Distinguishing between spatial coherence and temporal coherence of phonons

Abstract

Coherent phonon transport is regarded as a promising strategy for controlling thermal properties in solids using the wave nature of phonons. However, no clear distinction between the spatial and temporal phonon coherence has been accounted for and a formalism that quantifies these two effects is still to be found. In this work, we propose a statistical approach for calculating the spatial and temporal coherence spectra using molecular dynamics simulations. We provide a microscopic assessment of these properties and we theoretically demonstrate that, while temporal and spatial coherence can be analytically related under specific conditions, they represent two characteristic lengths that set apart different physical effects. The former is associated with the phonon mean free path while the latter can be regarded as a measure of localization, representing the spatial extension of phonon wave packets. This provides a framework to engineer heat conduction in solids by quantitatively revealing the wave/particle nature of the vibrational modes.