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 behaviour 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.Comment: 6 pages, 2 figures, v2: author added, major rewrite, mysterious off
real axis singularities in the Borel plane explained (!), see also
arXiv:1802.08225 [nucl-th] by Heller and Svensson; v3: references added,
minor improvements in the text, first 426 terms from Eq. (8) included in the
submission; v4: title changed, matches published versio
