boost-Invariant (2+1)-dimensional Anisotropic Hydrodynamics
• Hydrodynamic Approaches in Relativistic Heavy Ion Reactions
• The anisotropic non-equilibrium hydrodynamic attractor
• Anisotropic Hydrodynamics for Rapidly Expanding Systems
• Second-order (2+1)-dimensional anisotropic hydrodynamics
• A new exact solution of the relativistic Boltzmann equation and its hydrodynamic limit
• Highly-anisotropic hydrodynamics in 3+1 space-time dimensions
• Quarkonia in the Quark Gluon Plasma
• Momentum transport in strongly coupled anisotropic plasmas in the presence of strong magnetic fields
• Probing strongly coupled anisotropic plasma
• Thermal Upsilon(1s) and chi_b1 suppression in sqrt(s_NN)=2.76 TeV Pb-Pb collisions at the LHC
• Transport coefficients for bulk viscous evolution in the relaxation time approximation
• Relativistic hydrodynamics in heavy-ion collisions: general aspects and recent developments
• Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation
• Evolution of transverse flow and effective temperatures in the parton phase from a multi-phase transport model
• Dissipative Spin Dynamics in Relativistic Matter
• Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow
• Non-boost-invariant anisotropic dynamics
• Relativistic anisotropic hydrodynamics
• Quarkonium states in a complex-valued potential
• The non-equilibrium attractor for kinetic theory in relaxation time approximation
• On the relative importance of second-order terms in relativistic dissipative fluid dynamics
• Instabilities of an anisotropically expanding non-Abelian plasma: 3D+3V discretized hard-loop simulations
• Exact solution of the (0+1)-dimensional Boltzmann equation for a massive gas
• Bottomonium suppression in an open quantum system using the quantum trajectories method
• Bottomonia suppression in 2.76 TeV Pb-Pb collisions
• Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation
• 3+1d quasiparticle anisotropic hydrodynamics for ultrarelativistic heavy-ion collisions
• Bulk viscous evolution within anisotropic hydrodynamics
• Drag force in a strongly coupled anisotropic plasma
• The smallest fluid on earth
• Bottomonium suppression using a lattice QCD vetted potential
• Projection method and new formulation of leading-order anisotropic hydrodynamics
• Highly-anisotropic and strongly-dissipative hydrodynamics with transverse expansion
• The Glasma, Photons and the Implications of Anisotropy
• (3+1)-dimensional dissipative relativistic fluid dynamics at non-zero net baryon density
• Predictions for bottomonia suppression in 5.023 TeV Pb-Pb collisions
• How does relativistic kinetic theory remember about initial conditions?
• Non-equilibrium attractor in high-temperature QCD plasmas
• Shear-bulk coupling in nonconformal hydrodynamics
• Hydrodynamics of simply spinning black holes & hydrodynamics for spinning quantum fluids
• The Present and Future of QCD
• Exact solutions and attractors of higher-order viscous fluid dynamics for Bjorken flow
• Fluid Dynamics and Viscosity in Strongly Correlated Fluids
• Relativistic third-order viscous corrections to the entropy four-current from kinetic theory
• Relativistic Fluid Dynamics In and Out of Equilibrium -- Ten Years of Progress in Theory and Numerical Simulations of Nuclear Collisions
• Non-Boost Invariant Fluid Dynamics
• Hydrodynamic transport coefficients for the non-conformal quark-gluon plasma from holography
• Closing the equations of motion of anisotropic fluid dynamics by a judicious choice of moment of the Boltzmann equation
• Anisotropic hydrodynamic modeling of 2.76 TeV Pb-Pb collisions
• Anisotropic hydrodynamics for conformal Gubser flow
• Relativistic quantum transport coefficients for second-order viscous hydrodynamics
• Hydrodynamic attractor and the fate of perturbative expansions in Gubser flow
• Emergence of hydrodynamical behavior in expanding quark-gluon plasmas
• Quasiparticle equation of state for anisotropic hydrodynamics
• Theories of Relativistic Dissipative Fluid Dynamics
• Anisotropic plasma at finite $U(1)$ chemical potential
• Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow
• Color Instabilities in the Quark-Gluon Plasma
• QCD Equation of State at Finite Chemical Potentials for Relativistic Nuclear Collisions
• Chiral hydrodynamics in strong external magnetic fields
• Rigorous bounds on transport from causality
• ${}^{16}{\mathrm{O}}^{16}\mathrm{O}$ at RHIC and the LHC comparing $\alpha$ clustering vs substructure
• Leading-order anisotropic hydrodynamics for central collisions
• Coupled kinetic equations for quarks and gluons in the relaxation time approximation
• Inhomogeneous holographic thermalization
• Leading-order anisotropic hydrodynamics for systems with massive particles
• Jet quenching in a strongly coupled anisotropic plasma
• Non-perturbative rheological behavior of a far-from-equilibrium expanding plasma
• Anisotropic matching principle for the hydrodynamics expansion
• Thermal photon production in a strongly coupled anisotropic plasma
• Gradient expansion for anisotropic hydrodynamics
• Quarkonium dissociation by anisotropy
• Hydrodynamization and non-equilibrium Green's functions in kinetic theory
• Hydrodynamics of anisotropic quark and gluon fluids
• Projection method for boost-invariant and cylindrically symmetric dissipative hydrodynamics
• On non-conformal kinetic theory and hydrodynamics for Bjorken flow
• Anisotropic fluid dynamics for Gubser flow
• Electromagnetic signatures of a strongly coupled anisotropic plasma
• Onset of hydrodynamics for a quark-gluon plasma from the evolution of moments of distribution functions
• Electrical Conductivity of an Anisotropic Quark Gluon Plasma : A Quasiparticle Approach
• Inhomogeneous Thermalization in Strongly Coupled Field Theories
• Transport coefficients of the Gribov-Zwanziger plasma
• Quasiparticle anisotropic hydrodynamics for central collisions
• Model-independent determination of the shear viscosity of a trapped unitary Fermi gas: Application to high temperature data
• Dissipative fluid dynamics for the dilute Fermi gas at unitarity: Anisotropic fluid dynamics
• Hydrodynamics from free-streaming to thermalization and back again
• Establishing the Range of Applicability of Hydrodynamics in High-Energy Collisions
• Macroscopic approximation to relativistic kinetic theory from a nonlinear closure
• Photon production from a non-equilibrium quark-gluon plasma
• Development of transverse flow at small and large opacities in conformal kinetic theory
• Bottomonium suppression and elliptic flow from real-time quantum evolution
• On higher order and anisotropic hydrodynamics for Bjorken and Gubser flows
• Dilepton production from the quark-gluon plasma using (3+1)-dimensional anisotropic dissipative hydrodynamics
• Determination of the density and temperature dependence of the shear viscosity of a unitary Fermi gas based on hydrodynamic flow
• Dissipative Magnetohydrodynamics for Non-Resistive Relativistic Plasmas
• Conservative finite volume scheme for first-order viscous relativistic hydrodynamics
• Anisotropic hydrodynamic modeling of 200 GeV Au-Au collisions
• Hydrodynamic Modes of Homogeneous and Isotropic Fluids
• Shear viscosity, cavitation and hydrodynamics at LHC
• Evolution to the Quark-Gluon Plasma
• Hydrodynamic flow in small systems, or: "How the heck is it possible that a system emitting only a dozen particles can be described by fluid dynamics?"
• Exact solution for the non-equilibrium attractor in number-conserving relaxation time approximation
• A flow paradigm in heavy-ion collisions
• Global flow structure and exact formal transseries of the Gubser flow in kinetic theory
• Anisotropic hydrodynamics with a scalar collisional kernel
• Anisotropic Hydrodynamics: Motivation and Methodology
• Photon production and elliptic flow from momentum-anisotropic quark-gluon plasma
• Bulk observables at 5.02 TeV using quasiparticle anisotropic hydrodynamics
• Anisotropic hydrodynamics for conformal Gubser flow
• Holographic quark-antiquark potential in hot, anisotropic Yang-Mills plasma
• Bottomonium suppression and elliptic flow using Heavy Quarkonium Quantum Dynamics
• (3+1)-dimensional anisotropic fluid dynamics with a lattice QCD equation of state
• Equivalence between first-order causal and stable hydrodynamics and Israel-Stewart theory for boost-invariant systems with a constant relaxation time
• A hydrodynamic approach to boost invariant free streaming
• Indications of early thermalization in relativistic heavy-ion collisions
• The static hard-loop gluon propagator to all orders in anisotropy
• Anisotropic hydrodynamics for mixture of quark and gluon fluids
• Bjorken flow attractors with transverse dynamics
• Testing different formulations of leading-order anisotropic hydrodynamics
• Initialization of hydrodynamics in relativistic heavy ion collisions with an energy-momentum transport model
• Modified equilibrium distributions for Cooper--Frye particlization
• Anisotropic fluid dynamical simulations of heavy-ion collisions
• Exact solutions of the Boltzmann equation and optimized hydrodynamic approaches for relativistic heavy-ion collisions
• Kinetic evolution of the glasma and thermalization in heavy ion collisions
• Effective dynamics of a nonabelian plasma out of equilibrium
• Opacity dependence of transverse flow, pre-equilibrium and applicability of hydrodynamics in heavy-ion collisions
• Brighter Branes, enhancement of photon production by strong magnetic fields in the gauge/gravity correspondence
• Universality Classes of Relativistic Fluid Dynamics: Foundations
• Chromoelectric oscillations in a dynamically evolving anisotropic background
• A simple model for rapidity fluctuations in the initial state of ultra-relativistic heavy-ion collisions
• Non-boost-invariant dissipative hydrodynamics
• Two-particle correlations in pseudorapidity in a hydrodynamic model
• Flow in heavy-ion collisions - Theory Perspective
• Basic phenomenology for relativistic heavy-ion collisions
• Quasiparticle anisotropic hydrodynamics
• Anisotropic-hydrodynamics approach to a quark-gluon fluid mixture
• Effects of initial-state dynamics on collective flow within a coupled transport and viscous hydrodynamic approach
• Light Probes in a Strongly Coupled Anisotropic Plasma
• (3+1)-dimensional framework for leading-order non conformal anisotropic hydrodynamics
• Wigner function formalism and the evolution of thermodynamic quantities in an expanding magnetized plasma
• Drag force in strongly coupled, anisotropic plasma at finite chemical potential
• Introduction to Hydrodynamics
• Correspondence between Israel-Stewart and first-order casual and stable hydrodynamics for the boost-invariant massive case with zero baryon density
• Far-from-equilibrium attractors for massive kinetic theory in the relaxation time approximation
• Drag and Diffusion of Heavy Quarks in a hot and anisotropic QCD medium
• Quark self-energy in an ellipsoidally anisotropic quark-gluon plasma
• Including off-diagonal anisotropies in anisotropic hydrodynamics
• Relaxation time approximation with pair production and annihilation processes
• Parton self-energies for general momentum-space anisotropy
• Holographic Schwinger effect and electric instability with anisotropy
• Causal Relativistic Hydrodynamics of Conformal Fermi-Dirac Gases
• Anisotropic hydrodynamics with number-conserving kernels
• Initial Angular Momentum and Flow in High Energy Nuclear Collisions
• An improved anisotropic hydrodynamics ansatz
• Anisotropic hydrodynamics
• Pion interferometry at 200 GeV using anisotropic hydrodynamics
• Nonextensive hydrodynamics of boost-invariant plasmas
• Viscous hydrodynamics for strongly anisotropic expansion
• Shock Waves in Relativistic Anisotropic Hydrodynamics
• Thermodynamics and phase diagram of anisotropic Chern-Simons deformed gauge theories
• Momentum anisotropy effects for quarkonium in a weakly-coupled quark-gluon plasma below the melting temperature
• Relativistic second-order dissipative and anisotropic fluid dynamics in the relaxation-time approximation for an ideal gas of massive particles
• Universality Classes of Relativistic Fluid Dynamics: Applications
• Holographic study on the jet quenching parameter in anisotropic systems
• Anomalous Transport Processes in Turbulent non-Abelian Plasmas
• Holographic ${\mathrm{QCD}}_3$ and Chern-Simons theory from anisotropic supergravity
• Anisotropic hydrodynamic modeling of heavy-ion collisions at LHC and RHIC
• Collective flow and hydrodynamics in large and small systems at the LHC
• Toward parton equilibration with improved parton interaction matrix elements
• Hydrodynamic modeling of heavy-ion collisions
• A generalized Theory of Diffusion based on Kinetic Theory
• Paramagnetic squeezing of a uniformly expanding quark-gluon plasma in and out of equilibrium
• Hydrodynamic description of the baryon-charged quark-gluon plasma
• Metric anisotropies and emergent anisotropic hydrodynamics
• Phenomenological predictions of 3+1d anisotropic hydrodynamics
• Holographic charge transport in non commutative gauge theories
• On nonadditive anisotropic relativistic hydrodynamics
• Causality and stability in first-order conformal anisotropic hydrodynamics
• Recent progress in anisotropic hydrodynamics
• Thermoelectric response of a hot and weakly magnetized anisotropic QCD medium
• Metric anisotropies and nonequilibrium attractor for expanding plasma
• Spin hydrodynamics -- recent developments
• Transport coefficients in second-order non-conformal viscous hydrodynamics
• Bottomonia in the Quark Gluon Plasma
• Gluon dissociation of $J/\psi$ in anisotropic {\em Quark-Gluon-Plasma}
• Photon and dilepton production from a non-equilibrium quark-gluon plasma
• Quark contribution for center domain in heavy ion collisions
• Equilibrium and equilibration in a gluon plasma with improved matrix elements
• Non-conformal evolution of magnetic fields during reheating
• Projecting the likely importance of weak-interaction-driven bulk viscosity in neutron star mergers
• Far-from-equilibrium attractors with a realistic non-conformal equation of state
• Linear Stability of Shock Waves in Ultrarelativistic Anisotropic Hydrodynamics
• Dissipative type theories for Bjorken and Gubser flows
• Viscous anisotropic hydrodynamics for the Gubser flow
• Bottomonia suppression in an anisotropic quark-gluon plasma
• Hard gluon evolution in the last stage of the bottom-up thermalization
• Formulation of relativistic dissipative fluid dynamics and its applications in heavy-ion collisions
• Thermalization of parton spectra in the color-flux-tube model
• Anisotropic hydrodynamics -- basic concepts
• Hydrodynamics with spin --- recent developments
• Extended applicability domain of viscous anisotropic hydrodynamics in (2+1)-D Bjorken flow with transverse expansion
• Kinetic equations and anisotropic hydrodynamics for quark and gluon fluids
• Anisotropy effects on heavy quark dynamics in Gribov modified gluon plasma
• Inverse anisotropic catalysis and complexity
• Proper time evolution of magnetic susceptibility in a magnetized quark-gluon plasma
• Roundtable: What can we learn about confinement and anomalous effects in QCD using analog systems?
• Non-equilibrium hydrodynamics of the quark-gluon plasma
• Bottomonium suppression and flow in heavy-ion collisions
• Entropy Production in Dissipationless Hydrodynamics with an order parameter