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How physical systems approach hydrodynamic behavior is governed by the decayof nonhydrodynamic modes. Here, we start from a relativistic kinetic theorythat encodes relaxation mechanisms governed by different timescales thussharing essential features of generic weakly coupled nonequilib- rium systems.By analytically solving for the retarded correlation functions, we clarify howbranch cuts arise generically from noncollective particle excitations, how theyinterface with poles arising from collective hydrodynamic excitations, and towhat extent the appearance of poles remains at best an ambiguous signature forthe onset of fluid dynamic behavior. We observe that processes that are slowerthan the hydrodynamic relaxation timescale can make a system that has alreadyreached fluid dynamic behavior to fall out of hydrodynamics at late times. Inaddition, the analytical control over this model allows us to explicitlydemonstrate how the hydrodynamic gradient expansion of the correlationfunctions can be Borel resummed such that the full nonperturbative informationis recovered using perturbative input only.

Analytic structure of nonhydrodynamic modes in kinetic theory