Linear-Response Functions for Phonon-Mediated Heat Transport

Thermal transport is generally modeled assuming diffusive behavior, for example using Fourier's law. However, in many conditions, including in nanoscale or low-dimensional materials, transport is known to deviate strongly from Foruier's law. Specifically, ballistic or partially-ballistic transport is often observed. Theoretical models often make use of static, nonlocal thermal conductivity models. However, an approach to elucidate transport without the assumption of diffusive transport which can be computed using atomic-scale models does not exist.<br/>In this contribution, we demonstrate how linear-response functions can be used to model phonon-mediated thermal transport. Specifically, we have developed an approach based on the fluctuation-dissipation theorem to elucidate transport phenomena in diffusive and partially ballistic regimes. The response to heat pulses has been explicitly considered, but other perturbations can also be considered. Applciations to low-dimensional materials including oscillatory transport and ballistic transport is presented. A general discussion of how these methods might contribute to transport in unconventional conditions is also discussed.