An analytic approach to the RTA Boltzmann attractor

Abstract: We reformulate the Boltzmann equation in the relaxation time approximation undergoing Bjorken flow in terms of a novel partial differential equation for the generating function of the moments of the distribution function. This is used to obtain an approximate analytic description of this system's far-from-equilibrium attractor via a series expansion at early times. This expansion possesses a finite radius of convergence and can be analytically continued to late times. We find that this procedure reproduces the known values of shear viscosity and other transport coefficients to high accuracy. We also provide a simple approximate analytic expression that describes the attractor in the entire domain of interest for studies of quark-gluon plasma dynamics.