Novel Relaxation Time Approximation to the Relativistic Boltzmann Equation

Abstract

We show that the widely used relaxation time approximation to the relativistic Boltzmann equation contains basic flaws, being incompatible with microscopic and macroscopic conservation laws. We propose a new approximation that fixes such fundamental issues and maintains the basic properties of the linearized Boltzmann collision operator. We show how this correction affects transport coefficients, such as the bulk viscosity and particle diffusion.

arXiv comment7 pages, 4 figures

References in corpus (35)

• Derivation of transient relativistic fluid dynamics from the Boltzmann equation
• New theories of relativistic hydrodynamics in the LHC era
• Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation
• First-order relativistic hydrodynamics is stable
• Causality and existence of solutions of relativistic viscous fluid dynamics with gravity
• Fluid Dynamics far from Local Equilibrium
• Hydrodynamic gradient expansion in gauge theory plasmas
• Radiative energy loss and v2 spectra for viscous hydrodynamics
• Nonlinear causality of general first-order relativistic viscous hydrodynamics
• Testing viscous and anisotropic hydrodynamics in an exactly solvable case
• The anisotropic non-equilibrium hydrodynamic attractor
• Bulk viscosity, particle spectra and flow in heavy-ion collisions
• A new exact solution of the relativistic Boltzmann equation and its hydrodynamic limit
• Hydrodynamization in kinetic theory: Transient modes and the gradient expansion
• Stable and causal relativistic Navier-Stokes equations
• Derivation of fluid dynamics from kinetic theory with the 14--moment approximation
• Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation
• Fluid dynamics of out of equilibrium boost invariant plasmas
• What attracts to attractors?
• 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
• The non-equilibrium attractor for kinetic theory in relaxation time approximation
• Analytical attractor and the divergence of the slow-roll expansion in relativistic hydrodynamics
• How does relativistic kinetic theory remember about initial conditions?
• Exact hydrodynamic attractor of an ultrarelativistic gas of hard spheres
• Analytic solution of the Boltzmann equation in an expanding system
• Hydrodynamic attractor and the fate of perturbative expansions in Gubser flow
• Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow
• Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime
• Non-perturbative rheological behavior of a far-from-equilibrium expanding plasma
• Exact solution for the non-equilibrium attractor in number-conserving relaxation time approximation
• Anisotropic hydrodynamics with a scalar collisional kernel
• Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in ${\mathrm{AdS}}_2\otimes {\mathrm{S}}_2$
• Analytic solutions of the relativistic Boltzmann equation
• First-Order General-Relativistic Viscous Fluid Dynamics

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• Exponential Approach to the Hydrodynamic Attractor in Yang-Mills Kinetic Theory
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• Relativistic Hydrodynamics: A Singulant Perspective
• The linear mode analysis and spin relaxation
• Current-Conserving Relativistic Linear Response for Collisional Plasmas
• Linearized dispersion relations in viscous relativistic hydrodynamics
• Gapless non-hydrodynamic modes in relativistic kinetic theory
• Far-from-equilibrium kinetic dynamics of $\lambda {\varphi }^4$ theory in an expanding universe
• Relativistic second-order viscous hydrodynamics from kinetic theory with extended relaxation-time approximation
• Revisiting shear stress tensor evolution: Non-resistive magnetohydrodynamics with momentum-dependent relaxation time
• Quantum version of transport coefficients in Nambu--Jona-Lasinio model at finite temperature and strong magnetic field
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• Diffusion matrix associated with the diffusion processes of multiple conserved charges in a hot and dense hadronic matter
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• Pre-Equilibrium Evolution of Conserved Charges with ICCING Initial Conditions
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• Relaxation terms for anomalous hydrodynamic transport in Weyl semimetals from kinetic theory
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• Causality and stability analysis of first-order field redefinition in relativistic hydrodynamics from kinetic theory
• Transport coefficients of magnetized neutron star cores
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• Field Theory Approaches to Relativistic Hydrodynamics
• Infinite Order Hydrodynamics: An Analytical Example
• Mean free path of photons in relativistic heavy ion collisions
• Correspondence between momentum dependent relaxation time and field redefinition of relativistic hydrodynamic theory
• Nonlinear $q$-voter model involving nonconformity on networks
• Transport coefficients of transient hydrodynamics for the hadron-resonance gas and thermal-mass quasiparticle models
• Early time behavior of spatial and momentum anisotropies in a kinetic approach to nuclear collisions
• Relaxation time approximation revisited and non-analytical structure in retarded correlators
• Relativistic BGK hydrodynamics
• Shakhov-type extension of the relaxation time approximation in relativistic kinetic theory and second-order fluid dynamics
• Resurgence for the non-conformal Bjorken flow with Fermi-Dirac and Bose-Einstein statistics
• Normal mode analysis within a mutilated relaxation time approximation
• Quarks to Cosmos: Particles and Plasma in Cosmological evolution
• Transport coefficients of dense nucleon matter at low temperature
• Relaxation Time Approximation for a multi-species relativistic gas
• Effects of magnetic field on the evolution of energy density fluctuations
• Dynamic Magnetic Response of Quark-Gluon Plasma to Electromagnetic Fields
• Transport coefficients of chiral fluid dynamics using low-energy effective models
• Normal mode analysis within relativistic massive transport
• A general relativistic kinetic theory approach to linear transport in generic hydrodynamic frame
• Quarkonium in a QCD medium with momentum-dependent relaxation time
• Transport and response coefficients in second-order dissipative relativistic hydrodynamics with quantum corrections: probing the quark-gluon plasma
• Transient fluid dynamics with general matching conditions: a first study from the method of moments