Abstract
We investigate the non-linear transport processes and hydrodynamization of a system of gluons undergoing longitudinal boost-invariant expansion. The dynamics is described within the framework of the Boltzmann equation in the small-angle approximation. The kinetic equations for a suitable set of moments of the one-particle distribution function are derived. By investigating the stability and asymptotic resurgent properties of this dynamical system, we demonstrate, that its solutions exhibit a rather different behavior for large (UV) and small (IR) effective Knudsen numbers. Close to the forward attractor in the IR regime the constitutive relations of each moment can be written as a multiparameter transseries. This resummation scheme allows us to extend the definition of a transport coefficient to the non-equilibrium regime naturally. Each transport coefficient is renormalized by the non-perturbative contributions of the non-hydrodynamic modes. The Knudsen number dependence of the transport coefficient is governed by the corresponding renormalization group flow equation. An interesting feature of the Yang-Mills plasma in this regime is that it exhibits transient non-Newtonian behavior while hydrodynamizing. In the UV regime the solution for the moments can be written as a power-law asymptotic series with a finite radius of convergence. We show that radius of convergence of the UV perturbative expansion grows linearly as a function of the shear viscosity to entropy density ratio. Finally, we compare the universal properties in the pullback and forward attracting regions to other kinetic models including the relaxation time approximation and the effective kinetic Arnold-Moore-Yaffe (AMY) theory.
Highlights
Relativistic fluid dynamics is an effective theory which describes long-wavelength phenomena
This traditional paradigm has recently been challenged by the overwhelming success of hydrodynamic models in describing experimental data in high energy nuclear collisions [1–7] as well as cold atom systems [8–11]
Another interesting development in the understanding of far-from-equilibrium attractors in relativistic nonequilibrium dynamics is a phase space analysis using the language of nonautonomous dynamical systems1 [29–32]
Summary
Relativistic fluid dynamics is an effective theory which describes long-wavelength phenomena. This new insight might be able to explain why hydrodynamic models work very well when applied in extreme experimental scenarios such as ultrarelativistic heavy ion collisions [27,28] Another interesting development in the understanding of far-from-equilibrium attractors in relativistic nonequilibrium dynamics is a phase space analysis using the language of nonautonomous dynamical systems1 [29–32]. New solutions to the equations of motion of Legendre moments are derived by employing methods developed in the context of stability analysis of nonautonomous dynamical systems [38,39], as well as techniques from superasymptotic and hyperasymptotic analysis [51–54] These tools allow us to analyze the hydrodynamization process in two distinct regimes characterized by the size of dissipative corrections: Kn ≫ 1 (UV, early time) and Kn ≪ 1 (IR, late time). The technical details of our work are presented in the Appendixes
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