Convergence of hydrodynamic modes: insights from kinetic theory and holography
Abstract
We study the mechanisms setting the radius of convergence of hydrodynamic dispersion relations in kinetic theory in the relaxation time approximation. This introduces a qualitatively new feature with respect to holography: a nonhydrodynamic sector represented by a branch cut in the retarded Green's function. In contrast with existing holographic examples, we find that the radius of convergence in the shear channel is set by a collision of the hydrodynamic pole with a branch point. In the sound channel it is set by a pole-pole collision on a non-principal sheet of the Green's function. More generally, we examine the consequences of the Implicit Function Theorem in hydrodynamics and give a prescription to determine a set of points that necessarily includes all complex singularities of the dispersion relation. This may be used as a practical tool to assist in determining the radius of convergence of hydrodynamic dispersion relations.
Keywords
Cite
@article{arxiv.2012.15393,
title = {Convergence of hydrodynamic modes: insights from kinetic theory and holography},
author = {Michal P. Heller and Alexandre Serantes and Michał Spaliński and Viktor Svensson and Benjamin Withers},
journal= {arXiv preprint arXiv:2012.15393},
year = {2021}
}
Comments
v1: 25 pages, 13 figures; v2: typos corrected, version published in SciPost