Hydrodynamic and Non-hydrodynamic Excitations in Kinetic Theory -- A Numerical Analysis in Scalar Field Theory

TL;DR

This paper investigates the emergence of hydrodynamic behavior from microscopic kinetic theory in scalar fields by analyzing eigenmodes and Green's functions, revealing complex analytic structures beyond simple poles or cuts.

Contribution

It introduces a novel numerical method to compute eigenmodes of the kinetic evolution operator, enabling detailed analysis of hydrodynamic and non-hydrodynamic modes in scalar field theory.

Findings

Complex analytic structures in Green's functions are identified.

Hydrodynamic and non-hydrodynamic modes are characterized.

The approach paves the way for similar studies in QCD kinetic theory.

Abstract

Viscous hydrodynamics serves as a successful mesoscopic description of the Quark-Gluon Plasma produced in relativistic heavy-ion collisions. In order to investigate, how such an effective description emerges from the underlying microscopic dynamics we calculate the hydrodynamic and non-hydrodynamic modes of linear response in the sound channel from a first-principle calculation in kinetic theory. We do this with a new approach wherein we discretize the collision kernel to directly calculate eigenvalues and eigenmodes of the evolution operator. This allows us to study the Green's functions at any point in the complex frequency space. Our study focuses on scalar theory with quartic interaction and we find that the analytic structure of Green's functions in the complex plane is far more complicated than just poles or cuts which is a first step towards an equivalent study in QCD kinetic theory.