Analytic structure of nonhydrodynamic modes in kinetic theory

How physical systems approach hydrodynamic behavior is governed by the decay of nonhydrodynamic modes. Here, we start from a relativistic kinetic theory that encodes relaxation mechanisms governed by different timescales thus sharing essential features of generic weakly coupled nonequilibrium systems. By analytically solving for the retarded correlation functions, we clarify how branch cuts arise generically from noncollective particle excitations, how they interface with poles arising from collective hydrodynamic excitations, and to what extent the appearance of poles remains at best an ambiguous signature for the onset of fluid dynamic behavior. We observe that processes that are slower than the hydrodynamic relaxation timescale can make a system that has already reached fluid dynamic behavior to fall out of hydrodynamics at late times. In addition, the analytical control over this model allows us to explicitly demonstrate how the hydrodynamic gradient expansion of the correlation function can be resummed such that the complete and exact non-analytic form of the correlation function can be recovered.