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 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.
Highlights
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
We only assume the existence of local thermodynamic equilibrium and of small fluctuations around it, whose dynamics is described by hydrodynamics
Hydrodynamics is described by a finite set of hydrodynamic modes, which can be obtained from the knowledge of the conservation equations and the constitutive relations
Summary
Hydrodynamics is an effective field theory (EFT) formulated as a perturbative expansion in spatial and time gradients It governs the dynamics of conserved quantities which in Fourier space can be constructed as an infinite expansion in frequency ω and momentum k—from slow processes and large scales to fast dynamics and short lengths. [9,10] suggested that in order to answer such question, one has to formally extend the function Fðω; k2Þ in complex momentum space and treat it as a complex algebraic curve In this language, series like Eq (2) are known as Puiseux series, and their radius of convergence is fundamentally connected to the so-called critical points fωc; kcg—points at which. As we will discuss in detail, the reinterpretation of the available data will lead us to confirm some intuitive physical arguments and to new and unexpected findings such as the fact that hydrodynamics does not work better at strong electromagnetic coupling (as always advertised)
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