Unifying renormalized and bare viscosity in two-dimensional molecular dynamics simulations

TL;DR

This paper introduces a wavenumber-dependent viscosity in 2D molecular dynamics that unifies the concepts of renormalized and bare viscosity, linking microscopic fluctuations to macroscopic transport properties.

Contribution

It presents a novel approach to connect mesoscopic and macroscopic transport by defining a wavenumber-dependent viscosity from microscopic shear stress correlations.

Findings

Wavenumber-dependent viscosity diverges at small wavenumbers.

Large-wavenumber behavior corresponds to the bare viscosity.

Establishes a link between microscopic dynamics and macroscopic transport.

Abstract

Fluctuating hydrodynamics provides a framework connecting mesoscopic fluctuations with macroscopic transport behavior. To bridge mesoscopic and macroscopic transport from microscopic dynamics, we introduce a wavenumber-dependent viscosity, defined via the equilibrium correlation of time-averaged Fourier components of the fine-grained shear stress field. Two-dimensional molecular dynamics simulations reveal its small-wavenumber divergence characteristic of the renormalized viscosity, while its large-wavenumber behavior determines the bare viscosity, thereby establishing a link between mesoscopic and macroscopic transport based on microscopic dynamics.