Abstract
Hydrodynamic excitations corresponding to sound and shear modes in fluids are characterized by gapless dispersion relations. In the hydrodynamic gradient expansion, their frequencies are represented by power series in spatial momenta. We investigate the analytic structure and convergence properties of the hydrodynamic series by studying the associated spectral curve in the space of complexified frequency and complexified spatial momentum. For the strongly coupled N=4 supersymmetric Yang-Mills plasma, we use the holographic duality methods to demonstrate that the derivative expansions have finite nonzero radii of convergence. Obstruction to the convergence of hydrodynamic series arises from level crossings in the quasinormal spectrum at complex momenta.
Highlights
Introduction.—Hydrodynamics is an established universal language for describing near-equilibrium phenomena in fluids [1]
The constitutive relations ρa 1⁄4 ρaðφÞ, Ja 1⁄4 JaðφÞ are used in the conservation laws (1) in order to determine the macroscopic space-time evolution of the fluid [1]
The naive expectation is that going to higher orders in the derivative expansion improves the hydrodynamic description of the fluid, similar to how the Navier-Stokes equations improve the perfect-fluid approximation by including the viscous effects
Summary
Introduction.—Hydrodynamics is an established universal language for describing near-equilibrium phenomena in fluids [1]. Convergence of the Gradient Expansion in Hydrodynamics Hydrodynamic excitations corresponding to sound and shear modes in fluids are characterized by gapless dispersion relations.
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