We present an ab initio method of diffusion, relaxation, and dephasing processes of arbitrary observables and corresponding diffusion lengths and lifetimes in solids. The method is based on a linearized density-matrix master equation, with quantum treatment of electron scattering processes. It enables clear ab 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–$h$-BN 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.

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• Electron-phonon coupling
• Quantum transport
• Spin diffusion
• Spin-orbit coupling
• 2-dimensional systems
• Density functional theory
• Quantum master equation
• Wannier function methods