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 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.
Highlights
Additional motivations for studying nonhydrodynamic modes in relativistic equilibrating systems come from the apparent phenomenological need to understand how fluid dynamical behaviour arises in nucleus-nucleus, nucleusnucleon and possibly proton-proton collisions [13,14]
We conclude that the simple picture of a homogeneous and isotropic free-streaming dynamics explains the logarithmic branch cut found in interaction-free massless kinetic theory for retarded correlation functions like, e.g., the correlation function in the sound channel calculated in [33]
The path to equilibration in relativistic systems described by Boltzmann transport is governed by an interplay of collective hydrodynamic and non-collective particle excitations
Summary
Additional motivations for studying nonhydrodynamic modes in relativistic equilibrating systems come from the apparent phenomenological need to understand how fluid dynamical behaviour arises in nucleus-nucleus, nucleusnucleon and possibly proton-proton collisions [13,14]. This asks for a better understanding of where and how kinetic theory differs from hydrodynamics. The standard way of relating kinetic theory to viscous hydrodynamics is to derive the latter by truncating the former to a finite set of moments of the distribution function [18,19]. This truncation is based on the assumption that hydrodynamics works. To understand whether, when, and how it breaks down necessitates investigating kinetic theory beyond the moment expansion. The purpose of the present manuscript is to do so by studying how small deviations from thermal equilibrium relax in a full kinetic theory framework
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