Ultrafast phonon dynamics by solving the real-time Boltzmann equation with adaptive and multirate time integration

First-principles simulations of nonequilibrium dynamics are key to predicting charge and heat transport in electronic devices and interpreting ultrafast spectroscopy experiments. The real-time Boltzmann transport equation (rt-BTE) simulates the coupled dynamics of electrons and phonons using interactions calculated from first principles. However, the time and system size that can be modeled with this approach are limited by several challenges, including the different timescales of electron and phonon dynamics and the cost of computing collision integrals. Only a few examples of these calculations exist, mainly for 2D materials.

Here we leverage adaptive and multirate time integration methods to achieve a significant improvement in solving the coupled rt-BTEs. Relative to non-adaptive time-stepping, our approach achieves a 10x speedup for a given target accuracy, or a greater accuracy by 3-6 orders of magnitude for the same computational cost. We show results including ultrafast carrier relaxation in graphene and nonequilibrium lattice dynamics in a bulk material (Si), for which we model thermal diffuse scattering maps measured in experiments. These advances are made possible by implementing an interface between the PERTURBO code [1] and the SUNDIALS library [2], opening new possibilities for accurate modeling of nonequilibrium dynamics in materials.

[1] J.-J. Zhou, et al. Comput. Phys. Commun. 264, 107970 (2021)

[2] D. R. Reynolds, et al. ACM Trans. on Math. Software, 49(2), pp. 1-26 (2023)