Hydrodynamization in kinetic theory: Transient modes and the gradient expansion

We explore the transition to hydrodynamics in a weakly coupled model of quark-gluon plasma given by kinetic theory in the relaxation-time approximation with conformal symmetry. We demonstrate that the gradient expansion in this model has a vanishing radius of convergence due to the presence of a transient (nonhydrodynamic) mode, in a way similar to results obtained earlier in strongly coupled gauge theories. This suggests that the mechanism by which hydrodynamic behavior emerges is the same, which we further corroborate by a novel comparison between solutions of different weakly and strongly coupled models. However, in contrast with other known cases, we find that not all the singularities of the analytic continuation of the Borel transform of the gradient expansion correspond to transient excitations of the microscopic system; some of them reflect analytic properties of the kinetic equation when the proper time is continued to complex values.