How small hydrodynamics can go

Abstract

Numerous experimental and theoretical results in liquids and plasmas suggest the presence of a critical momentum at which the shear diffusion mode collides with a non-hydrodynamic relaxation mode, giving rise to propagating shear waves. This phenomenon, labelled as "k-gap", could explain the surprising identification of a low-frequency elastic behaviour in confined liquids. More recently, a formal study of the perturbative hydrodynamic expansion showed that critical points in complex space, such as the aforementioned k-gap, determine the radius of convergence of linear hydrodynamics, its regime of applicability. In this work, we combine the two new concepts and we study the radius of convergence of linear hydrodynamics in "real liquids" by using several data from simulations and experiments. We generically show that the radius of convergence increases with temperature and it surprisingly decreases with the electromagnetic interactions coupling. More importantly, for all the systems considered, we find that such radius is set by the Wigner-Seitz radius, the characteristic inter-atomic distance of the liquid, which provides a natural microscopic bound.

v2: matching the published version

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Cited by in corpus (19)

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• Convergence of hydrodynamic modes: insights from kinetic theory and holography
• A Holographic Superfluid Symphony
• On the universality of AdS${}_2$ diffusion bounds and the breakdown of linearized hydrodynamics
• Thermal Stress Tensor Correlators, OPE and Holography
• Hydrodynamic dispersion relations at finite coupling
• Breakdown of hydrodynamics from holographic pole collision
• Upper bound of the charge diffusion constant in holography
• Quasinormal modes of a semi-holographic black brane and thermalization
• Aspects of univalence in holographic axion models
• Critical behaviour of hydrodynamic series
• Collective modes of polarizable holographic media in magnetic fields
• Emergence of Debye scaling in the density of states of liquids under nanoconfinement
• Long-time tails in the SYK chain from the effective field theory with a large number of derivatives
• Characteristic momentum of Hydro+ and a bound on the speed of sound near the QCD critical point
• Transseries for causal diffusive systems