Hydrodynamic gradient expansion in linear response theory
Hydrodynamic gradient expansion in linear response theory
A foundational question in relativistic fluid mechanics concerns the properties of the hydrodynamic gradient expansion at large orders. We establish the precise conditions under which this gradient expansion diverges for a broad class of microscopic theories admitting a relativistic hydrodynamic limit, in the linear regime. Our result does not rely on highly symmetric fluid flows utilized by previous studies of heavy-ion collisions and cosmology. The hydrodynamic gradient expansion diverges whenever energy density or velocity fields have support in momentum space exceeding a critical momentum, and converges otherwise. This critical momentum is an intrinsic property of the microscopic theory and is set by branch point singularities of hydrodynamic dispersion relations.
hep-th, hep-ph, nucl-th, physics.flu-dyn
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
2 September 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)
Hydrodynamic gradient expansion in linear response theory.
Physical Review D, 104, [066002].
(doi:10.1103/PhysRevD.104.066002).
Abstract
A foundational question in relativistic fluid mechanics concerns the properties of the hydrodynamic gradient expansion at large orders. We establish the precise conditions under which this gradient expansion diverges for a broad class of microscopic theories admitting a relativistic hydrodynamic limit, in the linear regime. Our result does not rely on highly symmetric fluid flows utilized by previous studies of heavy-ion collisions and cosmology. The hydrodynamic gradient expansion diverges whenever energy density or velocity fields have support in momentum space exceeding a critical momentum, and converges otherwise. This critical momentum is an intrinsic property of the microscopic theory and is set by branch point singularities of hydrodynamic dispersion relations.
More information
Accepted/In Press date: 16 July 2021
Published date: 2 September 2021
Additional Information:
10 pages, 2 figures; v2: results unchanged, reorganized and expanded presentation with new figures and new appendix on purely temporal gradient expansion, matches published version
Keywords:
hep-th, hep-ph, nucl-th, physics.flu-dyn
Identifiers
Local EPrints ID: 455078
URI: http://eprints.soton.ac.uk/id/eprint/455078
ISSN: 1550-7998
PURE UUID: 1ff3e350-cc37-4681-97e6-646e3abd4155
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Date deposited: 08 Mar 2022 17:43
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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