Transverse viscous transport in classical solids

TL;DR

This paper investigates the transverse viscous transport in classical solids, revealing a solid-specific diffusive behavior in velocity correlations that is akin to viscosity in liquids, but arising from nonlinear inertia effects.

Contribution

It introduces the concept of a solid-specific viscous transport and interprets the resulting viscosity as a renormalized quantity due to nonlinear inertia effects.

Findings

Transverse velocity correlation function shows nonzero values at zero frequency in solids.

Solid-specific viscous transport leads to diffusive behavior in velocity fields.

Viscosity in solids can be understood as a renormalized viscosity from nonlinear inertia.

Abstract

The transverse velocity time correlation function ${\tilde C}_{\rm T}(k,\omega)$ with $k$ and $\omega$ being the wavenumber and the frequency, respectively, is a fundamental quantity in determining the transverse mechanical and transport properties of materials. In ordinary liquids, a nonzero value of ${\tilde C}_{\rm T}(k,0)$ is inevitably associated with viscous material flows. Curiously, even in solids where significant material flows are precluded due to frozen positional degrees of freedom, molecular dynamics simulations reveal that ${\tilde C}_{\rm T}(k,0)$ certainly takes a nonzero value, and in consequence, the time integration of the velocity field shows definite diffusive behavior with diffusivity ${\tilde C}_{\rm T}(k,0)/3$. We demonstrate that this diffusive behavior can be attributed to a solid-specific viscous transport. The resultant viscosity is interpreted as the renormalized viscosity accounting for the nonlinear inertia effect.