Relaxation-time approximation and relativistic third-order viscous hydrodynamics from kinetic theory

Abstract

Using the iterative solution of Boltzmann equation in the relaxation-time approximation, the derivation of a third-order evolution equation for shear stress tensor is presented. To this end we first derive the expression for viscous corrections to the phase-space distribution function, $f(x,p)$, up to second-order in derivative expansion. The expression for $\delta f(x,p)$ obtained in this method does not lead to violation of the experimentally observed $1/\sqrt{m_T}$ scaling of the femtoscopic radii, as opposed to the widely used Grad's 14-moment approximation. Subsequently, we present the derivation of a third-order viscous evolution equation and demonstrate the significance of this derivation within one-dimensional scaling expansion. We show that results obtained using third-order evolution equations are in excellent accordance with the exact solution of Boltzmann equation as well as with transport results.

4 pages, 2 figures, Flash Talk given at Quark Matter 2014, Darmstadt, Germany

References in corpus (21)

• The Effect of Shear Viscosity on Spectra, Elliptic Flow, and HBT Radii
• Derivation of transient relativistic fluid dynamics from the Boltzmann equation
• Thermalization of gluons in ultrarelativistic heavy ion collisions by including three-body interactions in a parton cascade
• Causal Theories of Dissipative Relativistic Fluid Dynamics for Nuclear Collisions
• Dissipative relativistic fluid dynamics: a new way to derive the equations of motion from kinetic theory
• Testing viscous and anisotropic hydrodynamics in an exactly solvable case
• Anisotropic Hydrodynamics for Rapidly Expanding Systems
• Transverse mass dependence of two-pion correlations in Au+Au collisions at sqrt(s_NN) = 130 GeV
• Relativistic third-order dissipative fluid dynamics from kinetic theory
• Third-order relativistic dissipative hydrodynamics
• Relativistic dissipative hydrodynamics from kinetic theory with relaxation time approximation
• Transport rates and momentum isotropization of gluon matter in ultrarelativistic heavy-ion collisions
• Constraining relativistic viscous hydrodynamical evolution
• Relativistic viscous hydrodynamics for heavy-ion collisions: A comparison between the Chapman-Enskog and Grad methods
• Complete relativistic second-order dissipative hydrodynamics from the entropy principle
• Shear viscosity and out of equilibrium dynamics
• New relativistic dissipative fluid dynamics from kinetic theory
• Two-kaon correlations in central Pb + Pb collisions at 158 A GeV/c
• Particle production in relativistic heavy-ion collisions: A consistent hydrodynamic approach
• Boltzmann equation with a nonlocal collision term and the resultant dissipative fluid dynamics
• Relativistic hydrodynamics from Boltzmann equation with modified collision term

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• High-order quadrature-based lattice Boltzmann models for the flow of ultrarelativistic rarefied gases
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