Convergence of hydrodynamic modes: insights from kinetic theory and holography
Convergence of hydrodynamic modes: insights from kinetic theory and holography
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.
hep-th, nucl-th, physics.flu-dyn
Heller, Michal P.
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Serantes, Alexandre
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Spaliński, Michał
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Svensson, Viktor
8a239c71-2e14-4d40-9aa1-2dc260d05507
Withers, Benjamin
e510375b-c5d2-4d5f-bd68-40ace13f0ec9
1 June 2021
Heller, Michal P.
5b6c6d3e-4731-414d-8556-bd8604ce5377
Serantes, Alexandre
e19687f5-de76-4cb3-9afa-c9d843c3f5e2
Spaliński, Michał
3fabf22d-7873-492c-8bc6-6101c914c2b0
Svensson, Viktor
8a239c71-2e14-4d40-9aa1-2dc260d05507
Withers, Benjamin
e510375b-c5d2-4d5f-bd68-40ace13f0ec9
Heller, Michal P., Serantes, Alexandre, Spaliński, Michał, Svensson, Viktor and Withers, Benjamin
(2021)
Convergence of hydrodynamic modes: insights from kinetic theory and holography.
Scipost Physics.
(doi:10.21468/SciPostPhys.10.6.123).
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.
Text
2012.15393v2
- Accepted Manuscript
Text
SciPostPhys_10_6_123 (1)
- Version of Record
More information
Accepted/In Press date: 26 May 2021
Published date: 1 June 2021
Additional Information:
v1: 25 pages, 13 figures; v2: typos corrected, version published in SciPost
Keywords:
hep-th, nucl-th, physics.flu-dyn
Identifiers
Local EPrints ID: 455097
URI: http://eprints.soton.ac.uk/id/eprint/455097
ISSN: 2542-4653
PURE UUID: ecde6bb4-b31b-4369-8232-461ecbd8ab33
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Date deposited: 09 Mar 2022 17:31
Last modified: 17 Mar 2024 02:28
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Contributors
Author:
Michal P. Heller
Author:
Alexandre Serantes
Author:
Michał Spaliński
Author:
Viktor Svensson
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