Convergence of hydrodynamic modes: insights from kinetic theory and holography

Heller, Michal P.; Serantes, Alexandre; Spalinski, Michal; Svensson, Viktor; Withers, Benjamin

doi:10.21468/SciPostPhys.10.6.123

SciPost Physics

Convergence of hydrodynamic modes: insights from kinetic theory and holography

Michal P. Heller, Alexandre Serantes, Michał Spaliński, Viktor Svensson, Benjamin Withers

SciPost Phys. 10, 123 (2021) · published 1 June 2021

doi: 10.21468/SciPostPhys.10.6.123
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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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.10.6.123
TI  - Convergence of hydrodynamic modes: insights from kinetic theory and holography
PY  - 2021/06/01
UR  - https://www.scipost.org/SciPostPhys.10.6.123
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 10
IS  - 6
SP  - 123
A1  - Heller, Michal P.
AU  - Serantes, Alexandre
AU  - Spalinski, Michal
AU  - Svensson, Viktor
AU  - Withers, Benjamin
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.10.6.123,
	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={SciPost Phys.},
	volume={10},
	pages={123},
	year={2021},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.10.6.123},
	url={https://scipost.org/10.21468/SciPostPhys.10.6.123},
}

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Authors / Affiliations: mappings to Contributors and Organizations

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¹ ² Michal P. Heller,
² Alexandre Serantes,
² ³ Michal Spalinski,
¹ ² Viktor Svensson,
⁴ Benjamin Withers

Funders for the research work leading to this publication