DSMC scheme to study phonon dynamics

In order to solve the Boltzmann transport equation (BTE) of phonons for investigating heat conduction in non-metallic solids, we propose employing a DSMC (direct simulation Monte Carlo) scheme to simulate the dynamics of phonons analogous to rarefied gas. In contrast to treating the BTE with conventional linear approximation, this scheme requires no relaxation times as input parameters. We can directly investigate couplings among phonons with different modes, although we have to assume an appropriate scattering model for phonon-phonon interactions. In this paper, we describe the DSMC scheme for phonon dynamics and present some results with our prototype codes for a simple solid model. In the first case of single-branch four-phonon processes, we carried out simulations of non-equilibrium thin films with a temperature gradient. We found that the temperature jump at the boundaries can be successfully achieved. For the second case of three phonon processes, we developed a simulation code that takes into consideration the different acoustic branches to evaluate the mode-dependent relaxation time and mean free path. This type of DSMC scheme for phonons enables us to include other relevant factors, such as optical branches and phonon-electron interactions.