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We establish an approach to compute linear-response functions to elucidateheat waves and non-local thermal transport. The theory is able to describe theresponse of a system to external heat sources that are nonuniform in space andtime. The response functions are computed using equilibrium molecular-dynamicssimulations of an Ar crystal modeled using the standard Lennard-Jonespotential. It is shown that for low temperatures and short length scales,transport can be partially or even completely ballistic, with the responseprimarily limited by the group velocity of lattice waves. By contrast, atlonger length scales and higher temperatures, the response functions correspondmore closely to diffusive transport characteristic of Fourier's law. It is alsoshown how the effective thermal conductivity can be determined in apartially-ballistic regime. The results demonstrate the known reduction in theeffective thermal conductivity observed when system dimensions are smaller thanthe mean-free path for lattice waves. Finally, we show how determination of therelevant response functions can be used to model heating of a crystal withoutrequiring additional atomic-scale simulations. Differences between computedresults and predictions from Fourier's law represent wave-like,partially-ballistic transport.

Non-local linear-response functions for thermal transport computed with equilibrium molecular-dynamics simulation