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 lim...

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Bibliographic Details
Published in:Physical review. D 2021-09, Vol.104 (6), p.1, Article 066002
Main Authors: Heller, Michal P., Serantes, Alexandre, Spaliński, Michał, Svensson, Viktor, Withers, Benjamin
Format: Article
Language:English
Subjects:
Cosmology
Fluid dynamics
Fluid flow
Fluid mechanics
Flux density
Heavy ions
Ionic collisions
Momentum
Relativistic effects
Relativistic theory
Velocity distribution
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Summary: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.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.104.066002