Hydrodynamic generators in relativistic kinetic theory

Abstract

We resum the non-equilibrium gradient corrections to a single-particle distribution function evolved by the Boltzmann equation in the relaxation time approximation (RTA). We first study a system undergoing Bjorken expansion and show that, for a constant relaxation time, the exact solution of the RTA Boltzmann equation at late times (i.e. after the decay of non-hydrodynamic modes) generates the Borel resummed Chapman-Enskog series. Extending this correspondence to systems without Bjorken symmetry, we construct a (3+1)-dimensional hydrodynamic generator for RTA kinetic theory, which is an integral representation of the Chapman-Enskog series in the limit of vanishing non-hydrodynamic modes. Relaxing this limit we find at earlier times a set of non-hydrodynamic modes coupled to the Chapman-Enskog expansion. Including the dynamics of these non-hydrodynamic modes is shown to control the emergence of hydrodynamics as an effective field theory description of non-equilibrium fluids, which works well even for far-off-equilibrium situations where the Knudsen number is initially large.

References in corpus (10)

• Origin of the Relaxation Time in Dissipative Fluid Dynamics
• Collectivity and electromagnetic radiation in small systems
• A kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion
• Do nuclear collisions create a locally equilibrated quark-gluon plasma?
• Relativistic Hydrodynamic Attractors with Broken Symmetries: Non-Conformal and Non-Homogeneous
• Shear-bulk coupling in nonconformal hydrodynamics
• Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow
• Hydrodynamics from free-streaming to thermalization and back again
• Holography, Hydrodynamization and Heavy-Ion Collisions
• Dynamics of critical fluctuations: Theory -- phenomenology -- heavy-ion collisions

Cited by in corpus (6)

• Hydrodynamic attractors in heavy ion collisions: a review
• On non-conformal kinetic theory and hydrodynamics for Bjorken flow
• Hydrodynamic Attractors in Ultrarelativistic Nuclear Collisions
• Anisotropic fluid dynamical simulations of heavy-ion collisions
• Hydrodynamic Attractor in a Hubble Expansion
• An improved anisotropic hydrodynamics ansatz