The efficient method of lattice dynamics calculation: Monte Carlo integration with importance sampling.

In this study, we aimed to accelerate the thermal conductivity calculations of crystalline nanostructures using anharmonic lattice dynamics. For this we implemented Monte Carlo (MC) integration for relaxation time calculations and achieved a dramatic acceleration of approximately two orders of magnitude. The relaxation times can be calculated by computing the scattering rates for all phonon combinations; however, in this MC integration, we instead calculated the scattering rates of a randomly sampled subset of combinations.