Analytic structure of nonhydrodynamic modes in kinetic theory

TL;DR

This paper analytically investigates how nonhydrodynamic modes decay and influence the transition to hydrodynamic behavior in relativistic kinetic theory, revealing complex structures like branch cuts and the limitations of pole signatures.

Contribution

It provides an analytical solution for retarded correlation functions in kinetic theory, clarifying the emergence of branch cuts and the interplay with hydrodynamic poles, and demonstrates Borel resummation of the gradient expansion.

Findings

Branch cuts arise from noncollective particle excitations.

Poles are ambiguous indicators of hydrodynamic onset.

Late-time deviations from hydrodynamics can occur due to slow processes.

Abstract

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 nonequilib- rium 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 functions can be Borel resummed such that the full nonperturbative information is recovered using perturbative input only.