Analytical structure of the binary collision integral and the ultrarelativistic limit of transport coefficients of an ideal gas

Abstract

In this paper we discuss the analytical properties of the binary collision integral for a gas of ultrarelativistic particles interacting via a constant cross-section. Starting from a near-equilibrium expansion over a complete basis of irreducible tensors in momentum space we compute the linearized collision matrices analytically. Using these results we then numerically compute all transport-coefficients of relativistic fluid dynamics with various power-counting schemes that are second-order in Knudsen and/or inverse Reynolds numbers. Furthermore, we also exactly compute the leading-order contribution with respect to the particle mass to the coefficient of bulk viscosity, the relaxation time, and other second-order transport coefficients of the bulk viscous pressure.

arXiv commentPublished version

References in corpus (18)

• Elliptic and triangular flow in event-by-event (3+1)D viscous hydrodynamics
• Derivation of transient relativistic fluid dynamics from the Boltzmann equation
• 3+1D hydrodynamic simulation of relativistic heavy-ion collisions
• Causal viscous hydrodynamics in 2+1 dimensions for relativistic heavy-ion collisions
• The production of photons in relativistic heavy-ion collisions
• A 3+1 dimensional viscous hydrodynamic code for relativistic heavy ion collisions
• Relativistic shock waves in viscous gluon matter
• On the relative importance of second-order terms in relativistic dissipative fluid dynamics
• Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation
• Investigation of shock waves in the relativistic Riemann problem: A comparison of viscous fluid dynamics to kinetic theory
• Analytic solution of the Boltzmann equation in an expanding system
• Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime
• Multicomponent relativistic dissipative fluid dynamics from the Boltzmann equation
• Inverse-Reynolds-Dominance approach to transient fluid dynamics
• Hydrodynamic theories for a system of weakly self-interacting classical ultra-relativistic scalar particles: microscopic derivations and attractors
• Development of relativistic shock waves in viscous gluon matter
• Transport coefficients of second-order relativistic fluid dynamics in the relaxation-time approximation
• Far-from-equilibrium kinetic dynamics of $\lambda {\varphi }^4$ theory in an expanding universe

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• Relaxation Time Approximation for a multi-species relativistic gas