Fokker-Planck description and diffusive phonon heat transport

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.