Analytical Green’s function of the multidimensional frequency-dependent phonon Boltzmann equation

Thermal phonon transport at length scales comparable to mean free paths is governed by the Boltzmann equation, which is challenging to solve due to its high dimensionality. Here, we present an analytical Green’s function for the frequency-dependent, multidimensional Boltzmann equation under the relaxation-time approximation. The new analytical solution is valid from diffusive to ballistic transport regimes and rigorously includes frequency dependence of phonon properties. We demonstrate that our result enables simple closed-form solutions for a number of multidimensional problems for which the only prior solution methods have been computationally expensive numerical simulations.