Hydrodynamic gradient expansion in linear response theory

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.

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

References in corpus (12)

• Relativistic viscous hydrodynamics, conformal invariance, and holography
• On the importance of viscous dissipation and heat conduction in binary neutron-star mergers
• On the convergence of the gradient expansion in hydrodynamics
• Causality of the Einstein-Israel-Stewart Theory with Bulk Viscosity
• Black Holes as Lumps of Fluid
• Linearized fluid/gravity correspondence: from shear viscosity to all order hydrodynamics
• All Order Linearized Hydrodynamics from Fluid/Gravity Correspondence
• Holography, Hydrodynamization and Heavy-Ion Collisions
• Divergence of the Chapman-Enskog expansion in relativistic kinetic theory
• Absorption Lengths in the Holographic Plasma
• Linearly resummed hydrodynamics in a weakly curved spacetime
• Transseries for causal diffusive systems

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