How small hydrodynamics can go

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 nonhydrodynamic relaxation mode, giving rise to propagating shear waves. This phenomenon, labeled k-gap, could explain the surprising identification of a low-frequency elastic behavior 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 a radius is set by the Wigner-Seitz radius-the characteristic interatomic distance of the liquid, which provides a natural microscopic bound.

Automated summary

This study explores the collision of shear diffusion mode and nonhydrodynamic relaxation mode in liquids and plasmas, leading to the formation of propagating shear waves known as k-gap, and explains the low-frequency elastic behavior in confined liquids. Additionally, it shows that critical points in complex space, such as the k-gap, determine the convergence radius of linear hydrodynamics. Furthermore, the study reveals that the convergence radius in real liquids is influenced by temperature and electromagnetic interactions, with the Wigner-Seitz radius serving as a natural microscopic bound.