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Calculations combining first-principles electron-phonon ($e$-ph) interactionswith the Boltzmann equation enable studies of ultrafast carrier and phonondynamics. However, in materials with weak Coulomb screening, electrons andholes form bound excitons and their scattering processes become correlated,posing additional challenges for modeling nonequilibrium physics. Here we showcalculations of ultrafast exciton dynamics and related time-domainspectroscopies using $ab~initio$ exciton-phonon (ex-ph) interactions togetherwith an excitonic Boltzmann equation. Starting from the nonequilibrium excitonpopulations, we develop simulations of time-domain absorption and photoemissionspectra that take into account electron-hole correlations. We use this methodto study monolayer WSe$_2$, where our calculations predict sub-picosecondtimescales for exciton relaxation and valley depolarization and reveal the keyrole of intermediate dark excitons. The approach introduced in this workenables a quantitative description of nonequilibrium dynamics and ultrafastspectroscopies in materials with strongly bound excitons.

First-Principles Ultrafast Exciton Dynamics and Time-Domain Spectroscopies: Dark-Exciton Mediated Valley Depolarization in Monolayer WSe$_2$