Fokker-Planck description and diffusive phonon heat transport

TL;DR

This paper introduces a Fokker-Planck framework with position- and time-dependent diffusion for modeling phonon heat transport in small structures, capturing non-Gaussian effects and aligning with Boltzmann equation results.

Contribution

It presents a novel Fokker-Planck approach with variable diffusion coefficients for phonon heat conduction, extending previous models and providing analytical solutions.

Findings

The model accurately fits Boltzmann equation results.

It describes non-Gaussian heat transport processes.

Analytical solutions are obtainable for various diffusion coefficients.

Abstract

We propose a prescription based on the Fokker-Planck equation in the Stratonovich approach, with the diffusion coefficient dependent on temporal and spatial coordinates, for describing heat conduction by phonons in small structures. This equation can be analytically solved for a broad class of diffusion coefficients. It can also describe non-Gaussian processes. Further, it generalizes the model investigated by Naqvi and Waldenstr$\phi $% m (PRL, 95 (2005), 065901). We show that our solutions can fit well the results derived from the Boltzmann equation.