The non-equilibrium attractor for kinetic theory in relaxation time approximation

Abstract

I demonstrate that the concept of a non-equilibrium attractor can be extended beyond the lowest-order moments typically considered in hydrodynamic treatments. Using a previously obtained exact solution to the relaxation-time approximation Boltzmann equation for a transversally homogeneous and boost-invariant system subject to Bjorken flow, I derive an equation obeyed by all moments of the one-particle distribution function. Using numerical solutions, I show that, similar to the pressure anisotropy, all moments of the distribution function exhibit attractor-like behavior wherein all initial conditions converge to a universal solution after a short time with the exception of moments which are sensitive to modes with zero longitudinal momentum and high transverse momentum. In addition, I compute the exact solution for the distribution function itself on very fine lattices in momentum space and demonstrate that (a) an attractor for the full distribution function exists and (b) solutions with generic initial conditions relax to this solution, first at low momentum and later at high momentum.

27 pages, 13 figures; v3: updates to Figs. 2, 3, 9, 10, and 11; note added; no changes required to discussion or conclusions

References in corpus (22)

• Horizon formation and far-from-equilibrium isotropization in supersymmetric Yang-Mills plasma
• Dissipative Dynamics of Highly Anisotropic Systems
• Highly-anisotropic and strongly-dissipative hydrodynamics for early stages of relativistic heavy-ion collisions
• Dissipative relativistic fluid dynamics: a new way to derive the equations of motion from kinetic theory
• A numerical relativity approach to the initial value problem in asymptotically Anti-de Sitter spacetime for plasma thermalization - an ADM formulation
• The anisotropic non-equilibrium hydrodynamic attractor
• A new exact solution of the relativistic Boltzmann equation and its hydrodynamic limit
• Origin of the Relaxation Time in Dissipative Fluid Dynamics
• Instabilities of an anisotropically expanding non-Abelian plasma: 1D+3V discretized hard-loop simulations
• Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation
• Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow
• Relativistic anisotropic hydrodynamics
• Plasma Instabilities in an Anisotropically Expanding Geometry
• On the hydrodynamic attractor of Yang-Mills plasma
• Relativistic Hydrodynamic Attractors with Broken Symmetries: Non-Conformal and Non-Homogeneous
• Holographic thermalization with radial flow
• Shear-bulk coupling in nonconformal hydrodynamics
• Relativistic quantum transport coefficients for second-order viscous hydrodynamics
• Coupled kinetic equations for quarks and gluons in the relaxation time approximation
• Anisotropic hydrodynamics with a scalar collisional kernel
• Exact solution of the (0+1)-dimensional Boltzmann equation for massive Bose-Einstein and Fermi-Dirac gases
• Anisotropic-hydrodynamics approach to a quark-gluon fluid mixture

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