Hydrodynamic and Non-hydrodynamic Excitations in Kinetic Theory -- A Numerical Analysis in Scalar Field 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.
Keywords
Cite
@article{arxiv.2308.04491,
title = {Hydrodynamic and Non-hydrodynamic Excitations in Kinetic Theory -- A Numerical Analysis in Scalar Field Theory},
author = {Stephan Ochsenfeld and Sören Schlichting},
journal= {arXiv preprint arXiv:2308.04491},
year = {2023}
}
Comments
30 pages and 8 figures. v2 changes: Added a more nuanced discussion about hydrodynamization in introduction. Clarified the potential differences between the QFT scalar \phi^4 theory and kinetic theory derived from it. Added some additional discussion of a hydrodynamic breakdown scale k_c to the conclusion of the paper. Fixed some typos. v3 changes: added code to source files