Predicting and understanding diffusion lengths and lifetimes in solids via a many-body $\mathit{\text{ab}}\mathit{\text{initio}}$ method: The role of coupled dynamics

We present an $\mathit{\text{ab}}\mathit{\text{initio}}$ method of diffusion, relaxation and dephasing processes of arbitrary observables, and corresponding diffusion lengths and lifetimes in solids. The method is based on linearized density-matrix master equation, with quantum treatment of electron scattering processes. It enables clear $\mathit{\text{ab}}\mathit{\text{initio}}$ descriptions of long lifetimes and diffusion lengths using approximate formulas at different levels, such as Dyakonov-Perel and drift-diffusion relations for spin decay and those beyond with coupled dynamics. Our results of graphene-hBN show that the coupling between dynamical processes can significantly affect spin diffusion and relaxation. Our method provides a transparent and powerful tool for predicting and understanding diffusion and relaxation.