Deviational Phonons and Thermal Transport at the Nanoscale

We present a new method for simulating phonon transport at the nanoscale. The proposed approach is based on the recently developed energy-based deviational Monte Carlo method by the authors [Phys. Rev. B 84, 205331, 2011] which achieves significantly reduced statistical uncertainty compared to standard Monte Carlo methods by simulating only the deviation from equilibrium. Here, we show that under linearized conditions (small temperature differences) the trajectories of individual particles simulating the deviation from equilibrium can be decoupled and can thus be simulated independently, without introducing any additional approximation. This leads to a particularly simple and efficient simulation method that can be used to treat steady and transient phonon transport problems in arbitrary three-dimensional geometries.